Mathematics Test 237

Result

Mathematics Test 237

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Weekly Quiz Competition

Question 1
4 / -1

If z is a complex number such that |z| ≥ 2, then the minimum value of

A

B
lies in the interval (1, 2)

C

D

Solution
Question 2
4 / -1

If g is the inverse of a function f and then g′(x) is equal to

A
1 + x⁵

B
5x⁴

C

D

Solution
Question 3
4 / -1

A

B

C

D
none of these

Solution

The correct answer is Option 1.
Question 4
4 / -1

Let a complex number be Let another complex number z be such that |zw| = 1 and arg(z) − arg(w) = π/2. Then the area of the triangle with vertices origin, z and w is equal to :

A
1/2

B
2

C
1/4

D
4

Solution

Explanation:

Given:
Question 5
4 / -1

A

B

C

D
none of these

Solution
Question 6
4 / -1

The equation 3sin²x + 10 cos x – 6 = 0 is satisfied if (n ∈ I)

A
x = nπ + cos^–1(1/3)

B
x = nπ – cos^–1(1/3)

C
x = 2nπ ± cos^–1(1/3)

D

Solution
Question 7
4 / -1

Let the population of rabbits surviving at a time t be governed by the differential equation then p(t) equals:

A
400 – 300 e^t/2

B
300 – 200 e^–t/2

C
600 – 500 e^t/2

D
400 – 300 e^–t/2

Solution
Question 8
4 / -1

If f(x) is continuous and differentiable everywhere, then

A

B

C
a = 1, b = –1

D
a = b = 1

Solution

Question 9

4 / -1

Which of the following is logically equivalent to ~ (p ⇔ q)

(~p) ⇔ q

~p ⇔ ~q

p → ~ q

p → q

Solution

Calculation:

We know that p ⇔ q = (p ⇒ q) ∧ (q ⇒ p)

= (~ p ∨ q) ∧ (~ q ∨ p)

∴ ~ (p ⇔ q)

= ~(~ p ∨ q) ∨ ~(~ q ∨ p)

= (p ∧ ~q) ∨ (q ∧ ~p)

p	q	(p ∧ ~q) ∨ (q ∧ ~p)	(~p) ⇔ q	~p ⇔ ~q	p → ~ q	p → q
T	T	F	F	T	F	T
T	F	T	T	F	T	F
F	T	T	T	F	T	T
F	F	F	F	T	T	T

From truth table, ~ (p ⇔ q) = (~p) ⇔ q

∴ (~p) ⇔ q is logically equivalent to ~ (p ⇔ q).

The correct answer is Option 1.

Question 10
4 / -1

Consider a hyperbola H ∶ x² − 2y² = 4. Let the tangent at a point meet the x-axis at Q and latus rectum at R(x₁, y₁), x₁ > 0. If F is a focus of H which is nearer to the point P, then the area of ΔQFR is equal to.

A

B

C

D

Solution