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

1

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

Topic: NIMCET 2018

2

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

Topic: NIMCET 2018

3

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

4

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

5

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

Topic: NIMCET 2018

6

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

7

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

Topic: NIMCET 2018

8

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

Topic: NIMCET 2018

9

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

Topic: NIMCET 2018

10

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

Topic: NIMCET 2018

1

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

2

Which of the following function is the inverse of itself?

Topic: NIMCET 2018

3

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

Topic: NIMCET 2018

4

In a survey where 100 students reported which subject they like, 32 students in total liked Mathematics, 38 students li…

Topic: NIMCET 2018

5

If A and B are two events and $P(A \cup B) = \dfrac{5}{6}$, $P(A \cap B) = \dfrac{1}{2}$, the A and B are two events wh…

Topic: NIMCET 2018

6

If $a_1, a_2,...a_n$  are positive real numbers whose product is a fixed number c, then the minimum of $a_1, …

Topic: NIMCET 2018

7

If \(a, b, c\) are the roots of the equation \(x^3 - 3x^2 + 3x + 7 = 0\), then the value of\[\begin{vmatrix}2bc - a^2 &…

Topic: NIMCET 2018

8

The coefficient of $x^n$ in the expansion of $(1 - 2x + 3x^2 - 4x^3 + \cdots \text{ to } \infty)^{-n}$ is

Topic: NIMCET 2018

9

Let $\alpha$ and $\beta$ be the roots of the equation $x^2 - px + r = 0$ and $\dfrac{\alpha}{2}, 2\beta$ are the roots …

Topic: NIMCET 2018

10

How many natural numbers smaller than $2 \times 10^8$ can be formed using the digits 1 and 2 only?

Topic: NIMCET 2018