1
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

The circle $x^2 + y^2 - 2x = 0$ is partitioned by line $y = x$ in two segments. Let $A_1, A_2$ be the areas of major and minor segments respectively.

What is the value of $\frac{2(A_1 + A_2)}{ A_1 - 3A_2}$?

A

$\pi$

B

$1$

C

$-1$

D

$-\pi$

2
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next two (02) items that follow :

Let $3f(x) + f\left(\frac{1}{x}\right) = \frac{1}{x} + 1$

What is $f(x)$ equal to?

A

$\frac{1}{8x} - \frac{x}{8} + \frac{1}{4}$

B

$\frac{3}{8x} - \frac{x}{8} + \frac{3}{4}$

C

$\frac{3}{8x} + \frac{x}{8} - \frac{1}{4}$

D

$\frac{3}{8x} - \frac{1}{8} + \frac{1}{4}$

3
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following for the next two (02) items that follow:

Let $3f(x) + f\left(\frac{1}{x}\right) = \frac{1}{x} + 1$

What is $8\int_1^2 f(x)dx$ equal to?

A

$\ln (8 \sqrt{e})$

B

$\ln (4 \sqrt{e})$

C

$\ln 2$

D

$\ln 2 - 1$

4
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

A bag contains 5 black and 4 white balls. A man selects two balls at random. What is the probability that both of these are of the same colour?

A

$\frac{1}{6}$

B

$\frac{5}{108}$

C

$\frac{4}{9}$

D

$\frac{5}{18}$

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