The locus of the point of intersection of tangents to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ which meet right angles is

1

If $\frac{n!}{2!(n-2)!}$ and $\frac{n!}{4!(n-4)!}$ are in the ratio 2:1, then the value of n is 

Topic: NIMCET 2021

2

If $F(\theta)=\begin{bmatrix}{\cos \theta} & {-\sin \theta} & {0} \\ {\sin \theta} & {\cos \theta} & {0} \\ {0} & {0} &…

Topic: NIMCET 2021

3

For what value of p, the polynomial  $x^4-3x^3+2px^2-6$ is exactly divisible by $(x-1)$

Topic: NIMCET 2021

4

Let $\vec{a}=2\widehat{i}\, +\widehat{j}\, +2\widehat{k}$ , $\vec{b}=\widehat{i}-\widehat{j}+2\widehat{k}$ and $\vec{c…

Topic: NIMCET 2021

5

In a ΔABC, if $\tan ^2\frac{A}{2}+\tan ^2\frac{B}{2}+\tan ^2\frac{C}{2}=k$ , then k is always

Topic: NIMCET 2021

6

The number of common tangents to the circle  $x^2+y^2=4$ and $x^2+y^2-6x-8y=24$ is

Topic: NIMCET 2021

7

$\lim_{x\to \infty} (\frac{x+7}{x+2})^{x+5}$ equal to

Topic: NIMCET 2021

8

If $\log (1-x+x^2)={{a}}_1x+{{a}}_{2{}^{{}^{}}}{x}^2+{{{}{{a}}_3{x}^3+.\ldots.}}^{}$  then ${{a}}_3+{{a}}_6+{…

Topic: NIMCET 2021

9

The area of the region bounded by x-axis and the curves defined by $y=tanx$, $-\frac{\pi}{3}\leq x\leq \frac{\pi}{…

Topic: NIMCET 2021

10

If |k|=5 and 0° ≤ θ ≤ 360°, then the number of distinct solutions of 3cos⁡θ + 4sin⁡θ = k is NIMCET 2021

Topic: NIMCET 2021

1

If the position vector of A and B relative to O be $\widehat{i}\, -4\widehat{j}+3\widehat{k}$ and $-\widehat{…

Topic: NIMCET 2021

2

The general value of $\theta$, satisfying the equation $\sin \theta=\frac{-1}{2},\, \tan \theta=\frac{1}{\sqrt[]{3}}$

Topic: NIMCET 2021

3

The area of the triangle formed by the vertices whose position vectors are $3\widehat{i}+\widehat{j}$ , $5\widehat{i}+2…

Topic: NIMCET 2021

4

The standard deviation of 20 numbers is 30. If each of the numbers is increased by 4, then the new standard deviation w…

Topic: NIMCET 2021

5

The function $f(x)=\frac{x}{1+x\tan x}$ , $0\leq x\leq\frac{\pi}{2}$ is maximum when 

Topic: NIMCET 2021

6

If $f\colon R\rightarrow R$ is defined by $f(x)=\begin{cases}{\frac{x+2}{{x}^2+3x+2}} & {,\, if\, x\, \in R-\{-1,-2\}} …

Topic: NIMCET 2021

7

A polygon has 44 diagonals, the number of sides are 

Topic: NIMCET 2021

8

The probability of occurrence of two events E and F are 0.25 and 0.50, respectively. the probability of their simultane…

Topic: NIMCET 2021

9

If $y={\tan }^{-1}\lgroup{\frac{3x-{x}^3}{1-3{x}^2}}\rgroup\, ,\, \frac{-1}{\sqrt[]{3}}{\lt}x{\lt}\frac{1}{\sqrt[]{3}}$…

Topic: NIMCET 2021

10

The value of $\tan 9{^{\circ}}-\tan 27{^{\circ}}-\tan 63{^{\circ}}+\tan 81{^{\circ}}$ is equal to

Topic: NIMCET 2021