Mathematics Test 153

Result

Mathematics Test 153

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
4 / -1

Let y = y(x) be the solution of the differential equation

0 < x < 2.1, with y(2) = 0. Then the value of dy/dx at x = 1 is equal to :

A

B

C

D

Solution
Question 2
4 / -1

The area bounded by the curve 4y² = x²(4 – x)(x – 2) is equal to :

A
π/8

B
3π/8

C
3π/2

D
π/16

Solution
Question 3
4 / -1

Let y = y(x) be the solution of the differential equation

cosx (3sinx + cosx + 3)dy =
(1 + y sinx (3sinx + cosx + 3))dx,

A

B

C

D

Solution
Question 4
4 / -1

A function f, defined for all x, y ∈ R is such that f(1) = 2 ; f(2) = 8 and f(x + y) – kxy = f(x) + 2y²; Where k is some constant ; then value of f(x) and k are :

A
6x – 4 ; k = 2

B
2x² ; k = 2

C
6x – 4 ; k = 4

D
2x² ; k = 4

Solution
Question 5
4 / -1

(where [.] denotes greatest integer function)

A
a

B
b

C
b/a

D
1 - b/a

Solution
Question 6
4 / -1

A
f(x) / x is differentiable in R

B
f(x) is continuous but not differentiable in R

C
f(x) is continuous in R

D
None

Solution
Question 7
4 / -1

A

B

C

D
Question 8
4 / -1

If p : 5 is not greater than 2 and

q : Jaipur is capital of Rajasthan,

are two statements. Then negation of statement p ⇒ q is the statement

A
5 is not greater than 2 or Jaipur is not capital of Rajasthan

B
5 is not greater than 2 and Jaipur is not capital of Rajasthan

C
5 is greater than 2 and Jaipur is capital of Rajasthan

D
5 is greater than 2 and Jaipur is not capital of Rajasthan

Solution

use ~(p ⇒ q) ≡ p ^ (–q)
Question 9
4 / -1

The set of values of 'λ' for which equation sin⁴x + cos⁴x = λ has a solution, is :-

A
(0, 1)

B
[½, 1]

C
[–1, 1]

D
[1, 3/2]

Solution

1 – 2 sin²θ cos²θ = λ

sin²(2θ) = 2 – 2λ

0 < 2 – 2λ < 1

–2 < –2λ < –1

1/2 < λ < 1
Question 10
4 / -1

Let 2p + 3q + 4r = 15 and if the expression p³q⁵r⁷ takes the maximum value, then p : q : r is equal to (where p, q, r ∈ R⁺) -

A
18 : 20 : 21

B
3 : 5 : 7

C
2 : 3 : 4

D
6 : 15 : 28

Solution