Math Question and Answers


To grasp the understanding of the basic concepts of mathematics it is essential for the students to solve questions, they give an idea of how math can help them in real-world situations and also enhancing their cognitive and inquisitive skills. The math questions allow creative minds to explore the different types of problems, recall the concepts, and apply them to reach a solution.

Solving maths questions instills a strong mathematical acumen in the young minds and also helps as a great tool for the teachers and the parents in assessing the student's understanding of any particular topic. Hence math questions and answers should be solved step by step to gain the most information out of it. Math worksheets are an important tool in continuing efforts to motivate students during class and to engage their minds. The math questions and answers stimulate imaginative thought as well.

Math Question and Answer

Using appropriate properties find: (i) -2/3 × 3/5 + 5/2 - 3/5 × 1/6 (ii) 2/5 × (-3/7) -1/6 × 3/2 + 1/14 × 2/5.
Write the additive inverse of each of the following (i) 2/8 (ii) -5/9 (iii) -6/-5 (iv) 2/-9 (v) 19/-6.
Verify that -(-x) = x for. (i) x = 11/15 (ii) x = -13/7
Find the multiplicative inverse of the following (i) -13 (ii) -13/19 (iii) 1/5 (iv) -5/8 × -3/7 (v) -1 × -2/5 (vi) -1.
Name the property under multiplication used in each of the following: (i) -4/5 × 1 = 1 × -4/5 = -4/5 (ii) -13/17 × -2/7 = -2/7 × -13/17 (iii) -19/29 × 29/-19 = 1
Multiply 6/13 by the reciprocal of -7/16. The multiplicative inverse of a number is defined as a number which when multiplied by the original number gives the product an identity
Tell what property allows you to compute 1/3 × (6 × 4/5) as (1/3 × 6) × 4/3? The Associative property tells us that we can add/multiply the numbers in an equation irrespective of the grouping of those numbers.
Is 8/9 the multiplicative inverse of -1 (1/8)? Why or why not?
Is 0.3 the multiplicative inverse of 3 (1/3)? Why or why not?
Write. (i) The rational number that does not have a reciprocal. (ii) The rational numbers that are equal to their reciprocals. (iii) The rational number that is equal to its negative.
Fill in the blanks. (i) Zero has ________ reciprocal. (ii) The numbers ________ and ________ are their own reciprocals (iii) The reciprocal of -5 is ________. (iv) Reciprocal of 1/x, where x ≠ 0 is ________. (v) The product of two rational numbers is always a _______. (vi) The reciprocal of a positive rational number is ________.
Represent these numbers on the number line. (i) 7/4 (ii) -5/6
Represent -2/11, -5/11, -9/11 on the number line.
Write five rational numbers which are smaller than 2.
Find ten rational numbers between -2/5 and 1/2
Find five rational numbers between (i) 2/3 and 4/5 (ii) -3/2 and 5/3 (iii) 1/4 and 1/2.
Write five rational numbers greater than -2.
Find ten rational numbers between 3/5 and 3/4
Solve the following equation: x - 2 = 7
Solve the following equation: y + 3 = 10
Solve the following equation: 6 = z + 2
Solve the following equation: 3/7 + x = 17/7
Solve the following equation: 6x = 12
Solve the following equation: t/5 = 10
Solve the following equation: 2x/3 = 18
Solve the following equation: 1.6 = y/1.5
Solve the following equation: 7x - 9 = 16
Solve the following equation: 14y - 8 = 13
Solve the following equation: 17 + 6p = 9
Solve the following equation: x/3 + 1 = 7/15
If you subtract 1/2 from a number and multiply the result by 1/2, you get 1/8. What is the number?
The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool?
The base of an isosceles triangle is 4/3. The perimeter of the triangle is 4 2/15. What is the length of either of the remaining equal sides?
Sum of two numbers is 95. If one exceeds the other by 15, find the numbers
Two numbers are in the ratio 5:3. If they differ by 18, what are the numbers?
Three consecutive integers add up to 51. What are these integers?
The sum of three consecutive multiples of 8 is 888. Find the multiples.
Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.
The ages of Rahul and Haroon are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present ages?
The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8 more than the number of girls. What is the total class strength?
Baichung’s father is 26 years younger than Baichung’s grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. What is the age of each one of them?
Fifteen years from now Ravi’s age will be four times his present age. What is Ravi’s present age?
A rational number is such that when you multiply it by 5/2 and add 2/3 to the product, you get -7/12. What is the number?
Lakshmi is a cashier in a bank. She has currency notes of denominations ₹100, ₹50 and ₹10, respectively. The ratio of the number of these notes is 2:3:5. The total cash with Lakshmi is ₹4,00,000. How many notes of each denomination does she have?
I have a total of ₹300 in coins of denomination ₹1, ₹2 and ₹5. The number of ₹2 coins is 3 times the number of ₹5 coins. The total number of coins is 160. How many coins of each denomination are with me?
The organisers of an essay competition decide that a winner in the competition gets a prize of ₹100 and a participant who does not win gets a prize of ₹25. The total prize money distributed is ₹3,000. Find the number of winners, if the total number of participants is 63.
Solve the following equation and check your result: 3x = 2x + 18
Solve the following equation and check your result: 5t - 3 = 3t - 5
Solve the following equation and check your result: 5x + 9 = 5 + 3x
Solve the following equation and check your result: 4z + 3 = 6 + 2z
Solve the following equation and check your result: 2x - 1 = 14 - x
Solve the following equation and check your result: 8x + 4 = 3(x - 1) + 7
Solve the following equation and check your result: x = 4/5 (x + 10)
Solve the following equation and check your result: 2x/3 + 1 = 7x/15 + 3
Solve the following equation and check your result: 2y + 5/3 = 26/3 - y
Solve the following equation and check your result: 3m = 5m - 8/5
Amina thinks of a number and subtracts 5/2 from it. She multiplies the result by 8. The result now obtained is 3 times the same number she thought of. What is the number?
A positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers?
Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?
One of the two digits of a two-digit number is three times the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?
Shobo’s mother’s present age is six times Shobo’s present age. Shobo’s age five years from now will be one third of his mother’s present age. What are their present ages?
There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11:4. At the rate ₹100 per metre it will cost the village panchayat ₹ 75000 to fence the plot. What are the dimensions of the plot?
Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him ₹50 per metre and trouser material that costs him ₹90 per metre. For every 3 meters of the shirt material he buys 2 metres of the trouser material. He sells the materials at 12% and 10% profit respectively. His total sale is ₹36,600. How much trouser material did he buy?
Half of a herd of deer are grazing in the field and three fourths of the remaining are playing nearby. The rest 9 are drinking water from the pond. Find the number of deer in the herd.
A grandfather is ten times older than his granddaughter. He is also 54 years older than her. Find their present ages.
