NDA (2) – 2025 – Medhashree

Q51. The focal length of a concave lens is 0.5m. The power of the lens is…

(A) +0.5D

(B) -0.5D

(D) -2.0D

Check Answer:

Correct Answer: (D) -2.0D

Explanation:

The power (P) of a lens is defined as the reciprocal of its focal length (f) when the focal length is expressed in meters. The unit of power is the diopter (D).

For a concave lens, the focal length is conventionally considered negative because it is a diverging lens. Therefore, the given focal length of 0.5 m must be written as f = -0.5 m.

Using the formula P = 1/f, the calculation is performed by substituting the negative focal length value: $latex P = \frac{1}{-0.5}$.

BBll ah $$P = \frac{1}{-0.5}$$.

Blah Blah $P = \frac{1}{-0.5}$

Performing the calculation yields a power of -2.0 D.

The power of the concave lens is -2.0 D, which corresponds to option (D).

Q52. The rule to determine the direction of a force experienced by a straight current carrying conductor placed in a magnetic field which is perpendicular to it is…

(A) Right-hand thumb rule

(B) Fleming’s left-hand rule

(D) Hund’s rule

Check Answer:

Correct Answer:

(B) Fleming’s left-hand rule

Explanation:

Exp:

One parsec in astronomical units (A.U.) is about…

(A) $latex 2 \times 10^{3} \text{ A.U.}$
(B) $latex 2 \times 10^{4} \text{ A.U.}$
(C) $latex 2 \times 10^{5} \text{ A.U.}$
(D) $latex 2 \times 10^{6} \text{ A.U.}$

Check Answer:

Correct Answer:

(C) $latex 2 \times 10^{5} \text{ A.U.}$

Explanation:

Exp:

One parsec in astronomical units (A.U.) is about…

(A) $latex 2 \times 10^{3} \text{ A.U.}$
(B) $latex 2 \times 10^{4} \text{ A.U.}$
(C) $latex 2 \times 10^{5} \text{ A.U.}$
(D) $latex 2 \times 10^{6} \text{ A.U.}$

Check Answer:

Correct Answer:

(C) $latex 2 \times 10^{5} \text{ A.U.}$

Explanation:

Exp:

Q51. The focal length of a concave lens is 0.5m. The power of the lens is…

(A) +0.5D

(B) -0.5D

(D) -2.0D

Check Answer:

Correct Answer: (D) -2.0D

Explanation:

The power (P) of a lens is defined as the reciprocal of its focal length (f) when the focal length is expressed in meters. The unit of power is the diopter (D).

For a concave lens, the focal length is conventionally considered negative because it is a diverging lens. Therefore, the given focal length of 0.5 m must be written as f = -0.5 m.

Using the formula P = 1/f, the calculation is performed by substituting the negative focal length value: $latex P = \frac{1}{-0.5}$.

BBll ah $$P = \frac{1}{-0.5}$$.

Blah Blah $P = \frac{1}{-0.5}$

Performing the calculation yields a power of -2.0 D.

The power of the concave lens is -2.0 D, which corresponds to option (D).

Q52. The rule to determine the direction of a force experienced by a straight current carrying conductor placed in a magnetic field which is perpendicular to it is…

(A) Right-hand thumb rule

(B) Fleming’s left-hand rule

(D) Hund’s rule

Check Answer:

Correct Answer:

(B) Fleming’s left-hand rule

Explanation:

Exp:

One parsec in astronomical units (A.U.) is about…

(A) $latex 2 \times 10^{3} \text{ A.U.}$
(B) $latex 2 \times 10^{4} \text{ A.U.}$
(C) $latex 2 \times 10^{5} \text{ A.U.}$
(D) $latex 2 \times 10^{6} \text{ A.U.}$

Check Answer:

Correct Answer:

(C) $latex 2 \times 10^{5} \text{ A.U.}$

Explanation:

Exp:

One parsec in astronomical units (A.U.) is about…

(A) $latex 2 \times 10^{3} \text{ A.U.}$
(B) $latex 2 \times 10^{4} \text{ A.U.}$
(C) $latex 2 \times 10^{5} \text{ A.U.}$
(D) $latex 2 \times 10^{6} \text{ A.U.}$

Check Answer:

Correct Answer:

(C) $latex 2 \times 10^{5} \text{ A.U.}$

Explanation:

Exp:

One parsec in astronomical units (A.U.) is about…

(A) $latex 2 \times 10^{3} \text{ A.U.}$
(B) $latex 2 \times 10^{4} \text{ A.U.}$
(C) $latex 2 \times 10^{5} \text{ A.U.}$
(D) $latex 2 \times 10^{6} \text{ A.U.}$

Check Answer:

Correct Answer:

(C) $latex 2 \times 10^{5} \text{ A.U.}$

Explanation:

Exp:

One parsec in astronomical units (A.U.) is about…

(A) $latex 2 \times 10^{3} \text{ A.U.}$
(B) $latex 2 \times 10^{4} \text{ A.U.}$
(C) $latex 2 \times 10^{5} \text{ A.U.}$
(D) $latex 2 \times 10^{6} \text{ A.U.}$

Check Answer:

Correct Answer:

(C) $latex 2 \times 10^{5} \text{ A.U.}$

Explanation:

Exp:

One parsec in astronomical units (A.U.) is about…

(A) $latex 2 \times 10^{3} \text{ A.U.}$
(B) $latex 2 \times 10^{4} \text{ A.U.}$
(C) $latex 2 \times 10^{5} \text{ A.U.}$
(D) $latex 2 \times 10^{6} \text{ A.U.}$

Check Answer:

Correct Answer:

(C) $latex 2 \times 10^{5} \text{ A.U.}$

Explanation:

Exp:

One parsec in astronomical units (A.U.) is about…

(A) $latex 2 \times 10^{3} \text{ A.U.}$
(B) $latex 2 \times 10^{4} \text{ A.U.}$
(C) $latex 2 \times 10^{5} \text{ A.U.}$
(D) $latex 2 \times 10^{6} \text{ A.U.}$

Check Answer:

Correct Answer:

(C) $latex 2 \times 10^{5} \text{ A.U.}$

Explanation:

Exp:

One parsec in astronomical units (A.U.) is about…

(A) $latex 2 \times 10^{3} \text{ A.U.}$
(B) $latex 2 \times 10^{4} \text{ A.U.}$
(C) $latex 2 \times 10^{5} \text{ A.U.}$
(D) $latex 2 \times 10^{6} \text{ A.U.}$

Check Answer:

Correct Answer:

(C) $latex 2 \times 10^{5} \text{ A.U.}$

Explanation:

Exp:

One parsec in astronomical units (A.U.) is about…

(A) $latex 2 \times 10^{3} \text{ A.U.}$
(B) $latex 2 \times 10^{4} \text{ A.U.}$
(C) $latex 2 \times 10^{5} \text{ A.U.}$
(D) $latex 2 \times 10^{6} \text{ A.U.}$

Check Answer:

Correct Answer:

(C) $latex 2 \times 10^{5} \text{ A.U.}$

Explanation:

Exp:

The sum of the first $ k $ terms of a series $ S $ is $ 3k^2 + 5k $. Which one of the following is correct?

(A) The terms of $ S $ form an arithmetic progression with common difference $ 14 $.

(B) The terms of $ S $ form an arithmetic progression with common difference $ 6 $.

(D) The terms of $ S $ form a geometric progression with common ratio $ \frac{11}{4} $.

The sum of the first 8 terms of a GP is five times the sum of its first 4 terms. If $ r \neq 1 $ is the common ratio, then what is the number of possible real values of $ r $?

(A) One

(B) Two

(D) More than three

If one root of the equation $ x^2 - kx + k = 0 $ exceeds the other by $ 2\sqrt{3} $, then which one of the following is a value of $ k $?

(A) 3

(B) 6

(D) 12

If $ x + \frac{5}{y} = 4 $ and $ y + \frac{5}{x} = -4 $, then what is $ (x + y) $ equal to?

(A) 0

(B) 1

(D) 5

If 5th, 7th, and 13th terms of an AP are in GP, then what is the ratio of its first term to its common difference?

(A) -3

(B) -2

(D) 3

If $ p, 1, q $ are in AP and $ p, 2, q $ are in GP, then which of the following statements is/are correct? I. $ p, 4, q $ are in HP. II. $ (1/p), 1/4, (1/q) $ are in AP. Select the answer using the code given below:

(A) I only

(B) II only

(D) Neither I nor II

If $ x = (1111)_2, y = (100)_2 $ and $ z = (110)_2 $, then what is $ x^3 - y^3 - z^3 - 3xyz $ equal to?

