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

1

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

Topic: NIMCET 2023

2

If ${{x}}_k=\cos \Bigg{(}\frac{2\pi k}{n}\Bigg{)}+i\sin \Bigg{(}\frac{2\pi k}{n}\Bigg{)}$ , then $\sum ^n_{k=1}({{…

Topic: NIMCET 2023

3

The coefficient of $x^{50}$ in the expression of ${(1 + x)^{1000} + 2x(1 + x)^{999} + 3x^2(1 + x)^{998} + ...... + 1001…

Topic: NIMCET 2023

4

The maximum value of $f(x) = (x – 1)^2 (x + 1)^3$ is equal to $\frac{2^p3^q}{3125}$  then the ordered pair of (p, …

Topic: NIMCET 2023

5

If f(x) is a polynomial of degree 4, f(n) = n + 1 & f(0) = 25, then find f(5) = ?

Topic: NIMCET 2023

6

Between any two real roots of the equation $e^x sin x = 1$, the equation $e^x cos x = –1$ has

Topic: NIMCET 2023

7

A bag contain different kind of balls in which 5 yellow, 4 black & 3 green balls. If 3 balls are drawn at random th…

Topic: NIMCET 2023

8

If A and B are square matrices such that $B=-A^{-1} BA$, then $(A + B)^2$ is

Topic: NIMCET 2023

9

Given to events A and B such that odd in favour A are 2 : 1 and odd in favour of $A \cup B$ are 3 : 1. Consistent with …

Topic: NIMCET 2023

10

Largest value of $cos^2\theta -6sin\theta cos\theta+3sin^2\theta+2 $ is

Topic: NIMCET 2023

1

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

Topic: NIMCET 2023

2

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

3

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

4

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

5

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

Topic: NIMCET 2023

6

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

7

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

Topic: NIMCET 2023

8

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

9

Which of the following number is the coefficient of $x^{100}$ in the expansion of $\log _e\Bigg{(}\frac{1+x}{1+{x}^2}\B…

Topic: NIMCET 2023

10

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