Aman’s age is three times his son’s age. Ten years ago he was five times his son’s age. Find their present ages.
Solve the linear equation: x/2 - 1/5 = x/3 + 1/4
Solve the linear equation: n/2 - 3n/4 + 5n/6 = 21
Solve the linear equation: x + 7 - 8x/3 = 17/6 - 5x/2
Solve the linear equation: (x - 5)/3 = (x - 3)/5
Solve the linear equation: (3t - 2)/4 - (2t + 3)/3 = 2/3 - t
Solve the linear equation: m - (m - 1)/2 = 1 - (m - 2)/3
Simplify and solve the linear equations: 3(t - 3) = 5(2t + 1)
Simplify and solve the linear equation: 15(y - 4) - 2(y - 9) + 5(y + 6) = 0
Simplify and solve the linear equation: 3(5z – 7) – 2(9z – 11) = 4(8z – 13) – 17
Simplify and solve the linear equation: 0.25(4f - 3) = 0.05(10f - 9)
Solve the following equation: (8x - 3)/3x = 2
Solve the following equation: 9x/ (7 - 6x) = 15
Solve the following equation: z/(z + 15) = 4/9
Solve the following equations: 3y + 4 / 2 - 6y = -2/5
Solve the following equations: 7y + 4 / y + 2 = -4/3
The ages of Hari and Harry are in the ratio 5:7. Four years from now the ratio of their ages will be 3:4. Find their present ages
The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the rational number.
Given here are some figures. Classify each of them on the basis of the following. (a) Simple curve (b) Simple closed curve (c) Polygon (d) Convex polygon (e) Concave polygon
How many diagonals does each of the following have? (a) A convex quadrilateral (b) A regular hexagon (c) A triangle
What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)
Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.) What can you say about the angle sum of a convex polygon with number of sides? (a) 7 (b) 8 (c) 10 (d) n
What is a regular polygon? State the name of a regular polygon of (i) 3 sides (ii) 4 sides (iii) 6 sides
Find the angle measure x in the following figures:
a) Find x +y +z b) Find x + y + z + w
Find x in the following figures
Find the measure of each exterior angle of a regular polygon of (i) 9 sides (ii) 15 sides.
How many sides does a regular polygon have if the measure of an exterior angle is 24°?
How many sides does a regular polygon have if each of its interior angles is 165°?
(a) Is it possible to have a regular polygon with measure of each exterior angle as 22°? (b) Can it be an interior angle of a regular polygon? Why?
(a) What is the minimum interior angle possible for a regular polygon? Why? (b) What is the maximum exterior angle possible for a regular polygon?
Given a parallelogram ABCD. Complete each statement along with the definition or property used. (i) AD = ...... (ii) ∠ DCB = ...... (iii) OC = ...... (iv) m ∠DAB + m ∠CDA = ......
Consider the following parallelograms. Find the values of the unknowns x, y, z.
Can a quadrilateral ABCD be a parallelogram if (i) ∠D + ∠B = 180°? (ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm? (iii) ∠A = 70° and ∠C = 65°?
Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.
The measures of two adjacent angles of a parallelogram are in the ratio 3:2. Find the measure of each of the angles of the parallelogram.
Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.
The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.
The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm)
In the above figure both RISK and CLUE are parallelograms. Find the value of x.
Explain how this figure is a trapezium. Which of its two sides are parallel? (Fig 3.32)
Find m∠C in the figure below if AB is parallel to DC.
Find the measure of ∠P and ∠S if SP is parallel to RQ in the below figure. (If you find m∠R , is there more than one method to find m∠P?)
State whether True or False. (a) All rectangles are squares (b) All rhombuses are parallelograms (c) All squares are rhombuses and also rectangles (d) All squares are not parallelograms. (e) All kites are rhombuses. (f) All rhombuses are kites.  (g) All parallelograms are trapeziums. (h) All squares are trapeziums.
Identify all the quadrilaterals that have: (a) four sides of equal length (b) four right angles
Explain how a square is. (i) a quadrilateral (ii) a parallelogram (iii) a rhombus (iv) a rectangle
Name the quadrilaterals whose diagonals. (i) bisect each other (ii) are perpendicular bisectors of each other (iii) are equal (i) parallelogram, rhombus, rectangle, and square bisect each other. (ii) square and rhombus are perpendicular bisectors of each other. (iii) rectangle and square are equal.
Explain why a rectangle is a convex quadrilateral.
ABC is a right-angled triangle and O is the mid point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you).
Construct the following quadrilaterals. (i) Quadrilateral ABCD AB = 4.5 cm, BC = 5.5 cm CD = 4 cm, AD = 6 cm, AC = 7 cm (ii) Quadrilateral JUMP JU = 3.5 cm, UM = 4 cm MP = 5 cm, PJ = 4.5 cm, PU = 6.5 cm (iii) Parallelogram MORE OR = 6 cm, RE = 4.5 cm EO = 7.5 cm (iv) Rhombus BEST BE = 4.5 cm and ET = 6 cm.
Construct the following quadrilaterals. (i) Quadrilateral LIFT LI = 4 cm, IF = 3 cm TL = 2.5 cm, LF = 4.5 cm, IT = 4 cm (ii) Quadrilateral GOLD OL = 7.5 cm, GL = 6 cm GD = 6 cm, LD = 5 cm, OD = 10 cm (iii) Rhombus BEND BN = 5.6 cm and DE = 6.5 cm.
Construct the following quadrilaterals. (i) Quadrilateral MORE MO = 6 cm, OR = 4.5 cm ∠M = 60°, ∠O = 105°, ∠R = 105° (ii) Quadrilateral PLAN PL = 4 cm, LA = 6.5 cm ∠P = 90°, ∠A = 110°, ∠N = 85° (iii) Parallelogram HEAR HE = 5 cm, EA = 6 cm ∠R = 85° (iv) Rectangle OKAY OK = 7 cm, KA = 5 cm
Construct the following quadrilaterals. (i) Quadrilateral DEAR DE = 4cm, EA = 5cm, AR = 4.5cm ∠E = 60°, ∠A = 90° (ii) Quadrilateral TRUE TR = 3.5cm, RU = 3cm, UE = 4cm ∠R = 75°, ∠U = 120°
Draw the following. 1. A square READ with RE = 1 cm. 2. A rhombus whose diagonals are 5.2 cm and 6.4 cm long. 3. A rectangle with adjacent sides of lengths 5 cm and 4 cm 4. A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm. Is it unique?
For which of these would you use a histogram to show the data? (a) The number of letters for different areas in a postman’s bag. (b) The height of competitors in an athletics meet. (c) The number of cassettes produced by 5 companies. (d) The number of passengers boarding trains from 7:00 a.m. to 7:00 p.m. at a station. Give reasons for each.
