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

If $a, b, c$ are in AP; $b, c, d$ are in GP; $c, d, e$ are in HP, then which of the following is/are correct?

1. $a, c,$ and $e$ are in GP

2. $\frac{1}{a}, \frac{1}{c}, \frac{1}{e}$ are in GP

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

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

What is the number of solutions of $\log_4(x - 1) = \log_2(x - 3)$?

A

Zero

B

One

C

Two

D

Three

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

For $x \geq y > 1$, let $\log_x\left( \frac{x}{y} \right) + \log_y\left(\frac{y}{x}\right) = k$, then the value of $k$ can never be equal to :

A

$-1$

B

$-\frac{1}{2}$

C

0

D

1

4
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
If $A=\left[\begin{array}{ccc}\sin 2 \theta & 2 \sin ^2 \theta-1 & 0 \\ \cos 2 \theta & 2 \sin \theta \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right]$, then which of the following statements is/are correct?

1. $A^{-1}=\operatorname{adj} A$

2. A is skew-symmetric matrix

3. $A^{-1}=A^T$

Select the correct answer using the code given below :
A

1 only

B

1 and 2

C

1 and 3

D

2 and 3

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