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

Let $\int \frac{d x}{\sqrt{x+1}-\sqrt{x-1}}=\alpha(x+1)^{\frac{3}{2}}+$ $$ \beta(x-1)^{\frac{3}{2}}+c $$

What is the value of $\alpha$?

A

$\frac{1}{3}$

B

$\frac{2}{3}$

C

$1$

D

$\frac{4}{3}$

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

Let $\int \frac{d x}{\sqrt{x+1}-\sqrt{x-1}}=\alpha(x+1)^{\frac{3}{2}}+$ $$ \beta(x-1)^{\frac{3}{2}}+c $$

What is the value of $\beta$?

A

$-\frac{2}{3}$

B

$-\frac{1}{3}$

C

$\frac{1}{3}$

D

$\frac{2}{3}$

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

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

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 $A_1$?

A

$\frac{\pi - 2}{4}$

B

$\frac{\pi + 2}{4}$

C

$\frac{3\pi - 2}{4}$

D

$\frac{3\pi + 2}{4}$

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

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

$-\pi$

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