The shoppers who come to a departmental store are marked as: man (M), woman (W), boy (B) or girl (G). The following list gives the shoppers who came during the first hour in the morning: W W W G B W W M G G M M W W W W G B M W B G G M W W M M W W W M W B W G M W W W W G W M M W W M W G W M G W M M B G G W Make a frequency distribution table using tally marks. Draw a bar grapha to illustrate it.
The weekly wages (in Rs) of 30 workers in a factory are: 830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 835, 836, 878, 840, 868, 890, 806, 840. Using tally marks, make a frequency table with intervals as 800 – 810, 810 – 820 and so on.
Draw a histogram for the frequency table made for the data in Question 3, and answer the following questions. (i) Which group has the maximum number of workers? (ii) How many workers earn Rs 850 and more? (iii) How many workers earn less than Rs 850?
The number of hours for which students of a particular class watched television during holidays is shown through the given graph. Answer the following: (i) For how many hours did the maximum number of students watch T.V.? (ii) How many students watched T.V. for less than 4 hours? (iii) How many students spent more than 5 hours in watching T.V.?
A survey was made to find the type of music that a certain group of young people liked in a city. Adjoining pie chart shows the findings of this survey. From this pie chart answer the following: (i) If 20 people liked classical music, how many young people were surveyed? (ii) Which type of music is liked by the maximum number of people? (iii) If a cassette company were to make 1000 CD’s, how many of each type would they make?
A group of 360 people were asked to vote for their favourite season from the three seasons rainy, winter and summer. (i) Which season got the most votes? (ii) Find the central angle of each sector. (iii) Draw a pie chart to show this information.
Draw a pie chart showing the following information. The table shows the colors preferred by a group of people.
The adjoining pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, answer the following questions. (i) In which subject did the student score 105 marks? (Hint: for 540 marks, the central angle = 360°. So, for 105 marks, what is the central angle?) (ii) How many more marks were obtained by the student in Mathematics than in Hindi? (iii) Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi. (Hint: Just study the central angles).
The number of students in a hostel, speaking different languages is given below. Display the data in a pie chart.
List the outcomes you can see in these experiments. (a) Spinning a wheel (b) Tossing two coins together.
When a die is thrown, list the outcomes of an event of getting (i) (a) a prime number (b) not a prime number. (ii) (a) a number greater than 5 (b) a number not greater than 5.
Find the. (a) Probability of the pointer stopping on D in (Question 1-(a))? (b) Probability of getting an ace from a well shuffled deck of 52 playing cards? (c) Probability of getting a red apple. (See figure below)
Numbers 1 to 10 are written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of . (i) getting a number 6? (ii) getting a number less than 6? (iii) getting a number greater than 6? (iv) getting a 1-digit number?
If you have a spinning wheel with 3 green sectors, 1 blue sector and 1 red sector, what is the probability of getting a green sector? What is the probability of getting a non blue sector?
Find the probability of the events given in Question 2.
What will be the unit digit of the squares of the following numbers? (i) 81 (ii) 272 (iii) 799 (iv) 3853 (v) 1234 (vi) 26387 (vii) 52698 (viii) 99880 (ix) 12796 (x) 55555
The following numbers are obviously not perfect squares. Give reason. (i) 1057 (ii) 23453 (iii) 7928 (iv) 222222 (v) 64000 (vi) 89722 (vii) 222000 (viii) 505050
The squares of which of the following would be odd numbers? (i) 431 (ii) 2826 (iii) 7779 (iv) 82004
Observe the following pattern and find the missing digits. 112 = 121 1012 = 10201 10012 = 1002001 1000012 = 1....2....1 100000012 = ...........
Observe the following pattern and supply the missing numbers. 112 = 121 1012 = 10201 101012 = 102030201 10101012 = ? ?2 = 10203040504030201
Using the given pattern, find the missing numbers. 12 + 22 + 22 = 32 22 + 32 + 62 = 72 32 + 42 + 122 = 132 42 + 52 + _2 = 212 52 + -2 + 302 = 312 62 + 72 + _2 = _2
Without adding, find the sum. (i) 1 + 3 + 5 + 7 + 9 (ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 +19 (iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
(i) Express 49 as the sum of 7 odd numbers. (ii) Express 121 as the sum of 11 odd numbers.
How many numbers lie between squares of the following numbers? (i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100
Find the squares of the following numbers. (i) 32 (ii) 35 (iii) 86 (iv) 93 (v) 71 (vi) 46
Write a Pythagorean triplet whose one member is: (i) 6 (ii) 14
What could be the possible ‘one’s’ digits of the square root of each of the following numbers? (i) 9801 (ii) 99856 (iii) 998001 (iv) 657666025
Without doing any calculation, find the numbers which are surely not perfect squares. (i) 153 (ii) 257 (iii) 408 (iv) 441
Find the square roots of 100 and 169 by the method of repeated subtraction.
Find the square roots of the following numbers by the Prime Factorisation Method. (i) 729 (ii) 400 (iii) 1764 (iv) 4096 (v) 7744 (vi) 9604 (vii) 5929 (viii) 9216 (ix) 529 (x) 8100
For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained. (i) 252 (ii) 180 (iii) 1008 (iv) 2028 (v) 1458 (vi) 768
For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained. (i) 252 (ii) 2925 (iii) 396 (iv) 2645 (v) 2800 (vi) 1620
The students of Class VIII of a school donated ₹ 2401 in all for the Prime Minister’s National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.
2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.
Find the smallest square number that is divisible by each of the numbers 4, 9 and 10.
Find the smallest square number that is divisible by each of the numbers 8, 15 and 20.
Find the square root of each of the following numbers by Division method. (i) 2304 (ii) 4489 (iii) 3481 (iv) 529 (v) 3249 (vi) 1369 (vii) 5776 (viii) 7921 (ix) 576 (x) 1024 (xi) 3136 (xii) 900
Find the number of digits in the square root of each of the following numbers (without any calculation). (i) 64 (ii) 144 (iii) 4489 (iv) 27225 (v) 390625
Find the square root of the following decimal numbers. (i) 2.56 (ii) 7.29 (iii) 51.84 (iv) 42.25 (v) 31.36
Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained. (i) 402 (ii) 1989 (iii) 3250 (iv) 825 (v) 4000
Find the least number which must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained. (i) 525 (ii) 1750 (iii) 252 (iv) 1825 (v) 6412
Find the length of the side of a square whose area is 441 m2.
In a right triangle ABC, ∠B = 90°. (a) If AB = 6 cm, BC = 8 cm, find AC (b) If AC = 13 cm, BC = 5 cm, find AB
A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain same. Find the minimum number of plants he needs more for this.
There are 500 children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement.
