7th Ch:Integers Practice Question Paper

1. Compare the following fractions by using the symbol > or < or = : 

(i) 7/9 and 8/13    (ii) 11/9 and 5/9 

2. Arrange the following fractions in ascending order: 

(i) 3/8, 5/6, 6/8, 2/4, 1/3  (ii) 4/6, 3/8, 6/12, 5/16
3. Arrange the following fractions in descending order: 

(i) 4/5, 7/10, 11/15, 17/20 (ii) 2/7, 11/35, 9/14, 13/28

4. Write five equivalent fractions of (a)3/5(b)-5/3

5. Find the sum: 
(i) 4³/₄ + 9²/₅         (ii) 5/6 +(- 3) + ¾            (iii) 2³/₅ + (-4⁷/₁₀) + 2⁴/₁₅ 

6. Find the difference of: 

(i) 13/24 and 7/16 (ii) 3³/₁₀ and 2⁷/₁₅  (iii) 9 – 5²/₃     (iv) 4³/₁₀ – 1²/₁₅
8. Simplify: 

(i) 2/3 + 1/6 – 2/9        (ii) 7⁵/₆ – 4³/₈ + 2⁷/₁₂

9. What should be added to 3¹/₂ to get 12? 

10. What should be added to 5¹/₁₅ to get 12¹/₅? 

11. Patty studies for 5²/₃ hours daily. She devotes 2⁴/₅ hours of her time for Science and Mathematics. How much time does she devote for other subjects? 


12. A piece of wire is of length 12³/₄ m. If it is cut into two pieces in such a way that the length of one piece is 5¹/₄ m. What is the length of the other piece? 


13. A rectangular sheet of paper is 12¹/₂ cm long and 10²/₃ cm wide. Find the perimeter. 


14. The cost of Mathematics book is $25³/₄ and that of Science book is $20¹/₂. Which costs more and by how much? 

15. Find the two integers whose sum is less than both the integers.

CCE CBSE Sample Papers Class VIII Mathematics

CCE CBSE Sample Papers Class VIII Mathematics 

Section-A

1. The Compound interest is

a) always less than the simple interest      
 b) always equal to the simple interest

c) always greater than simple interest       
d) always greater than or equal to simple interest.

2. In case of Compound interest, the principal

a) increases every year                                    b) remains same

c) decreases every year                                    d) increase for the first year and then decreases

3. Bananas are bought at the rate of 4 for Rs. 3. At what rate must they be sold to get a gain of 20% for each banana?

a) Rs 0.50 b) Rs 0.75 c) Rs 0.85 d) Rs 0.90

4. The square root of 0.09 is

a) 0.03 b) 0.3 c) 0.003 d) 3.0

5. The smallest number by which 9408 must be divided so that the quotient is a perfect square is

a) 2 b) 3 c) 7 d) None

6. The square root of ( 2⁵/2³)

a) 4 b) 10 c) 1 d) 2

7. A parallelogram each of whose angles measures 90o is ______.

(a)rectangle      (b)rhombus      (c)kite                   (d)trapezium

8. A parallelogram whose all sides are equal is called

(a)square     (b)rhombus  (c)rectangle    (d) trapezium

9. The two diagonals are not necessarily equal in a ………………. .

(a) rectangle      (b) square       (c) rhombus  (d) isosceles trapezium

10. The degree of the polynomial x² - 5x² y³ + 30x y - 576xy is ______

(A) – 576 (B) 4 (C) 5 (D) 7

Section B

11. Name each of the following parallelograms.

(i) The diagonals are equal and the adjacent sides are unequal.

(ii) The diagonals are equal and the adjacent sides are equal.

(iii) The diagonals are unequal and the adjacent sides are equal.

12. A trader buys an article for Rs. 1,200 and marks it 30% above the C.P. He then sells it after allowing a discount of 20%. Find the S.P. and profit percent.

13. A television set was sold after giving successive discounts of 10% and 20% respectively. Find sigle discount ?

14. In how much time will a sum of Rs. 1600 amount to ` 1852.20 at 5% per annum compound interest.

15. Find the difference between Simple Interest and Compound Interest for a sum of Rs.  8,000 lent at 10% p. a. in 2 years.

