NDA Mathematics 14th September 2025 | NDA Year Wise Previous Years Questions

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NDA Mathematics 14th September 2025

MCQ (Single Correct Answer)

+2.5

-0.833

What is the value of $\tan \left[\frac{1}{2}\sec ^{-1}\left(\frac{2}{\sqrt{3}}\right)\right]?$

$2-\sqrt{3}$

$2+\sqrt{3}$

$\sqrt{3}-1$

$\sqrt{3}+1$

NDA Mathematics 14th September 2025

MCQ (Single Correct Answer)

+2.5

-0.833

For the following two (02) items:
A plane P is parallel to the line having direction ratios $\langle1, 3, 2\rangle $ and contains the line of intersection of the planes 6x + 4y - 5z = 2 and x - 2y + 3z = 0

Which of the following are the direction ratios of the line of intersection of the given planes?

$\langle2, 23, 16\rangle$

$\langle2, - 23, - 16\rangle$

$\langle2, 3, 2\rangle$

$ \langle- 1, 3, - 2\rangle$

NDA Mathematics 14th September 2025

MCQ (Single Correct Answer)

+2.5

-0.833

What is the equation of the plane P?

2x - 20y + 29z + 2 = 0

2x + 3y + 2z - 4 = 0

2x - 20y + 29z - 2 = 0

x - 3y + 2z + 5 = 0

NDA Mathematics 14th September 2025

MCQ (Single Correct Answer)

+2.5

-0.833

For the following two (02) items:
Suppose S is the sphere with the smallest radius that passes through the points A(1, 0, 0) B(0, 1, 0) and C(0, 0, 1)

What is the radius of S?

$ \sqrt{\frac{1}{3}} $

$\sqrt{\frac{2}{3}} $

$\frac{1}{3} $

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