Which of the following numbers are not perfect cubes?(i) 216 (ii) 128 (iii) 1000 (iv) 100 (v) 46656
Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.(i) 243 (ii) 256 (iii) 72 (iv) 675 (v) 100
Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube.(i) 81 (ii) 128 (iii) 135 (iv) 192 (v) 704.
Parikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube?
Find the cube root of each of the following numbers by prime factorization method. (i) 64 (ii) 512 (iii) 10648 (iv) 27000 (v) 15625 (vi) 13824 (vii) 110592 (viii) 46656 (ix) 175616 (x) 91125
State true or false. (i) Cube of any odd number is even. (ii) A perfect cube does not end with two zeros. (iii) If square of a number ends with 5, then its cube ends with 25. (iv) There is no perfect cube which ends with 8. (v) The cube of a two digit number may be a three digit number. (vi) The cube of a two digit number may have seven or more digits. (vii) The cube of a single digit number may be a single digit number.
You are told that 1,331 is a perfect cube. Can you guess without factorisation what is its cube root? Similarly, guess the cube roots of 4913, 12167, 32768.
Find the values of the letters in the following and give reasons for the steps involved. 3 A + 2 5 = B 2.
Find the values of the letters in the following and give reasons for the steps involved. 4 A + 9 8 = C B 3
Find the values of the letters in the following and give reasons for the steps involved. 1 A × A = 9 A.
Find the values of the letters in the following and give reasons for the steps involved. A B + 3 7 = 6 A
Find the values of the letters in the following and give reasons for the steps involved. A B × 3 = C A B
Find the values of the letters in the following and give reasons for the steps involved. A B × 5 = C A B
Find the values of the letters in the following and give reasons for the steps involved. A B × 6 = B B B.
Find the values of the letters in the following and give reasons for the steps involved. A 1 + 1 B = B 0.
Find the values of the letters in the following and give reasons for the steps involved. 2 A B + A B 1 = B 1 8.
Find the values of the letters in the following and give reasons for the steps involved. 1 2 A + 6 A B = A 0 9.
If 21y5 is a multiple of 9, where y is a digit, what is the value of y?
If 31z5 is a multiple of 9, where z is a digit, what is the value of z? You will find that there are two answers for the last problem. Why is this so?
If 24x is a multiple of 3, where x is a digit, what is the value of x? (Since 24x is a multiple of 3, its sum of digits 6 + x is a multiple of 3; so 6 + x is one of these numbers: 0, 3, 6, 9, 12, 15, 18, ... . But since x is a digit, it can only be that 6 + x = 6 or 9 or 12 or 15. Therefore, x = 0 or 3 or 6 or 9. Thus, x can have any of four different values.)
If 31z5 is a multiple of 3, where z is a digit, what might be the values of z?
Find the common factors of the terms (i) 12x, 36 (ii)2y, 22xy (iii)14pq, 28p2q2 (iv)2x, 3x2, 4 (v) 6abc, 24ab2, 12a2b (vi) 16x3, - 4x2, 32x (vii)10 pq, 20qr, 30rp (viii)3x2 y3, 10x3y2, 6x2y2z
Factorise the following expressions (i) 7x - 42 (ii) 6p-12q (iii) 7a2+14a (iv) -16z + 20z3 (v) 20l2m + 30alm (vi) 5x2y -15xy2 (vii) 10a2 -15b2 + 20c2 (viii) -4a2 + 4ab - 4ca (ix) x2yz + xy2z + xyz2 (x) ax2y + bxy2 + cxyz 
Factorize: (i) x2+ xy + 8x + 8 y (ii) 15xy- 6x + 5 y - 2 (iii) ax+ bx - ay - by (iv) 15 pq +15 + 9q + 25 p (v) z - 7 + 7xy - xyz
Factorize the following expressions. (i) a2 + 8a +16 (ii) p2 -10 p + 25 (iii) 25m2 + 30m + 9 (iv) 49 y2 + 84 yz + 36z2 (v) 4x2 - 8x + 4 (vi) 121b2 - 88bc +16c2 (vii) (l +m)2 - 4lm (Hint: Expand (l + m)2 first) (viii) a4+ 2a2b2 + b4.
Factorize (i) 4 p2 - 9q2 (ii) 63a2 - 112b2 (iii) 49x2 - 36 (iv) 16x5 - 144x3 (v) (l + m)2 - (l - m)2 (vi) 9x2y2 - 16 (vii) (x2 - 2xy + y2) - z2 (viii) 25a2 - 4b2 + 28bc - 49c2
Factorise the expressions. (i) ax2 + bx (ii) 7p2 + 21q2 (iii) 2x3 + 2xy2 + 2xz2 (iv) am2 + bm2 + bn2 + an2 (v) (lm + l) + m + 1 (vi) y(y + z) + 9( y + z) (vii) 5y2 - 20 y - 8z + 2yz (viii) 10ab + 4a + 5b + 2 (ix) 6xy - 4 y + 6 - 9x.
Factorise (i) a4 - b4 (ii) p4 - 81 (iii) x4 - ( y + z)4 (iv) x4 - (x - z)4 (v) a4 - 2a2b2 + b4
Factorise the following expressions (i) p2 + 6 p + 8 (ii) q2 - 10q + 21 (iii) p2 + 6 p - 16
Carry out the following divisions. (i) 28x4 ÷ 56x (ii) -36 y3 ÷ 9 y2 (iii) 66 pq2r3 ÷ 11qr2 (iv) 34x3y3z3 ÷ 51xy2 z3 (v) 12a8b8 ÷ (-6a6b4 )
Divide the given polynomial by the given monomial. (i) (5x2 - 6x) ÷ 3x (ii) (3y8 - 4y6 + 5y4) ÷ y4 (iii) 8(x3y2z2 + x2y3z2 + x2y2z3) ÷ 4x2y2z2 (iv) (x3 + 2x2 + 3x) ÷ 2x (v) (p3q6 - p6q3) ÷ p3q3
Work out the following divisions. (i) (10x - 25) ÷ 5 (ii) (10x - 25) ÷ (2x - 5) (iii) 10y(6y + 21) ÷ 5(2y + 7) (iv) 9x2y2(3z - 24) ÷ 27xy(z - 8) (v) 96abc(3a -12)(5b - 30) ÷ 144(a - 4)(b - 6)
Divide as directed. (i) 5(2x +1)(3x + 5) ÷ (2x +1) (ii) 26xy(x + 5)(y - 4) ÷ 13x( y - 4) (iii) 52 pqr(p + q)(q + r)(r + p) ÷ 104pq(q + r)(r + p) (iv) 20(y + 4) (y2 + 5y + 3) ÷ 5(y + 4) (v) x(x +1)(x + 2)(x + 3) ÷ x(x +1)
Factorize the expressions and divide them as directed. (i) (y2 + 7y + 10) ÷ (y + 5) (ii) (m2 -14m - 32) ÷ (m + 2) (iii) (5p2 - 25p + 20) ÷ (p -1) (iv) 4yz(z2 + 6z -16) ÷ 2y(z + 8) (v) 5pq(p2 - q2) ÷ 2p(p + q) (vi) 12xy(9x2 -16y2) ÷ 4xy(3x + 4y) (vii) 39y3(50y2 - 98) ÷ 26y2(5y + 7).
