If the volume of the parallelepiped whose adjacent edges are $\vec{a}=2\hat{i}+3\hat{j}+4\hat{k}$, $\vec{b}=\hat{i}+\alpha \hat{j}+2\hat{k}$ and $\vec{c}=\hat{i}+2\hat{j}+\alpha \hat{k}$ is 15, then $\alpha$ is equal to

1

The domain of the function $f(x)=\frac{{\cos }^{-1}x}{[x]}$ is

Topic: NIMCET 2022

2

If $a{\lt}b$ then $\int ^b_a\Bigg{(}|x-a|+|x-b|\Bigg{)}dx$ is equal to

Topic: NIMCET 2022

3

A particle is at rest at the origin. It moves along the x −axis with an acceleration $x-x^2$ , where x is the distance…

Topic: NIMCET 2022

4

If the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{b^2}=1$ and the hyperbola $\frac{x^2}{144}-\frac{y^2}{81}=\frac{1…

Topic: NIMCET 2022

5

Angles of elevation of the top of a tower from three points (collinear) A, B and C on a road leading to the foot of t…

Topic: NIMCET 2022

6

The 10th and 50th percentiles of the observation 32, 49, 23, 29, 118 respectively are

Topic: NIMCET 2022

7

Suppose that the temperature at a point (x,y), on a metal plate is $T(x,y)=4x^2-4xy+y^2$, An ant, walking on the plate…

Topic: NIMCET 2022

8

The correct expression for $cos^{-1} (-x)$ is

Topic: NIMCET 2022

9

Let $\vec{a}, \vec{b}, \vec{c} $ be distinct non-negative numbers. If the vectors $a\hat{i}+a\hat{j}+c\hat{k}$ , $\hat{…

Topic: NIMCET 2022

10

Inverse of the function $f(x)=\frac{10^x-10^{-x}}{10^{x}+10^{-x}}$ is 

Topic: NIMCET 2022

1

Let $a$ be the distance between the lines $−2x + y = 2$ and $2x − y = 2$, and $b$ be the distance between the lines $4x…

Topic: NIMCET 2022

2

If $cosec\theta-cot \theta=2$, then the value of $cosec\theta$ is

Topic: NIMCET 2022

3

The solution of the equation ${4\cos }^2x+6{\sin }^2x=5$ are

Topic: NIMCET 2022

4

The function $f(x)=\begin{cases}{{(1+2x)}^{1/x}} & {,x\ne0} \\ {{e}^2} & {,x=0}\end{cases}$, is

Topic: NIMCET 2022

5

Let $\vec{a}=2\hat{i}+2\hat{j}+\hat{k}$ and $\vec{b}$ be another vector such that $\vec{a}.\vec{b}=14$ and $\vec{a} \ti…

Topic: NIMCET 2022

6

Which term of the series $\frac{\sqrt[]{5}}{3},\, \frac{\sqrt[]{5}}{4},\frac{1}{\sqrt[]{5}},\, ...$ is $\frac{\sqrt{5}}…

Topic: NIMCET 2022

7

The first three moments of a distribution about 2 are 1, 16, -40 respectively. The mean and variance of the distributio…

Topic: NIMCET 2022

8

A survey is done among a population of 200 people who like either tea or coffee. It is found that 60% of the pop lation…

Topic: NIMCET 2022

9

The value of $\cot \Bigg{(}{cosec}^{-1}\frac{5}{3}+{\tan }^{-1}\frac{2}{3}\Bigg{)}$ is

Topic: NIMCET 2022

10

If $0{\lt}P(A){\lt}1$ and $0{\lt}P(B){\lt}1$ and $P(A\cap B)=P(A)P(B)$, then

Topic: NIMCET 2022