(A) (111100)_2

(B) (100111)_2

(D) (0)_2

If $ \Delta = \begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} $ and $ A, B, C, D, G $ are the cofactors of the elements $ a, b, c, d, g $ respectively, then what is $ bB + cC - dD - gG $ equal to?

(A) 0

(B) 1

(D) $ -\Delta $

Consider the following statements in respect of the determinant $ \Delta = \begin{vmatrix} k(k+2) & 2k+1 & 1 \\ 2k+1 & k+2 & 1 \\ 3 & 3 & 1 \end{vmatrix} $: I. $ \Delta $ is positive if $ k > 0 $. II. $ \Delta $ is negative if $ k < 0 $. III. $ \Delta $ is zero if $ k = 0 $. How many of the statements given above are correct?

(A) None

(B) One

(D) All three

If $ \begin{vmatrix} 2 & 3 + i & -1 \\ 3 - i & 0 & i - 1 \\ -1 & -1 - i & 1 \end{vmatrix} = A + iB $ where $ i = \sqrt{-1} $, then what is $ A + B $ equal to?

(A) -10

(B) -6

(D) 6

If $ A^2 + B^2 + C^2 = 0 $, then what is the value of the following determinant? $ \begin{vmatrix} 1 & \cos C & \cos B \\ \cos C & 1 & \cos A \\ \cos B & \cos A & 1 \end{vmatrix} $

(A) -1

(B) 0

(D) 2

If $ \omega $ is a non-real cube root of unity, then what is a root of the following equation? $ \begin{vmatrix} x + 1 & \omega & \omega^2 \\ \omega^2 & 1 & x + \omega^2 \\ \omega & x + \omega & 1 \end{vmatrix} = 0 $

(A) $ x = 0 $

(B) $ x = 1 $

(D) $ x = \omega^2 $

What is $ \left( \frac{\sqrt{3} + i}{\sqrt{3} - i} \right)^3 $ equal to?

(A) -1

(B) 0

(D) 3

If $ x^2 - x + 1 = 0 $, then what is $ \left( x - \frac{1}{x} \right)^2 + \left( x - \frac{1}{x} \right)^4 + \left( x - \frac{1}{x} \right)^8 $ equal to?

(A) 81

(B) 85

(D) 90

How many 7-letter words (with or without meaning) can be constructed using all the letters of the word CAPITAL so that all consonants come together in each word?

(A) 360

(B) 300

(D) 240

If $ z \neq 0 $ is a complex number, then what is $ \text{amp}(z) + \text{amp}(\overline{z}) $ equal to?

(A) 0

(B) $ \pi/2 $

(D) $ 2\pi $

How many sides are there in a polygon which has 20 diagonals?

(A) 6

(B) 7

(D) 10

In how many ways can the letters of the word DELHI be arranged keeping the positions of vowels and consonants unchanged?

(A) 6

(B) 9

(D) 24

What is the number of positive integer solutions of $ x + y + z = 5 $?

(A) 3

(B) 5

(D) 9

What is the number of rational terms in the expansion of $ (3^{1/5} + 5^{1/3})^{12} $?

(A) 2

(B) 3

(D) 6

If the sum of binomial coefficients in the expansion of $ (x + y)^n $ is 256, then the greatest binomial coefficient occurs in which one of the following terms?

(A) Third

(B) Fourth

(D) Ninth

If $ k < (\sqrt{2} + 1)^3 < k + 2 $, where $ k $ is a natural number, then what is the value of $ k $?

(A) 11

(B) 13

(D) 17

If $ \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \begin{bmatrix} x \\ 1 \\ 1 \end{bmatrix} = \begin{bmatrix} 45 \\ 45 \\ 45 \end{bmatrix} $, then which one of the following is a value of $ x $?

(A) -2

(B) -1

(D) 1

If $ A = \begin{bmatrix} y & z & x \\ z & x & y \\ x & y & z \end{bmatrix} $ where $ x, y, z $ are integers, is an orthogonal matrix, then what is the value of $ x^2 + y^2 + z^2 $?

(A) 0

(B) 1

(D) 14

Leave a Reply Cancel reply