Find and correct the errors in the statement: 4(x - 5) = 4x - 5
Find and correct the errors in the statement: x(3x + 2) = 3x2 + 2.
Find and correct the errors in the statement: 2x + 3y = 5xy.
Find and correct the errors in the statement: x + 2x + 3x = 5x
Find and correct the errors in the statement: 5y + 2y + y - 7y = 0
Find and correct the errors in the statement: 3x + 2x = 5x2
Find and correct the errors in the statement: (2x)2 + 4(2x) + 7 = 2x2 + 8x + 7.
Find and correct the errors in the statement: (2x)2 + 5x = 4x + 5x = 9x
Find and correct the errors in the statement: (3x + 2)2 = 3x2 + 6x + 4
Find and correct the errors in the following mathematical statement. Substituting x = -3 in (a) x2+ 5x + 4 gives (-3)2 + 5(-3) + 4 = 9 + 2 + 4 = 15 (b) x2 - 5x + 4 gives (-3)2 - 5(-3) + 4 = 9 - 15 + 4 = -2 (c) x2 + 5x gives (-3)2 + 5(-3) = -9 - 15 = -24
Find and correct the errors in the statement: (y - 3)2 = y2 - 9
Find and correct the errors in the statement: (z + 5)2 = z2 + 25
Find and correct the errors in the statement: (2a + 3b)(a - b) = 2a2 - 3b2
Find and correct the errors in the statement : (a + 4)(a + 2) = a2 + 8.
Find and correct the errors in the statement: (a - 4)(a - 2) = a2 - 8
Find and correct the errors in the statement: 3x2/3x2 = 0.
Find and correct the errors in the statement: (3x 2 + 1) / 3x 2 = 1 + 1 = 2
Find and correct the errors in the statement: 3x/(3x + 2) = 1/2.
Find and correct the errors in the statement: 3 / (4x + 3) = 1 / (4x).
Find and correct the errors in the statement: (4x + 5)  / 4x = 5
Find and correct the errors in the statement: (7x + 5) / 5 = 7x.
The following graph shows the temperature of a patient in a hospital, recorded every hour. a) What was the patient’s temperature at 1p.m.? b) When was the patient’s temperature 38.50C? c) The patient’s temperature was the same two times during the period What were the two times? d) What was the temperature at 1.30p.m.? How did you arrive at your answer?
The following line graph shows the yearly sales figure for a manufacturing company. a) What were the sales in (i)2002 (ii)2006? b) What were the sales in (i)2003 (ii)2005? c) Compute the difference between the sales in 2002 and 2006 d) In which year was there the greatest difference between the sales as compared to its previous year?
For an experiment in Botany, two different plants, plant A and plant B were grown under similar laboratory conditions. Their heights were measured at the end of each week for 3 weeks. The results are shown by the following graph. a) How high was Plant A after (i) 2 weeks (ii) 3 weeks? b) How high was Plant B after (i) 2 weeks (ii) 3 weeks? c) How much did Plant A grow during the 3rd week? d) How much did Plant B grow from the end of the 2nd week to the end of the 3rd week? e) During which week did Plant A grow most? f) During which week did Plant B grow least? g) Were the two plants of the same height during any week shown here? Specify.
The following graph shows the temperature forecast and the actual temperature for each day of a week. a) On which days was the forecast temperature the same as the actual temperature? b) What was the maximum forecast temperature during the week? c) What was the minimum actual temperature during the week? d) On which day did the actual temperature differ the most from the forecast temperature?
Use the tables below to draw linear graphs. a) The number of days a hill side city received snow in different b) Population(in thousands) of men and women in a village in different years.
A courier-person cycles from a town to a neighbouring suburban area to deliver a parcel to a merchant. His distance from the town at different times is shown by the following graph. a) What is the scale taken for the time axis? b) How much time did the person take for the travel? c) How far is the place of the merchant from the town? d) Did the person stop on his way? e) During which period did he ride fastest?
Can there be a time-temperature graph as follows? Justify your answer.
Plot the following points on a graph sheet. Verify if they lie on a line. (a) A(4, 0), B(4, 2), C(4, 6), D(4, 2.5) (b) P(1,1), Q(2, 2), R(3, 3), S(4, 4) (c) K(2, 3), L(5, 3), M(5, 5), N(2, 5)
Draw the line passing through (2, 3) and (3, 2). Find the coordinates of the points at which this line meets the x-axis and y-axis.
Write the coordinates of the vertices of each of these adjoining figures.
State whether True or False. Correct that are false. (i) A point whose x-coordinate is zero and y-coordinate is non-zero will lie on the y-axis. (ii) A point whose y-coordinate is zero and x-coordinate is 5 will lie on the y-axis. (iii) The coordinates of the origin are (0,0).
Draw the graphs for the following tables of values, with suitable scales on the axes. (a) Cost of apples (b)Distance travelled by a car (i) How much distance did the car cover during the period 7.30 a.m.to 8 a.m.? (ii) What was the time when the car had covered a distance of 100 km since its start? (c) Interest on deposits for a year: (i) Does the graph pass through the origin? (ii) Use the graph to find the interest on Rs 2500 for a year: To get an interest of Rs 280 per year, how much money should be deposited?
Draw a graph for the following. (i) Is it a linear graph? (ii) Is it a linear graph?
Evaluate (i) 3-2 (ii) (4)-2 (iii) (1/2)-5.
