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

1

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

Topic: NIMCET 2018

2

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

3

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

4

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

5

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

Topic: NIMCET 2018

6

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

Topic: NIMCET 2018

7

Which of the following function is the inverse of itself?

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

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

10

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

Topic: NIMCET 2018

1

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

Topic: NIMCET 2018

2

Question

Topic: NIMCET 2018

3

If  and , then the value of  is

Topic: NIMCET 2018

4

Question

Topic: NIMCET 2018

5

Differential coefficient of $\log_{10} x$ with respect to $\log_{x} 10$ to

Topic: NIMCET 2018

6

$f(x) = x + |x|$ is continuous for

Topic: NIMCET 2018

7

If $\vec{a}, \vec{b}$ and $\vec{c}$ are unit vectors, then $|\mathbf{a} - \mathbf{b}|^2 + |\mathbf{b} - \mathbf{c}|^2 +…

Topic: NIMCET 2018

8

The vector $\vec{a} = \alpha\hat{i} + 2\hat{j} + \beta\hat{k}$ lies in the plane of the vector $\vec{b} = \hat{i} + \ha…

Topic: NIMCET 2018

9

Forces $4\hat{i} - 3\hat{j} + 7\hat{k}$ and $-2\hat{i} + 2\hat{j} - 8\hat{k}$ are acting on a particle and displaced it…

Topic: NIMCET 2018

10

A bird is flying in a straight line with velocity vector 10i+6j+k, measured in km/hr. If the starting point is (1,2,3),…

Topic: NIMCET 2018