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 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
If 3x + y - 5 = 0 is the equation of a chord of the circle x+ y2 - 25 = 0, then what are the coordinates of the mid-point of the chord ?
A
$ \left(\frac{3}{4}, \frac{1}{4}\right)$
B
$ \left(\frac{3}{2}, \frac{1}{2}\right) $
C
$ \left(\frac{3}{4},-\frac{1}{4}\right) $
D
$ \left(\frac{3}{2},-\frac{1}{2}\right)$
3
NDA Mathematics 3 September 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Consider the following in respect of the circle 4x+ 4y- 4ax - 4ay + a2 = 0:

1. The circle touches both the axes. 

2. The diameter of the circle is 2a.

3. The centre of the circle lies on the line x + y = a.

How many of the statements given above are correct?

A
Only one
B
Only two
C
All three
D
None
4
NDA Mathematics 16 April 2023
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

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

The line y = x partitions the circle (x - a)2 + y2 = a2 in two segments.

What is the area of minor segment ?
A
$\frac{(\pi-2) a^2}{4}$
B
$\frac{(\pi-1) a^2}{4}$
C
$\frac{(\pi-2) a^2}{2}$
D
$\frac{(\pi-1) a^2}{2}$
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