Simplify and express the result in power notation with positive exponent. (i) (−4) 5 ÷ (−4) 8 (ii) (1 / 23) 2 (iii) (−3) 4 × (5/3) 4 (iv) (3 -7 ÷ 3 -10) × 3 -5 (v) 2 -3 × (−7) -3
Find the value of (i) (30 × 4−1) × 22 (ii) (2−1 × 4−1) ÷ 2−2 (iii) (1/2)−2 + (1/3)−2 + (1/4)−2 (iv) (3−1 +4−1 + 5−1)0 (v) {(−2/3)−2}2
Evaluate (i) (8−1× 53)/2−4 (ii) (5−1× 2−1)×6−1
Find the value of m for which (5m ÷ 5−3) = 55
Evaluate (i) [(1/3)−1 − (1/4)−1]−1 (ii) [5/8]−7× [8/5]−4
Simplify. (i) (25×t−4)/(5−3×10×t−8) (t ≠ 0) (ii) (3−5×10−5×125)/(5−7×6−5)
Express the following numbers in standard form. (i) 0.0000000000085 (ii) 0.00000000000942 (iii) 6020000000000000 (iv) 0.00000000837 (v) 31860000000
Express the following numbers in usual form.  (i) 3.02×10−6 (ii) 4.5×104 (iii) 3×10−8 (iv) 1.0001×109 (v) 5.8×1012 (vi) 3.61492×106
Express the number appearing in the following statements in standard form. (i) 1 micron is equal to 1/100000 m (ii) Charge of an electron is 0.000,000,000,000,000,000,16 coulomb. (iii) Size of a bacteria is 0.0000005 m (iv) Size of a plant cell is 0.00001275 m (v) Thickness of a thick paper is 0.07 mm
In a stack there are 5 books each of thickness 20 mm and 5 paper sheets each of thickness 0.016 mm. What is the total thickness of the stack.
A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?
Mrs. Kaushik has a square plot with the measurement as shown in the figure. She wants to construct a house in the middle of the plot. A garden is developed around the house. Find the total cost of developing a garden around the house at the rate of ₹ 55 per m².
The shape of a garden is rectangular in the middle and semi circular at the ends as shown in the diagram. Find the area and the perimeter of this garden [Length of rectangle is 20 - (3.5 + 3.5) meters].
A flooring tile has the shape of a parallelogram whose base is 24 cm and the corresponding height is 10 cm. How many such tiles are required to cover a floor of area 1080 m²? (If required you can split the tiles in whatever way you want to fill up the corners).
An ant is moving around a few food pieces of different shapes scattered on the floor. For which food-piece would the ant have to take a longer round? Remember, the circumference of a circle can be obtained by using the expression c = 2πr, where r is the radius of the circle.
The shape of the top surface of a table is a trapezium. Find its area if its parallel sides are 1 m and 1.2 m and perpendicular distance between them is 0.8 m.
The area of a trapezium is 34 cm² and the length of one of the parallel sides is 10 cm and its height is 4cm. Find the length of the other parallel side.
Length of the fence of a trapezium shaped field ABCD is 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC.
The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.
The diagonals of a rhombus are 7.5 cm and 12 cm. Find its area.
Find the area of a rhombus whose side is 5 cm and whose altitude is 4.8 cm. If one of its diagonals is 8 cm long, find the length of the other diagonal.
The floor of a building consists of 3000 tiles which are rhombus shaped and each of its diagonals are 45 cm and 30 cm in length. Find the total cost of polishing the floor, if the cost per m² is ₹ 4.
Mohan wants to buy a trapezium shaped field. Its side along the river is parallel to and twice the side along the road. If the area of this field is 10500 m2 and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.
Top surface of a raised platform is in the shape of a regular octagon as shown in the figure. Find the area of the octagonal surface.
There is a pentagonal shaped park as shown in the figure. For finding its area Jyoti and Kavita divided it in two different ways. Find the area of this park using both ways. Can you suggest some other way of finding its area?
Diagram of the adjacent picture frame has outer dimensions = 24 cm × 28 cm and inner dimensions 16 cm × 20 cm. Find the area of each section of the frame, if the width of each section is same.
There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?
A suitcase with measures 80 cm × 48 cm × 24 cm is to be covered with a tarpaulin cloth. How many meters of tarpaulin of width 96 cm is required to cover 100 such suitcases?
Find the side of a cube whose surface area is 600 cm².
Rukhsar painted the outside of the cabinet of measure 1 m × 2 m × 1.5 m. How much surface area did she cover if she painted all except the bottom of the cabinet?
Daniel is painting the walls and ceiling of a cuboidal hall with length, breadth and height of 15 m, 10 m and 7 m respectively. From each can of paint 100 m² of area is painted. How many cans of paint will she need to paint the room?
Describe how the two figures at the right are alike and how they are different. Which box has larger lateral surface area?
A closed cylindrical tank of radius 7 m and height 3 m is made from a sheet of metal. How much sheet of metal is required?
The lateral surface area of a hollow cylinder is 4224 cm² .It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet?
A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84 cm and length is 1 m.
A company packages its milk powder in cylindrical container whose base has a diameter of 14 cm and height 20 cm. Company places a label around the surface of the container (as shown in the figure). If the label is placed 2 cm from top and bottom, what is the area of the label.
Given a cylindrical tank, in which situation will you find surface area and in which situation volume. (a) To find how much it can hold. (b) Number of cement bags required to plaster it. (c) To find the number of smaller tanks that can be filled with water from it.
Diameter of cylinder A is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area?
Find the height of a cuboid whose base area is 180 cm² and volume is 900 cm³?
A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?
Find the height of the cylinder whose volume is 1.54 m³ and diameter of the base is 140 cm?
A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in litres that can be stored in the tank?
If each edge of a cube is doubled, (i) how many times will its surface area increase? (ii) how many times will its volume increase?
Water is pouring into a cuboidal reservoir at the rate of 60 liters per minute. If the volume of reservoir is 108 m³, find the number of hours it will take to fill the reservoir.
For each of the given solid, the two views are given. Match for each solid the corresponding top and front views. The first one is done for you.
For each of the given solid, the three views are given. Identify for each solid the corresponding top, front and side views.
For each given solid, identify the top view, front view, side view.
Draw the top view, front view and side view of the given objects.
Can a polyhedron have for its faces (i) 3 triangles? (ii) 4 triangles? (iii) a square and four triangles?
Is it possible to have a polyhedron with any given number of faces? (Hint: Think of a pyramid).
Which are prisms among the following?(i) How are prisms and cylinders alike? (ii) How are pyramids and cones alike?
(i) How are prisms and cylinders alike? (ii) How are pyramids and cones alike?
Is a square prism same as a cube? Explain.
Verify Euler’s formula for these solids.
Using Euler’s formula find the unknown.
Can a polyhedron have 10 faces, 20 edges and 15 vertices?
