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

If $\log{a} = p$, $\log{c} = 2p$ and $\log{e} = 3p$, then what is $(ace)^\frac{1}{p}$ equal to?

A

$bd^2 f^3$

B

$bdf$

C

$b^3 d^2 f$

D

$b^2 d^2 f^2$

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

If $\sqrt{2}$ and $\sqrt{3}$ are roots of the equation $a_0 + a_1 x + a_2 x^2 + a_3 x^3 + x^4 = 0$ where $a_0, a_1, a_2, a_3$ are integers, then which one of the following is correct?

A

$a_2 = a_3 = 0$

B

$a_2 = 0$ and $a_3 = -5$

C

$a_0 = 6$, $a_3 = 0$

D

$a_1 = 0$ and $a_2 = 5$

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

Let $z_1$ and $z_2$ be two complex numbers such that $\left|\frac{z_1 + z_2}{z_1 - z_2}\right| = 1$, then what is $\operatorname{Re} \left(\frac{z_1}{z_2}\right) + 1$ equal to?

A

$-1$

B

$0$

C

$1$

D

$5$

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

If $26! = n8^k$, where $k$ and $n$ are positive integers, then what is the maximum value of $k$?

A

$6$

B

$7$

C

$8$

D

$9$

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