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

If a variable line passes through the point of intersection of the lines $x + 2y - 1 = 0$ and $2x - y - 1 = 0$ and meets the coordinate axes in $A$ and $B$, then what is the locus of the mid-point of $AB$?

A

$3x + y = 10xy$

B

$x + 3y = 10xy$

C

$3x + y = 10$

D

$x + 3y = 10$

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

What is the equation to the straight line passing through the point $(-sin\theta, cos\theta)$ and perpendicular to the line $xcos\theta + ysin\theta = 9$?

A

$xsin\theta - ycos\theta - 1 = 0$

B

$xsin\theta - ycos\theta + 1 = 0$

C

$xsin\theta - ycos\theta = 0$

D

$xcos\theta - ysin\theta + 1 = 0$

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

Two points $P$ and $Q$ lie on line $y = 2x + 3$. These two points $P$ and $Q$ are at a distance 2 units from another point $R(1, 5)$. What are the coordinates of the points $P$ and $Q$?

A

$(1 + \frac{2}{\sqrt{5}}, 5 + \frac{4}{\sqrt{5}}), (1 - \frac{2}{\sqrt{5}}, 5 - \frac{4}{\sqrt{5}})$

B

$(3 + \frac{2}{\sqrt{5}}, 5 + \frac{4}{\sqrt{5}}), (-1 - \frac{2}{\sqrt{5}}, 5 - \frac{4}{\sqrt{5}})$

C

$(1 - \frac{2}{\sqrt{5}}, 5 + \frac{4}{\sqrt{5}}), (1 + \frac{2}{\sqrt{5}}, 5 - \frac{4}{\sqrt{5}})$

D

$(3 - \frac{2}{\sqrt{5}}, 5 + \frac{4}{\sqrt{5}}), (-1 + \frac{2}{\sqrt{5}}, 5 - \frac{4}{\sqrt{5}})$

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

If two sides of a square lie on the lines $2x + y - 3 = 0$ and $4x + 2y + 5 = 0$, then what is the area of the square in square units?

A

6.05

B

6.15

C

6.25

D

6.35

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