Kendriya Vidyalaya Bellary

Subject : MathematicsClass – X

-------------------------------------------------------------------------------------Chapter – 1 (Real Numbers)

1. For some integer m, every even integer is of the form (a) m (b) m + 1 (c) 2m (d) 2m + 12. For some integer q, every odd integer is of the form (a) q (b) q + 1 (c) 2q (d) 2q + 13. The product of a non-zero rational and an irrational number is (a) always irrational (b) always rational (c) rational or irrational (c) one4. 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

5. The decimal expansion of the rational number will

terminate after: (a) one decimal place (b) two decimal places (c) three decimal places (d) four decimal places

6. The number is

(a) rational (b) irrational (c) both (d) none of these

7. The rational number between and is

(a) (b)

(c) 1.5 (d) 1.8

-2-8. If the H.C.F of 210 and 55 is expressible in the form 210 x 5 –

55y,

then y = (a) 17 (b) 18 (c) 19 (d) 209. Let a and b be co-prime, then a2 and b2 are (a) co-prime (b) not co-prime (c) odd numbers (d) even numbers 10. The largest number which divides 70 and 125, leaving remainder 5 and 8, respectively, is (a) 13 (b) 65 (c) 875 (d) 1750

Chapter – 2 (Polynomials)1. If one of the zeroes of the quadratic polynomial (k – 1 )x2 + kx + 1 is – 3 ,then the value of k is

(a) (b) (c) (d)

2. A quadratic polynomial, whose zeroes are – 3 and 4, is (a) x2 – x + 12 (b) x2 + x + 12

(c) -- – 6 (d) 2x2 + 2x – 24

3. If the zeroes of the quadratic polynomial x2 + (a+1)x + b are 2 and – 3 then (a) a = -7 , b = -1 (b) a = 5 , b = -1 (c) a = 2 , b = - 6 (d) a = 0 , b = - 64. The number of polynomials having zeroes as – 2 and 5 is (a) 1 (b) 2 (c) 3 (d) more than 3

5. x3 + 2x2 + ax + b is exactly divisible by (x2 – 1 ). Then the values of ‘a’ and ‘b’ are (a) a = -1 , b = -2 (b) a = 1 , b = 2 (c) a = - 1 , b = 2 (d) a = 1 , b = - 2

-3-6.In Fig , the graph of a polynomial p(x) is shown. The number of zeroes of p(x) is

(a) 1 (b) 2 (c) 0 (d) more than 27. The remainder when x4 + 15 x3 + 6x2 – 12 x + 3 is divided by x+2 is (a) 52 (b) 53 (c) -52 (d) -538.The HCF of 2x2 – x – 1 and 4x2 + 8x + 3 is (a) 2x + 1 (b) 2x – 1 (c) 2x + 3 (d) x – 19. If 1 is a zero of x2 – 7x + 6, then its other zero is (a) 6 (b) 3 (c) 2 (d) 410. If α and β are the zeroes of p(x) = x2 – 5x + b and α – β = 1 ,then b is (a) 1 (b) 6 (c) 4 (d) 011. If the graph of a polynomial p(x) passing through the points (-1,0) , (-2 , 5) , (0,0), (2,-6) , (7, 0) then the zeroes of this polynomial are (a) -1 , 0, 7 (b) -1 , -2 , 2 (c) -2 , 0 ,2 (d) None of these

Chapter – 3 (Pair of Linear Equations in Two Variables)

1. The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have (a) a unique solution (b) exactly two solutions (c) infinitely many solutions (d) no solution2. 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

-4-3. The pair of equations y = 0 and y = - 7 has (a) one solution (b) two solutions (c) infinitely many solutions (d) no solution4.The pair of equations x = a and y = b graphically represent lines which are (a) parallel (b) intersecting at ( b, a ) (c) coincident (d) intersecting at ( a, b )5.One equation of a pair of dependent linear equation 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 6. For what value of ‘p’ does the system of equations 2x – py = 0 , 3x + 4y = 10 has no solution ?

(a) p = - 6 (b) p = (c) p = (d) p =

7. The sum of two numbers is 20 and their product is 64.Then one of the numbers is (a) 14 (b) 16 (c) 8 (d) none of these8. Two positive numbers differ by 3 and their product is 54. The numbers are (a) 9 and -6 (b) 3 and 18 (c) 9 and 6 (d) 27 and 29. A pair of linear equations which has a unique solution x = 2 , y = - 3 is (a) x + y = - 1 ; 2x – 3y = - 5 (b) 2x + 5y = - 11 ; 4x + 10y = - 22 (c) 2x – y = 1 ; 3x + 2y = 0 (d) x – 4y – 14 =0 ; 5x – y – 13 = 010.The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 4 will have infinitely many solutions is

(a) 3 (b) - 3 (c) -12 (d) none of these

-5-

Chapter – 6 (Triangles)1. The length of the diagonals of a rhombus are 16 cm and 12 cm .Then the length of the side of the rhombus is (a) 9 cm (b) 10 cm (c) 8 cm (d) 20 cm

2. If ABC QRP , = , AB = 18 cm and BC = 15 cm , then

PR is equal to

(a) 10 cm (b) 12 cm (c) cm (d) 8 cm

3. It is given that ABC PQR , with = . Then, is equal

to

(a) 9 (b) 3 (c) (d)

