Dakshana Cumulative Test Class 10 "Mathematics - I"

1] What is the square root of (9 + 2 √14) ?

i. 1+2√2
ii. √3 + √6
iii. √2 + √7
iv. √2 + √5

2] An equivalent expression of (5/(7+4√5)) after rationalizing the denominator is

i. (20√5-35)/31
ii. (20√5-35)/129
iii. (35-20√5)/31
iv. (35-20√5)/121

3] If a = √6 + √5; b = √6 - √5 then, find the value of 2a²+2b²-5ab

i. 36
ii. 37
iii. 39
iv. 41

4]
then find the value of k.

i. 6
ii. 3
iii. 2
iv. 1

5] A positive integer n when divided by 9, gives 7 as remainder. What will be the remainder when (3n-1) is divided by 9 ?

i. 1
ii. 2
iii. 3
iv. 4

6] If polynomial P(x) = 3x³ – x² – ax – 45 has one zero of 3, then a = .....

i. 3
ii. 6
iii. 9
iv. 12

7] If α, β are the zeros of polynomial f(x) = x² – p(x + 1) – c, then (α + 1)(β + 1) = ...

i. c - 1
ii. 1 – c
iii. c
iv. 1 + c

8]

i. -5
ii. 0
iii. 5
iv. 10

9]
,a > 0, b > 0, c > 0, then the value of x is:

i. -(a² + b² + c²)
ii. (a + b + c)
iii. – (a + b + c)
iv. √(a + b + c)

10] The graph of y = p(x) is given below. The number of zeroes of polynomial p(x), is

i. 3
ii. 2
iii. 1
iv. 0

11] Find the value of

i. 3
ii. 2x
iii. 5x
iv. 1

12] If x² – 3x + 1 = 0, then the value of x⁵ + 1/x⁵ is

i. 87
ii. 123
iii. 135
iv. 201

13] If f(x) = x⁴ + ax³ + bx² + cx + d is a polynomial such that f(1) = 5, f(2) = 10, f(3) = 15, f(4) = 20. Find the value of [ f(12)+f(-8)] ÷ 100 is

i. 198
ii. 198.4
iii. 198.2
iv. 199.2

14] If three times the larger of two number is divided by the smaller, the quotient and the remainder, each is equal to 6. If five times the smaller is divided by the larger, the quotient is 2 and the remainder is 3. The smaller number is :

i. 6
ii. 7
iii. 8
iv. 9

15] The ratio of the number of boys and girls in a school is 3:2. If 20% of the boys and 30% of the girls are scholarship holders, the percentage of the students who are not scholarship holders is

i. 50
ii. 72
iii. 75
iv. 76

16] The sum and product of two numbers is 20 and 40 respectively. The sum of the reciprocal of the numbers will be

i. 0.5
ii. 0.1
iii. 4
iv. 2

17] A change making machine contains 1 ₹, 2 ₹ and 5 ₹ coins. The total number of coins is 300. The amount is ₹ 960. If the number of 1 rupee coins and the number of 2 rupee coins are interchanged, the value comes down by ₹ 40. The total number of 5 rupee coins is

i. 100
ii. 140
iii. 60
iv. 150

18] If the system of equations
kx + 3y – (k – 3) = 0
12x + ky – k = 0
has infinitely many solutions, then k = ?

i. 6
ii. -6
iii. 0
iv. None of these

19] In the equations 3x + 2y = 13xy and 4x – 5y = 2xy, the values of x and y that satisfy the equations are

i. (2,3)
ii. (3,2)
iii. (1/2,1/3)
iv. (1/3,1/2)

20] A boat takes 7 hours to travel 30 km upstream and 28 km downstream. It takes 5 hours to travel 21 km upstream and to return back. Find the speed of the boat in still water.

i. 10 km/hr
ii. 20 km/hr
iii. 1 km/hr
iv. 6 km/hr

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