Section C

16. Two adjacent angles of a parallelogram are in the ratio 4 : 5. Find the measure of each of its angles.

17. Two adjacent angles of a parallelogram are (3x - 4)° and (3x + 16)°. Find the value of x and hence find the measure of each of its angles

18. A and B together can do a piece of work in 8 days, but A alone can do it 12 days. How many days would B alone take to do the same work?

19. Two persons A and B are engaged in a work. A can do a piece of work in 12 days and B can do the same work in 20 days. They work together for 3 days and then A goes away. In how many days 
will B finish the work?

20. A can do a piece of work in 10 days and B can do it in 15 days. How much does each of them get if they finish the work and earn Rs. 1500?

Section-C

21. Find the least number of six digits which is a perfect square. Find the square root of this number.

22. Six men working 10 hours a day can do a piece of work in 24 days. In how many days will 9 men working for 8 hours a day do the same work?

23. ABCD is a square and  Ac is a diagonal . Find the measure of ∠CAD.

24.  x + y + z = 0, prove that x ³+ y³ + z³ = 3xyz.

25. Factorize   (i)   y² –7y +12  (ii)  x⁴ – (y + z)⁴          

(iii) a⁴ – 2a²b² + b⁴  (iv) (l + m) ² – 4lm

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CBSE Sample Papers Class VIII Mathematics (2012-2013)

CBSE Sample Papers Class VIII Mathematics (2012-2013)

Section-A

1) A dealer buys a wrist watch for Rs.225 and spends RS.15 on its repairs. If he sells the same for RS.300, find his profit percent.

(a) 75% (b) 60% (c) 25% (d) 20%

2) Mona gets 98 marks in her exams. This amounts to 56% of the total marks. What are the maximum marks?

(a) 175 (b) 150 (c) 200 (d) 160

3) Akhil has to pay 4% sales tax in addition to the price of a certain article. Find the price of the article, if he pays Rs.260 in all.

(a) Rs.220 (b) Rs.250 (c) Rs.256 (d) Rs.200

4) The value of a machine depreciates every year by 10%. What will be its value after 2 years, if its present value is Rs.50,000?

(a) Rs.40,500 (b) Rs.40,050 (c) Rs.40,000 (d) Rs.45,000

5) Aby lent Rs.8,000 to his friend for 3 years at the rate of 5% per annum compounded annually. What amount does Aby get afer 3 years?

(a) Rs.9,000 (b) Rs.9,200 (c)Rs.9,216 (d) Rs.9,261

6) Find the amount on Rs.4,096 at the rate of 12 ½% per annum for 18 months compounded half-yearly.

(a) Rs.5,000 (b) Rs.4,913 (c) Rs.4,931 Rs.5,832

7) The present population of a town is 28,000. If it increases at the rate of 5% per annum, what will be its population after 2 years?

(a) 30,000 (b) 30,800 (c) 30,870 (d) 30,870

9) If the cost price of 18 mangoes is the same as the selling price of 16 mangoes, find the gain percent.

(a) 15% (b) 12.5% (c0 15.5% (d) 12%

10) What is the value of „m‟, if = ?  (5²)ⁿ m = (5^-7)²

a) 5 b) -2 c) -7 d) 2

Section-B( 3 marks questions)

11. What least number must be subtracted from 7250 to get a perfect square? Also, find the square root of this perfect square

12. What is the least number by which 12348must be divided to obtain a perfect square?

13. x+ y + z = 0, prove that x³+ y³ + z3 = 3xyz.    Or,  Factorize:  (a8 – b8)

14.  If ( x2 + 1/x2) = 83 .  Find   X³- 1/X³

15.  Factorize (i) 25a² – 4b² + 28bc – 49c²     (ii) 5y² – 20y – 8z + 2yz         

16.A motor boat covers a certain distance downstream in a river in 5 hours. It covers the same distance upstream in 6 hours. The speed of water is 2 km/hr . Find the speed of the boat in still water.

17. Each side of a triangle is increased by 10 cm. If the ratio of the perimeters of the new  triangle and the given triangle is 5 : 4, find the perimeter of the given triangle

18. A dealer buys an article for Rs.380. At what price must he mark it so that after allowing a  discount of 5%, he still makes a profit of 25%?

