Mathematics Test 162

Result

Mathematics Test 162

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Weekly Quiz Competition

Question 1
4 / -1

Equation of common tangents with positive slope to the circle x² + y² = 5 and hyperbola 4x² – 9y² = 36 is

A

B

C

D

Solution
Question 2
4 / -1

Let z = x + iy, x, y ∈ R such that z ≠ 1 and |z – 1| ≠ 1. If

A
1 / √3

B
√3

C
1

D
1/2

Solution
Question 3
4 / -1

If the function f : [0, 27] → R is diffrentiable and 0 < α < 1 < β < 2 < γ < 3, then is equal to

A

B

C

D

Solution
Question 4
4 / -1

Let ^pC_q be the number of ways in which 5 tickets are selected from 20 tickets from 1 to 20 so that no two consecutive numbered tickets are selected, then p – q may be

A
20

B
13

C
12

D
11

Solution

Required ways = ¹⁶C₅

∴ p – q = 16 – 5 or 16 – 11

= 11 or 5
Question 5
4 / -1

The logically equivalent statement of is

A

B

C

D

Solution
Question 6
4 / -1

A curve passing through (1, 2) and satisfying the differential equation

A
x²y = 2

B
x² + y² = 5

C

D
y² = 4x

Solution

Differentiate both sides w.r.t. x

x².y(x) = 3x².y(x) + x³.y'(x)
Question 7
4 / -1

A
tan^–1(a_2n–1) – tan^–1(a₃)

B
tan^–1(a_2n) – tan^–1(a₁)

C
tan^–1(a₁) – tan^–1(a_2n–1)

D
tan^–1(a_2n–1) – tan^–1 a₁

Solution
Question 8
4 / -1

If f : R → R⁺ be a decreasing function and such that

A

B
1 / √2

C
1 / √3

D
1

Solution
Question 9
4 / -1

Let , then A⁴⁸ is

A

B

C

D

Solution
Question 10
4 / -1

If tanα, tanβ are the roots of the equation x² + px + q = 0, then the value of expression sin²(α + β) + psin(α + β) cos(α + β) + qcos²(α + β) is equal to

A
p + q

B
p + q / q

C
q

D
p / p + q

Solution