Let $\vec{A} = 2\hat{i} + \hat{j} – 2\hat{k}$ and $\vec{B} = \hat{i} + \hat{j}$, If $\vec{C}$ is a vector such that $|\vec{C} – \vec{A}| = 3$ and the angle between A × B and C is ${30^{\circ}}$, then $|(\vec{A} × \vec{B}) × \vec{C}|$ = 3 then the value of $\vec{A}.\vec{C}$ is equal to

1

If $\overrightarrow{{a}}$ and $\overrightarrow{{b}}$ are vectors in space, given by $\overrightarrow{{a}}=\frac{\hat{i}…

Topic: NIMCET 2023

2

A speaks truth in 60% and B speaks the truth in 50% cases. In what percentage of cases they are likely incontradict eac…

Topic: NIMCET 2023

3

If $\prod ^n_{i=1}\tan ({{\alpha}}_i)=1\, \forall{{\alpha}}_i\, \in\Bigg{[}0,\, \frac{\pi}{2}\Bigg{]}$ where i=1,2,3,..…

Topic: NIMCET 2023

4

The equation of the tangent at any point of curve $x=a cos2t, y=2\sqrt{2} a sint$ with $m$ as its slope is

Topic: NIMCET 2023

5

The value of $\int ^{\pi/3}_{-\pi/3}\frac{x\sin x}{{\cos }^2x}dx$ is

Topic: NIMCET 2023

6

If $f(x)=\lim _{{x}\rightarrow0}\, \frac{{6}^x-{3}^x-{2}^x+1}{\log _e9(1-\cos x)}$ is a real number then $\lim _{{…

Topic: NIMCET 2023

7

The sum of infinite terms of decreasing GP is equal to the greatest value of the function $f(x) = x^3 + 3x – 9$ in the…

Topic: NIMCET 2023

8

Consider the following frequency distribution table. Class interval 10-20 20-3030-40 40-50 &nb…

Topic: NIMCET 2023

9

For a group of 100 candidates, the mean and standard deviation of scores were found to be 40 and 15 respectively. Later…

Topic: NIMCET 2023

10

In an examination of nine papers, a candidate has to pass in more papers than the number of papers in which he fails in…

Topic: NIMCET 2023

1

Let A and B be sets. $A\cap X=B\cap X=\phi$ and $A\cup X=B\cup X$ for some set X, relation between A & B

Topic: NIMCET 2023

2

If a, b, c, d are in HP and arithmetic mean of ab, bc, cd is 9 then which of the following number is the value of ad?

Topic: NIMCET 2023

3

Find foci of the equation $x^2 + 2x – 4y^2 + 8y – 7 = 0$

Topic: NIMCET 2023

4

The locus of the mid-point of all chords of the parabola $y^2 = 4x$ which are drawn through its vertex is

Topic: NIMCET 2023

5

If $\vec{a}=\hat{i}-\hat{k}$, $\vec{b}=x\hat{i}+\hat{j}+(1-x)\hat{k}$ and $\vec{c}=y\hat{i}+x\hat{j}+(1+x-y)\hat{k}$, t…

Topic: NIMCET 2023

6

If $\vec{a}, \vec{b}$ are unit vectors such that $2\vec{a}+\vec{b} =3$ then which of the following statement is true?

Topic: NIMCET 2023

7

$\int f(x)\mathrm{d}x=g(x)$, then $\int {x}^5f({x}^3)\mathrm{d}x$

Topic: NIMCET 2023

8

$\lim _{{x}\rightarrow1}\frac{{x}^4-1}{x-1}=\lim _{{x}\rightarrow k}\frac{{x}^3-{k}^2}{{x}^2-{k}^2}=$, then find k

Topic: NIMCET 2023

9

The graph of function $f(x)=\log _e({x}^3+\sqrt[]{{x}^6+1})$ is symmetric about:

Topic: NIMCET 2023

10

If the equation $|x^2 – 6x + 8| = a$ has four real solution then find the value of $a$?

Topic: NIMCET 2023