19. Ajit buys a motorcycle for Rs.17600 including Value Added Tax. If the rate of VAT is 10%, what is the sale price of motorcycle?

20. Two sides of a parallelogram are in the ratio 5 : 3. If its perimeter is 64 cm, find the lengths of its sides.

Section-C ( 5 marks questions)

21. ABCD is a rectangle. If BM and DN are perpendiculars from B and D on AC, prove that ∆ BMC ≅ ∆ DNA. Is it true that BM = DN?

23. If (x + l)(x + m) = x² + 4x+ 2 find l² +  m² and (l - m)²

24. ABCD is a parallelogram and line segments AE and CF bisect the angles A and C and meet DC and  AB at E and F respectively. Show that AE ∥ CF.

25. The lengths of the diagonals of a rhombus are 16 cm and 12 cm respectively. Find the length of each of its sides. 

Pair of Linear Equations in two variables MCQ X CBSE Mathematics

Pair of Linear Equations in two variables MCQ X CBSE Mathematics

1. The number of solutions of the pair of linear equations x + 2y – 8 = 0 and 2x + 4y = 16 is :

(a) 0 (b) 1 (c) infinitely many (d) none of these

2. The graphical representation of the pair of equations x + 2y – 4 = 0 and 2x + 4y – 12 = 0 represents :

(a) intersecting lines (b) parallel lines (c) coincident lines (d) all of these

3. If a pair of linear equations is consistent, then the lines will be :

(a) parallel (b) always coincident (c) intersecting or coincident (d) always intersecting

4. The condition so that the pair of linear equations kx + 3y + 1 = 0, 2x + y + 3 = 0 has exactly one solution is :

(a) k = 6 (b) k ≠ 6 (c) k = 3 (d) k ≠ 3

5. The lines representing the linear equations 2x – y = 3 and 4x – y = 5 :

(a) intersect at a point   (b) are parallel (c) are coincident (d) intersect at exactly two points

6. The pair of linear equations 2x + 5y = –11 and 5x + 15y = –44 has :

(a) many solutions (b) no solution (c) one solution (d) two solutions

7. The pair of equations y = 0 and y = –7 has :

(a) one solution (b) two solutions (c) infinitely many solutions (d) no solution

8. If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is :

(a) –5/4 (b) 2/5 (c) 15/4 (d) 3/2

9. The pair of linear equations 8x – 5y = 7 and 5x – 8y = –7 have :

(a) one solution (b) two solutions (c) no solution (d) many solutions

10. The pair of linear equations x – 2y = 0 and 3x + 4y = 20 have :

(a) one solution (b) two solutions (c) many solutions (d) no solution

11. The pair of linear equations kx + 2y = 5 and 3x + y = 1 has unique solution, if :

(a) k = 6 (b) k ≠ 6 (c) k = 0 (d) k has any value

12. One equation of a pair of dependent linear equations is –5x + 7y = 2, the second equation can be : (a) 10x + 14y + 4 = 0 (b) –10x = 14y + 4 – 0 (c) –10x + 14y + 4 = 0 (d) 10x – 14y = –4

13. The value of k for which the pair of equations : kx – y = 2 and 6x – 2y = 3 has a unique solution is

(a) k = 3 (b) k ≠ 3 (c) k ≠ 0 (d) k = 0

14. The value of k for which the pair of linear equations 4x + 6y – 1 = 0 and 2x + ky – 7 = 0 represents parallel lines is :

(a) k = 3 (b) k = 2 (c) k = 4 (d) k = –2

15. If x = a, y = b is the solution of the equations x – y = 2 and x + y = 4, then the values of a and b respectively are

(a) 3 and 5 (b) 5 and 3 (c) 3 and 1 (d) –1 and –3

X Real Number MCQ Assignments in Mathematics Class X (Term I)

X Real Number MCQ  Assignments in Mathematics Class X (Term I)

1. Euclid’s division algorithm can be applied to :

(a) only positive integers            (b) only negative integers

(c) all integers                            (d) all integers except 0.

