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

If $p$ is the perpendicular distance from origin to the plane passing through $(1, 0, 0)$, $(0, 1, 0)$ and $(0, 0, 1)$, then what is $3p^2$ equal to?

A

4

B

3

C

2

D

1

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

If the direction cosines <l, m, n> of a line are connected by relation $l + 2m + n = 0, 2l - 2m + 3n = 0$, then what is the value of $l^{2} + m^{2} - n^{2}$?

A

$\frac{1}{101}$

B

$\frac{29}{101}$

C

$\frac{41}{101}$

D

$\frac{92}{101}$

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

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

$x + 3y = 10$

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

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

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

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