NDA MATHEMATICS SECTIONAL TEST 2

Question 1:

The solution set of the inequation $\frac{x+12}{x-5}>0$ is:

$(-\infty,-12) \cup(5, \infty)$

$(-12,5)$

$\mathrm{R}-\{12\}$

$(-\infty,-7)$

Question 2:

If x, p > 0 and $x < p-4$ then which of the following is correct?

$-x < -p$

$-x > -p$

$x=p$

$-x \leq-p$

Question 3:

If $a, b$ and $c$ are real numbers such that $a < b$ and $c < 0$ then

$\frac{\mathrm{a}}{\mathrm{c}}>\frac{\mathrm{b}}{\mathrm{c}}$

$\frac{\mathrm{a}}{\mathrm{b}} \leq \frac{\mathrm{b}}{\mathrm{c}}$

$\frac{a}{c}<\frac{b}{c}$

$\frac{\mathrm{a}}{\mathrm{c}}=\frac{\mathrm{b}}{\mathrm{c}}$

Question 4:

If $|p-1|+|p-3| \leq 8$ then value of $p$ lies in the interval.

$]-\infty, 2]$

$[-4,6]$

$[-2,2]$

$[3, \infty[$

Question 5:

For the equation $|x|^{2}-|x|-6=0$ the roots are

One and only one real number

Real with sum 2

Real with product zero.

Real with sum zero.

Question 6:

The solution set of equation $\left|x^{2}-x-6\right|=x+2$; where $x$ is a positive real number is.

$\{-2,4\}$

$\{3,2,4\}$

$\{2,4\}$

$\{1,2,4\}$

Question 7:

The number of real solutions of the equation $|x|^{2}-3|x|–4=0$ is

2.0

1.0

4.0

3.0

Question 8:

The value of $\frac{1}{\log _{2} \pi}+\frac{1}{\log _{4.5} \pi}$ is always less than.

$-2$

0.0

–1

2.0

Question 9:

The solution set of the inequality $4^{-x+0.5}-5 \cdot 2^{-x}-3<0$ is.

$(\log 2, \infty)$

$\left(\log _{2} 3, \infty\right)$

$\left(-\log _{2} 3, \infty\right)$

None of these

Question 10:

If $\mathrm{x}, \mathrm{y}, \mathrm{z}$ be three positive real numbers then the minimum value of the

expression $ \frac{y+z}{x}+\frac{x+z}{y}+\frac{x+y}{z}$ is:

6.0

9.0

3.0

8.0

Question 11:

Suppose $0< x_{i}<1$ for each $i \in N$
$s_{n}=x_{1}+x_{2}+x_{3}+\ldots \ldots . .+x_{n}$ then
$\left(1-x_{1}\right)\left(1-x_{2}\right)\left(1-x_{3}\right) \ldots \ldots \ldots . .\left(1-x_{n}\right)$ is

greater than $\frac{1}{1+s_{n}}$

equal ot $\frac{1}{1+s_{n}}$

less than $\frac{1}{1+s_{n}}$

equal to $\frac{1}{\sqrt{\left(1-s_{n}\right)}}$

Question 12:

If 0 < x, y, z < 1 where x + y + z = 1 then the minimum value of $\frac{(1-x)(1-y)(1-z)}{x y z}$ is.

9.0

8.0

2.0

6.0

Question 13:

If $\mathrm{p}+2>\sqrt{\mathrm{p}+4}$ then

$\mathrm{p}<-4$

$p>0$

$-3 < p < 0$

$3<\mathrm{p}<\infty$

Question 14:

If $x^{2}+2 p x+10-3 p>0$ for all $x \in R$ then

$\mathrm{p}<-5$

$-5<\mathrm{p}<2$

$-4<\mathrm{p}<7$

$-3<\mathrm{p}<0$

Question 15:

The solution set of $\frac{x+5}{x-2} \leq 2$ is

$(-\infty, 2) \cup[9, \infty[$

$(-\infty, 9)$

$]-\infty, 2]$

$\quad(-\infty, 3) \cup(7, \infty)$

Question 16:

If $x$ is real then the value of $k=\frac{x^{2}+x+1}{x^{2}-x+1}$ is given by.

$\mathrm{k} \geq 4$

$\mathrm{k} \leq-1$

$\frac{1}{3} \leq \mathrm{k} \leq 3$

$5 \leq \mathrm{k} \leq \infty$

Question 17:

If $|x-5| \leq 2 x+7$ then $x$ lies in the interval .

$-\frac{2}{3} \leq x<\infty$

$-12 \leqslant \mathrm{x}<\infty$

$-3 < x < 11$

$-\infty < x < 11$

Question 18:

If $3 \leqslant 3 p-15 \leqslant 18$ then $p$ lies in the interval ?

$2 \leqslant \mathrm{p} \leqslant 6$

$5 \leqslant \mathrm{p} \leqslant 11$

$6 \leqslant \mathrm{p} \leqslant 11$

$4 \leqslant \mathrm{p} \leqslant 10$

Question 19:

If $\mathrm{s}$ is the soultion set of $\mathrm{x}$ such that the in equation $\frac{3 x-1}{2 x^{3}+3 x^{2}+x}>0$ holds then $s$ contains.

$(-\infty,-1)$

$\left(-\frac{1}{2}, 0\right)$

$\left(\frac{1}{3}, \infty\right)$

All of $(\mathrm{a}, \mathrm{b}$, c) are correct

Question 20:

The set of all $x$ satisfying $-x^{2}-x+12 \geqslant 0$ is.

$3 \leqslant \mathrm{x} \leqslant 4$

$-4 \leq x \leq 3$

$-2 \leq x<\infty$

$(-\infty,-4) \cup(3, \infty)$