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

If the 4th term in the expansion of $\left(mx + \frac{1}{x}\right)^n$ is $\frac{5}{2}$, then what is the value of $mn$?

A

-3

B

3

C

6

D

12

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

If $a$, $b$, and $c$ $(a > 0, c > 0)$ are in GP, then consider the following in respect of the equation $ax^2 + bx + c = 0$:

1. The equation has imaginary roots.

2. The ratio of the roots of the equation is $1 : \omega$ where $\omega$ is a cube root of unity.

3. The product of roots of the equation is $\left(\frac{b^2}{a^2}\right)$.

Which of the statements given above are correct?

A

1 and 2 only

B

2 and 3 only

C

1 and 3 only

D

1, 2 and 3

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

If $x^2 + mx + n$ is an integer for all integral values of $x$, then which of the following is/are correct?

1. $m$ must be an integer

2. $n$ must be an integer

Select the correct answer using the code given below:

A

1 only

B

2 only

C

Both 1 and 2

D

Neither 1 nor 2

4
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
In a binomial expansion of $(x+y)^{2 n+1}(x-y)^{2 n+1}$, the sum of middle terms is zero. What is the value of $\left(\frac{x^2}{y^2}\right)$ ?
A

1

B

2

C

4

D

8

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