Which of the following number is the coefficient of $x^{100}$ in the expansion of $\log _e\Bigg{(}\frac{1+x}{1+{x}^2}\Bigg{)},\, |x|{\lt}1$ ?

1

The range of values of θ in the interval (0, π) such that the points (3,5) and (sinθ, cosθ) lie on the same side of t…

Topic: NIMCET 2023

2

If $| x - 6|= | x - 4x | -| x^2- 5x +6 |$ , where x is a real variable

Topic: NIMCET 2023

3

Let R be reflexive relation on the finite set a having 10 elements and if m is the number of ordered pair in R, then

Topic: NIMCET 2023

4

$\theta={\cos }^{-1}\Bigg{(}\frac{3}{\sqrt[]{10}}\Bigg{)}$ is the angle between $\vec{a}=\hat{i}-2x\hat{j}+2y\hat{k}$ &…

Topic: NIMCET 2023

5

Let a, b, c, d be no zero numbers. If the point of intersection of the line 4ax + 2ay + c = 0 & 5bx + 2by + d=0 lie…

Topic: NIMCET 2023

6

If $\int x\, \sin x\, sec^3x\, dx=\frac{1}{2}\Bigg{[}f(x){se}c^2x+g(x)\Bigg{(}\frac{\tan x}{x}\Bigg{)}\Bigg{]}+C$, then…

Topic: NIMCET 2023

7

A point P in the first quadrant, lies on $y^2 = 4ax$, a > 0, and keeps a distance of 5a units from its focus. Which …

Topic: NIMCET 2023

8

The negation of $\sim S\vee(\sim R\wedge S)$ is equivalent to

Topic: NIMCET 2023

9

If n1 and n2 are the number of real valued solutions x = | sin–1 x | & x = sin (x) respectively, then the valu…

Topic: NIMCET 2023

10

Number of point of which f(x) is not differentiable $f(x)=|cosx|+3$ in $[-\pi, \pi]$

Topic: NIMCET 2023

1

A real valued function f is defined as $f(x)=\begin{cases}{-1} & {-2\leq x\leq0} \\ {x-1} & {0\leq x\leq2}\end{…

Topic: NIMCET 2023

2

A line segment AB of length 10 meters is passing through the foot of the perpendicular of a pillar, which is standing a…

Topic: NIMCET 2023

3

If a vector having magnitude of 5 units, makes equal angle with each of the three mutually perpendicular axes, then the…

Topic: NIMCET 2023

4

Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ballsis trans…

Topic: NIMCET 2023

5

Let $f(x)=\frac{x^2-1}{|x|-1}$. Then the value of $lim_{x\to-1} f(x)$ is

Topic: NIMCET 2023

6

If yellow is called white, white is called black, black is called green, green is called pink, pink is called blue and …

Topic: NIMCET 2023

7

P, Q, R, S, T, U, V, W are sitting around a round table in the same order, for group discussion at equal distances. The…

Topic: NIMCET 2023

8

Find a number from the given options which best completes the series:39, 416, 525,…......................., 749, 864

Topic: NIMCET 2023

9

In the half yearly exam only 60% of the students were passed. Out of these (passed in half-yearly) only 70% students ar…

Topic: NIMCET 2023

10

Fill the blanks with the most appropriate combination of options.Further, to augment bond market liquidity, corporates …

Topic: NIMCET 2023