Identify the terms, their coefficients for each of the following expressions. (i) 5xyz2 - 3zy (ii) 1 + x + x2 (iii) 4x2y2 - 4x2y2z2 + z2 (iv) 3 - pq + qr - rp (v) x + y - xy (vi) 0.3a - 0.6ab + 0.5b
Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories? x + y, 1000, x + x2 + x3 + x4, 7 + y + 5x, 2y - 3y2, 2 y - 3y2 + 4 y3, 5x - 4 y + 3xy, 4z - 15z2, ab + bc + cd + da, pqr, p2q + pq2, 2p + 2q
Add the following. (i) ab - bc, bc - ca, ca - ab (ii) a - b + ab, b - c + bc , c - a + ac (iii) 2 p2q2 - 3 pq + 4, 5 + 7 pq - 3 p2q2 (iv) l2 + m2, m2 + n2, n2 + l2, 2lm + 2mn + 2nl
(a) Subtract 4a - 7ab + 3b + 12 from 12a - 9ab + 5b - 3 (b) Subtract 3xy + 5yz - 7zx from 5xy - 2 yz - 2zx +10xyz (c) Subtract 4p2q - 3pq + 5pq2 - 8p + 7q - 10 from 18 - 3p - 11q + 5 pq - 2 pq2 + 5 p2q
Find the product of the following pairs of monomials.  (i) 4,7 p (ii ) -4p, 7p (iii ) -4p, 7pq (iv) 4p3, 3p (v) 4p, 0
Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively. (i) ( p, q) (ii) (10m, 5n) (iii) (20x2, 5y2) (iv) (4x, 3x2) (v) (3mn, 4np)
Complete the table of products.
Obtain the volume of rectangular boxes with the following length, breadth and height respectively. (i) 5a, 3a2,7a4 (ii) 2 p, 4q, 8r (iii) xy, 2x2 y, 2xy2 (iv) a, 2b, 3c
Obtain the product of (i) xy, yz, zx (ii ) a, a2,a3 (iii) 2, 4 y, 8 y2, 16 y3 (iv) a, 2b, 3c, 6abc (v) m, - mn, mnp
Carry out the multiplication of the expressions in each of the following pairs. (i) 4 p, q + r (ii) ab, a - b (iii) a + b, 7a2b2 (iv) a2 - 9, 4a (v) pq + qr + rp, 0
Complete the table.
Find the product. (i) (a2 ) × (2a22 ) × (4a26) (ii) (2/3 xy) × (-9/10 x2 y2) (iii) (-10/3 pq3 ) × (6/5 p3q) (iv) x × x2 × x3 × x4
(a) Simplify 3x(4x - 5) + 3 and find its values for (i) x = 3 (ii) x = 1/2  (b) Simplify a (a2 + a + 1)+ 5 and find its values for (i) a = 0, (ii) a =1, (iii) a = - 1
(a) Add: p( p - q), q(q - r ) and r (r - p) (b) Add: 2x (z - x - y) and 2y(z- y - x) (c) Subtract: 3l (l - 4m + 5n) from 4l (10n - 3m + 2l ) (d) Subtract: 3a(a + b + c) - 2b(a - b + c) from 4c (-a + b + c)
Multiply the binomials. (i) (2x + 5) and(4x - 3) (ii) (y - 8) and (3y - 4) (iii) (2.5l - 0.5m) and (2.5l + 0.5m) (iv) (a + 3b) and (x + 5) (v) (2pq + 3q2) × (3pq - 2q2) (vi) 3a2/4 + 3b2 and 4(a2 - (2b2/3))
Find the product. (i) (5 – 2x) (3 + x) (ii) (x + 7y) (7x – y) (iii) (a2 + b) (a + b2 ) (iv) (p2 - q2)(2p + q)
Simplify. (i) (x2 - 5) (x + 5) + 25 (ii) (a2 + 5)(b3 + 3) + 5 (iii) (t + s2) (t 2 - s) (iv) (a + b)(c - d) + (a -b)(c+ d ) + 2(ac+ bd) (v) (x + y )(2x + y) + (x + 2y)(x - y) (vi) (x + y)(x2 - xy + y2) (vii) (1.5x - 4y)(1.5x + 4y + 3) - 4.5x + 12 y (viii) (a + b + c)(a + b - c)
Use a suitable identity to get each of the following products. (i) (x + 3)(x + 3) (ii) (2y + 5)(2y + 5) (iii) (2a - 7)(2a - 7) (iv) (3a - (1/2))(3a - (1/2)) (v) (1.1 m - 0.4)(1.1 m + 0.4) (vi)(a2 + b2)(-a2 + b2) (vii) (6x - 7)(6x + 7) (viii) (-a + c)(-a + c) (ix) (x/2 + 3y/4)(x/2 + 3y/4) (x) (7a - 9b)(7a - 9b)
Use the identity (x + a)(x + b) = x2 + (a + b)x + ab to find the following products. (i) (x + 3)(x + 7) (ii) (4x + 5)(4x + 1) (iii) (4x - 5)(4x -1) (iv) (4x + 5)(4x -1) (v) (2x + 5y)(2x + 3 y) (vi) (2a2 + 9)(2a2 + 5) (vii) (xyz - 4)(xyz - 2)
Find the following squares by using the identities. (i)(b - 7)2 (ii) (xy + 3z)2 (iii) (6x2 - 5 y)2 (iv) (2m/3 + 3n/2)2 (v) (0.4 p - 0.5q)2 (vi) (2xy + 5 y)2
Simplify (i)(a2 - b2)2 (ii) (2x + 5)2 - (2x - 5)2 (iii) (7m - 8n)2 + (7m + 8n)2 (iv) (4m + 5n)2 + (5m + 4n)2 (v) (2.5p - 1.5q)2 - (1.5p - 2.5q)2 (vi) (ab + bc)2 - 2ab2c (vii) (m2 - n2m)2 + 2m3n2
Show that (i)(3x + 7)2 - 84x = (3x - 7)2 (ii) (9p - 5q)2 + 180pq = (9p + 5q)2 (iii) (4m/3 - 3n/4)2 + 2mn = 16m2/9 + 9n2/16 (iv) (4pq + 3q)2 - (4pq - 3q)2 = 48pq2 (v) (a - b)(a + b) + (b - c)(b + c) + (c - a)(c + a) = 0
Using identities, evaluate. i) 712 ii) 992 iii) 1022 iv) 9982 v) (5.2)2 vi) 297 × 303 vii) 78 × 82 viii) 8.92 ix) 1.05 × 9.5
Using a2 - b2 = (a + b)(a - b), find (i) 512 – 492 (ii) (1.02)2 - (0.98)2 (iii) 1532 -1472 (iv) 12.12 - 7.92
Using (x + a)(x + b) = x2 + (a + b)x + ab (i) 103 × 104 (ii) 5.1 × 5.2 (iii) 103 × 98 (iv) 9.7 × 9.8
Find the ratio of the following.(i) Speed of a cycle 15 km per hour to the speed of scooter 30 km per hour.(ii) 5 m to 10 km(iii) 50 paise to Rs 5
Convert the following ratios to percentages(i) 3:4 (ii) 2:3
72% of 25 students are interested in mathematics. How many are not interested in mathematics?
A football team won 10 matches out of the total number of matches they played. If their win percentage was 40, then how many matches did they play in all?
If Chameli had Rs 600 left after spending 75% of her money, how much did she have in the beginning?
If 60% people in a city like cricket, 30% like football and the remaining like other games, then what per cent of the people like other games? If the total number of people is 50 lakh, find the exact number who like each type of game.
