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

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 $a_2 = 5$

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

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
Change Language

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
Change Language

Under which one of the following conditions does the equation $\left(\cos \beta-1\right)x^2+(\cos \beta)x+\sin \beta=0$ in $x$ have a real root for $\beta \in [0, \pi]$?

A

$1-\cos \beta <0$

B

$1-\cos \beta \leq 0$

C

$1-\cos \beta>0$

D

$1-\cos \beta \geq 0$

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