4. In ABC, DE BC , then x =

(a) 9 cm (b) 8 cm (c) 4 cm (d) 6 cm 5. If ABC QRP. If AB = 6cm , BC = 4cm , AC = 8cm , PR = 6cm,then PQ + QR = (a) 9 cm (b) 10 cm (c) 7.5 cm (d) 9 cm

6. In ABC , D and E are mid – points of AB and AC. Then DE : BC = (a) 2 : 1 (b) 1 : 2 (c) 1 : 1 (d) 4 : 17. In fig = 90o and AD BC. Then,

-6-8. A man goes 15 m due west and then 8 m due north. Its distance from the starting point is (a) 34 cm (b) 17 cm (c) 23 cm (d) none of these9. In ABC , D and E are points on the sides AB and AC respectively, such that DE BC. If AD = 4 , AE = 8 DB = x – 4 and EC = 3x – 19 , then x is equal to (a) 7 units (b) 15 units (c) 14 units (d) 11 units10. If in an isosceles triangle ABC, AB = BC and AC2 = 2 AB2 , then

is equal to (a) 30o (b) 45o (c) 60o (d) 90o

Chapter – 8 (Trigonometry)1. If cos A = , then the value of tan A is

(a) (b) (c) (d)

2.If sin A = , then the value of cot A is

(a) (b) (c) (d) 1

3.The value of the expression [ cosec(75o + ) – sec(15o – ) –

(a) BD . CD = BC2

(b) AB . AC = BC2

(c) BD . CD = AD2

(d) AB . AC = AD2

tan(55o + + cot (35o – )] is

(a) - 1 (b) 0 (c) 1 (d)

4. If cos (α + β) = 0,then sin(α – β) can be reduced to (a) cos β (b) cos 2β (c) sin α (d) sin 2α 5. The value of (tan1otan2otan3o . . . tan89o) is

(a) 0 (b) 1 (c) 2 (d)

6. If ABC is right angled at C, then the value of cos (A+B) is

(a) 0 (b) 1 (c) (d)

7. If sin A + sin2A = 1, then the value of the expression( cos2A+cos4A) is

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

-7-

8. Given that sin α = and cos β = , then the value of (α + β) is

(a) 0o (b) 30o (c) 60o (d) 90o

9. If sin - cos = 0 , then the value of (sin4 + cos4 ) is

(a) 1 (b) (c) (d)

10. sin(45o + ) – cos(45o – ) is equal to

(a) 2 cos (b) 0 (c) 2sin (d) 1

11. A pole 6 m high casts a shadow 2 m long on the ground, then the Sun’s elevation is (a) 60o (b) 45o (c) 30o (d) 90o

12. If cos 9 α = sin α and 9α < 90o , then the value of tan 5α is

(a) (b) (c) 1 (d) 0

13.If sin 3 = cos( - 6o),where 3 and ( - 6o) are both acute angles, then the value of is (a) 18o (b) 24o (c) 36o (d) 30o

14.If sec A = cosec B = , then A+B is equal to

(a) Zero (b) 90o (c) < 90o (d) >90o

15.The value of sec 70o sin20o + cos20ocosec70o = (a) 1 (b) 0 (c) 2 (d) 3

16. If tan = 3 sin , then (sin2 - cos2 ) =

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

17. 1 – tan 2 45 o is equal 1 + tan245o 

(a) tan 90o (b) 1 o (c) sin 45o (d) sin 0o

18. If tan245o – cos230o = x sin45o cos45o, then x =

(a) 2 (b) – 2 (c) - (d)

19. 9sec2A – 9tan2A = (a) 1 (b) 9 (c) 8 (d) 020.The value of sin 45o + cos 45o is

(a) (b) (c) (d) 1

-8-

Chapter – 14 (Statistics)1. For a given data with 70 observations the’less than ogive’ and the ‘more than ogive’ intersect at (20.5 , 35). Then median of the data is (a) 20 (b) 35 (c) 70 (d) 20.52. The median of first five prime numbers is (a) 5 (b) 6 (c) 7 (d) 43. The arithmetic mean of 1, 2, 3, ........... n is

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

4. If the mode of data is 45 and mean is 27, then the median is (a) 30 (b) 27 (c) 33 (d) 415. If fi xi = 17, fi = 4p + 63 and mean = 7, then p = (a) 12 (b) 13 (c) 14 (d) 15

6. Construction of a cumulative frequency table is useful in determining the (a) mean (b) median (c) mode (d) all the three

7. For a symmetrical distribution (a) mean > mode > median (b) mean < mode < median (c) mean = mode = median (d) 3 median = mode + 2 mean8. Which measure of central tendency can be found from the ‘ogive graph’ (a) mean (b) median (c) mode (d) none of these9. Consider the following frequency distribution of the heights of 60 students of a class Height 150-155 155-160 160-165 165-170 170-175 175-180No.of students

15 13 10 8 9 5

- 9 –The sum of the lower limit of the modal class and upper limit of the median class is

(a) 310 (b) 315 (c) 320 (d) 33010. The mean of the following data is 14 then find k

xi 5 10 15 20 25fi 7 k 8 4 5

(a) 5 (b) 6 (c) 7 (d) 8

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Prepared by, N.Venkatesulu,

TGT (Maths) Kendriya Vidyalaya Bellary Please mail the answers to the following mail id:

1. nvs1969@gmail.com – XA, C2. krnath2958@rediffmail.com - XB