Let $P = \{\theta : \sin\theta - \cos\theta = \sqrt{2}\cos\theta \}$ and $Q = \{\theta : \sin\theta + \cos\theta = \sqrt{2}\sin\theta \}$ be two sets. Then 

1

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

Topic: NIMCET 2018

2

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

Topic: NIMCET 2018

3

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

Topic: NIMCET 2018

4

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

5

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

Topic: NIMCET 2018

6

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

7

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

Topic: NIMCET 2018

8

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

Topic: NIMCET 2018

9

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

Topic: NIMCET 2018

10

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

Topic: NIMCET 2018

1

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

2

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

3

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

4

Equation of the common tangents with a positive slope to the circle $x^2+y^2-8x=0$ and$\dfrac{x^2}{9}-\dfrac{y^2}{4}=1$…

Topic: NIMCET 2018

5

The area enclosed between the curves $y^2=x$&nbsp;and $y=|x|$&nbsp;is

Topic: NIMCET 2018

6

Equation of the line perpendicular to x-2y=1 and passing through (1,1) is

Topic: NIMCET 2018

7

If $A = \begin{bmatrix} 0 & 5 \\ 0 & 0 \end{bmatrix}$ and $f(x) = 1 + x + x^2 + \cdots + x^{16}$, then $f(A) =$

Topic: NIMCET 2018

8

9 balls are to be placed in 9 boxes and 5 of the balls cannot fit into 3 small boxes. The number of ways of arranging o…

Topic: NIMCET 2018

9

Which of the following function is the inverse of itself?

Topic: NIMCET 2018

10

A student council has 10 members. From this one President, one Vice-President, one Secretary, one Joint-Secretary and t…

Topic: NIMCET 2018