A man got a 10% increase in his salary. If his new salary is Rs 1,54,000, find his original salary. Percentage is a fraction or a ratio in which the value of whole is always 100.
On Sunday 845 people went to the Zoo. On Monday only 169 people went. What is the per cent decrease in the people visiting the Zoo on Monday?
A shopkeeper buys 80 articles for ₹ 2,400 and sells them for a profit of 16%. Find the selling price of one article.
The cost of an article was ₹ 15,500. ₹ 450 was spent on its repairs. If it is sold for a profit of 15%, find the selling price of the article.
A VCR and TV were bought for ₹ 8,000 each. The shopkeeper made a loss of 4% on the VCR and a profit of 8% on the TV. Find the gain or loss percent on the whole transaction.
During a sale, a shop offered a discount of 10% on the marked price of all the items. What would a customer have to pay for a pair of jeans marked at ₹ 1450 and two shirts marked at ₹ 850 each?
A milkman sold two of his buffaloes for ₹ 20,000 each. On one he made a gain of 5% and on the other a loss of 10%. Find his overall gain or loss. (Hint: Find CP of each).
The price of a TV is ₹ 13,000. The sales tax charged on it is at the rate of 12%. Find the amount that Vinod will have to pay if he buys it.
Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is ₹ 1,600 find the marked price. 
I purchased a hairdryer for ₹ 5,400 including 8% VAT. Find the price before VAT was added.
An article was purchased for ₹ 1239 including GST of 118%. Find the price of the article before GST was added?
Calculate the amount and compound interest on (i) ₹ 10,800 for 3 years at 12(1/2)% per annum compounded annually. (ii) ₹ 18,000 for 2(1/2) years at 10% per annum compounded annually. (iii) ₹ 62,500 for 1(1/2)years at 8% per annum compounded half yearly. (iv) ₹ 8,000 for 1 year at 9% per annum compounded half yearly. (You could use the year by year calculation using SI formula to verify). (v) ₹ 10,000 for 1 year at 8% per annum compounded half yearly.
Kamala borrowed ₹ 26400 from a Bank to buy a scooter at a rate of 15% p.a. compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan? (Hint: Find A for 2 years with interest is compounded yearly and then find SI on the 2nd year amount for 4/12 years.)
Fabina borrows ₹ 12,500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much? 
I borrowed ₹ 12000 from Jamshed at 6% per annum simple interest for 2 years. Had I borrowed this sum at 6% per annum compound interest, what extra amount would I have to pay?
Vasudevan invested ₹ 60,000 at an interest rate of 12% per annum compounded half-yearly. What amount would he get (i) after 6 months? (ii) after 1 year?
Arif took a loan of ₹ 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after 1(1/2) years if the interest is (i) Compounded annually (ii) Compounded half-yearly
Maria invested ₹ 8,000 in a business. She would be paid interest at 5% per annum compounded annually. Find: (i) The amount credited against her name at the end of the second year (ii) The interest for the 3rd year.
Find the amount and the compound interest on ₹ 10,000 for 1(1/2) years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?
Find the amount which Ram will get on ₹ 4096 if he gave it for 18 months at 12(1/2)% per annum, interest being compounded half yearly.
The population of a place increased to 54,000 in 2003 at a rate of 5% per annum (i) find the population in 2001. (ii) what would be its population in 2005?
In a Laboratory, the count of bacteria in a certain experiment was increasing at the rate of 2.5% per hour. Find the bacteria at the end of 2 hours if the count was initially 5, 06,000.
A scooter was bought at ₹ 42,000. Its value depreciated at the rate of 8% per annum. Find its value after one year.
Following are the car parking charges near a railway station up to: 4 hours ₹60 8 hours ₹100 12 hours ₹140 24 hours ₹180 Check if the parking charges are in direct proportion to the parking time.
A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base. In the following table, find the parts of base that need to be added.
In question (2), above if 1 part of red pigment requires 75 ml of base, how much red pigment should we mix with 1800 ml of base?
A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?
A photograph of a bacteria is enlarged 50,000 times attains a length of 5 cm as shown in the diagram. What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, what would be its enlarged length?
In a model of a ship, the mast is 9 cm high, while the mast of the actual ship is 12 cm high. If the length of the actual ship is 28 m, how long is the model ship?
Suppose 2 kg of sugar contains 9 × 106 crystals. How many sugar crystals are there in (1) 5 kg of sugar? (2) 1.2 kg of sugar?
Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road for 72 km. What would be her distance covered in the map?
A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time (i) the length of the shadow cast by another pole 10 m 50 cm high (ii) the height of a pole which casts a shadow 5m long.
A loaded truck travels 14 km in 25 minutes. If the speed remains the same, how far it travels in 5 hours?
Which of the following are in inverse proportion? (i) The number of workers on a job and the time to complete the job. (ii) The time taken for a journey and the distance travelled in a uniform speed. (iii) Area of cultivated land and the crop harvested. (iv) The time taken for a fixed journey and the speed of the vehicle. (v) The population of a country and the area of land per person.
In a television game show, the prize money of ₹ 1,00,000 is to be divided equally amongst the winners. Complete the following table and find whether the prize money given to an individual winner is directly or inversely proportional to the number of winners?
Rehman is making a wheel using spokes. He wants to fix equal spokes n such a way that the angles between any pair of consecutive spokes are equal. Help him by completing the following table. (i) Are the number of spokes and the angle formed between the pairs of consecutive spokes in inverse proportion? (ii) Calculate the angle between a pair of consecutive spokes on a wheel with 15 spokes. (iii) How many spokes would be needed, if the angle between a pair of consecutive spokes is 40∘?
If a box of sweets is divided among 24 children, they will get 5 sweets each. How many would each get, if the number of the children is reduced by 4?
A farmer has enough food to feed 20 animals in his cattle for 6 days. How long would the food last if there were 10 more animals in his cattle?
A contractor estimates that 3 persons could rewire Jasminder’s house in 4 days. If, he uses 4 persons instead of three, how long should they take to complete the job?
A batch of bottles were packed in 25 boxes with 12 bottles in each box. If the same batch is packed using 20 bottles in each box, how many boxes would be filled?
A factory requires 42 machines to produce a given number of articles in 63 days. How many machines would be required to produce the same number of articles in 54 days?
A car takes 2 hours to reach a destination by travelling at the speed of 60 km/h. How long will it take when the car travels at the speed of 80 km/h?
Two persons could fit new windows in a house in 3 days. (i) One of the persons fell ill before the work started. How long would the job take now? (ii) How many persons would be needed to fit the windows in one day?
A school has 8 periods a day each of 45 minutes of duration. How long would each period be, if the school has 9 periods a day assuming the number of school hours to be the same?
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