2. For some integer m, every even integer is of the form :

(a) m (b) m + 1 (c) 2m (d) 2m + 1

3. If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is :

(a) 1 (b) 2 (c) 3 (d) 4

4. If two positive integers p and q can be expressed as p = ab2 and q = a3b, a; b being prime numbers, then LCM (p, q) is :

(a) ab (b) a2b2 (c) a3b2 (b) a3b3

5. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is :

(a) 10 (b) 100 (c) 504 (d) 2520

6. 7 × 11 × 13 × 15 + 15 is :

(a) composite number                 (b) prime number

(c) neither composite nor prime  (d) none of these

7. 1.23 is :

(a) an integer (b) an irrational number (c) a rational number (d) none of these

8. If two positive integers p and q can be expressed as p = ab2 and q = a2b; a, b being prime numbers, then LCM (p, q) is :

(a) a2b2 (b) ab (c) ac3b3 (d) a3b2

9. Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where :

(a) 0 < r ≤ b (b) 1 < r < b (c) 0 < r < b (d) 0 ≤ r < b

10. 3.24636363... is :

(a) a terminating decimal number (b) a non-terminating repeating decimal number

(c) a rational number                    (d) both (b) and (c)

11.(n + 1)2 – 1 is divisible by 8, if n is :

(a) an odd integer (b) an even integer (c) a natural number (d) an integer

12. The largest number which divides 71 and 126, leaving remainders 6 and 9 respectively is :

(a) 1750 (b) 13 (c) 65 (d) 875

13. For some integer q, every odd integer is of the form :

(a) 2q (b) 2q + 1 (c) q (d) q + 1

14. If the HCF of 85 and 153 is expressible in the form 85m – 153, then the value of m is :

(a) 1 (b) 4 (c) 3 (d) 2

15. According to Euclid’s division algorithm, HCF of any two positive integers a and b with a > b is obtained by applying Euclid’s division lemma to a and b to find q and r such that a = bq + r, where r must satisfy :

(a) 1 < r < b (b) 0 < r < b (c) 0 ≤ r < b (d) 0 < r ≤ b

X Real Number MCQ Assignments in Mathematics Class X (Term I)

X Real Number MCQ  Assignments in Mathematics Class X (Term I)

1. Euclid’s division algorithm can be applied to :

(a) only positive integers            (b) only negative integers

(c) all integers                            (d) all integers except 0.

2. For some integer m, every even integer is of the form :

(a) m (b) m + 1 (c) 2m (d) 2m + 1

3. If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is :

(a) 1 (b) 2 (c) 3 (d) 4

4. If two positive integers p and q can be expressed as p = ab2 and q = a3b, a; b being prime numbers, then LCM (p, q) is :

(a) ab (b) a2b2 (c) a3b2 (b) a3b3

5. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is :

(a) 10 (b) 100 (c) 504 (d) 2520

6. 7 × 11 × 13 × 15 + 15 is :

(a) composite number                 (b) prime number

(c) neither composite nor prime  (d) none of these

7. 1.23 is :

(a) an integer (b) an irrational number (c) a rational number (d) none of these

8. If two positive integers p and q can be expressed as p = ab2 and q = a2b; a, b being prime numbers, then LCM (p, q) is :

(a) a2b2 (b) ab (c) ac3b3 (d) a3b2

9. Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where :

(a) 0 < r ≤ b (b) 1 < r < b (c) 0 < r < b (d) 0 ≤ r < b

10. 3.24636363... is :

(a) a terminating decimal number (b) a non-terminating repeating decimal number

(c) a rational number                    (d) both (b) and (c)

11.(n + 1)2 – 1 is divisible by 8, if n is :

(a) an odd integer (b) an even integer (c) a natural number (d) an integer

12. The largest number which divides 71 and 126, leaving remainders 6 and 9 respectively is :

(a) 1750 (b) 13 (c) 65 (d) 875

13. For some integer q, every odd integer is of the form :

(a) 2q (b) 2q + 1 (c) q (d) q + 1

14. If the HCF of 85 and 153 is expressible in the form 85m – 153, then the value of m is :

(a) 1 (b) 4 (c) 3 (d) 2

15. According to Euclid’s division algorithm, HCF of any two positive integers a and b with a > b is obtained by applying Euclid’s division lemma to a and b to find q and r such that a = bq + r, where r must satisfy :

(a) 1 < r < b (b) 0 < r < b (c) 0 ≤ r < b (d) 0 < r ≤ b