$\int_0^{\pi} x\, f(\sin x)\, dx$ is equal to

1

The set of points, where $f(x)=\frac{x}{1+|x|}$  is differentiable in 

Topic: NIMCET 2018

2

If the mean of the squares of first n natural numbers be 11, then n is equal to?

Topic: NIMCET 2018

3

If A is an invertible skew-symmetric matrix, then  is a

Topic: NIMCET 2018

4

Suppose that m and n are fixed numbers such that the mth term of an HP is equal to n and the nth term is equal to m, (m…

Topic: NIMCET 2018

5

Sum to infinity of a geometric is twice the sum of the first two terms. Then what are the possible values of common rat…

Topic: NIMCET 2018

6

The quadratic equation whose roots are $\sin^218^o$ and $\cos^236^o$  is

Topic: NIMCET 2018

7

A and B play a game where each is asked to select a number from 1 to 25. If the two number match, both of them win a pr…

Topic: NIMCET 2018

8

Three numbers a,b and c are chosen at random (without replacement) from among the numbers 1, 2, 3, ..., 99. The probabi…

Topic: NIMCET 2018

9

Two person A and B agree to meet 20 april 2018 between 6pm to 7pm with understanding that they will wait no longer…

Topic: NIMCET 2018

10

The function $f(x) = \log\left(x + \sqrt{x^2 + 1}\right)$ is

Topic: NIMCET 2018

1

Let $f: R \rightarrow R$ be defined by $f(x) = \begin{cases} x + 2 & \text{if } x < 0 \\ |x - 2| & \text{if } x \geq 0 …

Topic: NIMCET 2018

2

The slope of two-lines $6x^2-xy-2y^2=0$&nbsp;differ by

Topic: NIMCET 2018

3

If the radius of the circle changes at the rate of $-\dfrac{2}{\pi}$ m/s, at what rate does the circle's area change wh…

Topic: NIMCET 2018

4

The point of intersection os circle $x^2+y^2+10x-12y+51=0$&nbsp;and the line $3y+x=3$&nbsp;is

Topic: NIMCET 2018

5

The number of solutions of the equation&nbsp;sinx + sin5x = sin3x lying in the interval $[0, \pi]$&nbsp;is

Topic: NIMCET 2018

6

In an acute-angled ΔABC the least value of secA+secB+secC is&nbsp;

Topic: NIMCET 2018

7

Let $P = \{\theta : \sin\theta - \cos\theta = \sqrt{2}\cos\theta \}$ and $Q = \{\theta : \sin\theta + \cos\theta = \s…

Topic: NIMCET 2018

8

If $\dfrac{\tan x}{2} = \dfrac{\tan y}{3} = \dfrac{\tan z}{5}$ and $x + y + z = \pi$, then the value of $\tan^2 x + \ta…

Topic: NIMCET 2018

9

The circles whose equations are $x^2+y^2+c^2=2ax$&nbsp;and $x^2+y^2+x^2-2by=0$ will touch one another externally, if

Topic: NIMCET 2018

10

The locus of the orthocentre of the triangle formed by the lines (1+p)x-py+p(1+p)=0, (1+p)(x-q)+q(1+ q)=0 and y=0 where…

Topic: NIMCET 2018