An experiment has $10$ equally likely outcomes. Let $A$ and $B$ be two non-empty events of the experiment. If $A$ consists of $4$ outcomes, the number of outcomes that $B$ must have so that $A$ and $B$ are independent is

1

If $\cos\theta = \dfrac{5}{13},; \dfrac{3\pi}{2} < \theta < 2\pi$, then $\tan 2\theta$ is

Topic: NIMCET 2016

2

In a triangle $ABC$, $a = 4$, $b = 3$, $\angle BAC = 60^\circ$, then the equation for which $c$ is the root is

Topic: NIMCET 2016

3

The area of region bounded by the lines $y = |x - 1|$ and $y = 3 - |x|$ is

Topic: NIMCET 2016

4

If $2x^2 + 7xy + 3y^2 + 8x + 14y + \lambda = 0$ represents a pair of straight lines, the value of $\lambda$ is

Topic: NIMCET 2016

5

The vector perpendicular to the plane passing through $(1,-1,0),; (2,1,-1)$ and $(-1,1,2)$ is

Topic: NIMCET 2016

6

The volume of the parallelepiped determined by $u = i + 2j - k,; v = -2i + 3k$ and $w = 7j - 4k$

Topic: NIMCET 2016

7

Which of the following statements is False ?

Topic: NIMCET 2016

8

$\int \left(\dfrac{\log x - 1}{1 + (\log x)^2}\right)^2 dx$ is equal to

Topic: NIMCET 2016

9

If $X={4^n-3n-1,; n\in N}$ and $Y={9n-9,; n\in N}$, then $X\cup Y$ is equal to

Topic: NIMCET 2016

10

The line 3x + 5y = k touches the ellipse 16&nbsp;x2 &nbsp;+ 25 y2&nbsp;= 400,&nbsp;&nbsp;if k is

Topic: NIMCET 2016

1

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three non-zero vectors, no two of which are collinear, if the vector $\vec{a}+2…

Topic: NIMCET 2016

2

The minimum value of $a$, for which the sum of the squares of the roots of the equation $x^2-(a-2)x-(a+1)=0$

Topic: NIMCET 2016

3

For any two events $A$ and $B$, the probability that atleast one of them occur is $0.6$. If $A$ and $B$ occur simultane…

Topic: NIMCET 2016

4

Two finite sets $A$ and $B$ are having $m$ and $n$ elements. The total number of subsets of the first set is $56$ more …

Topic: NIMCET 2016

5

The probability that $A$ speaks truth is $4/5$ while this probability for $B$ is $3/4$. The probability that they contr…

Topic: NIMCET 2016

6

The sum of the expression $\dfrac{1}{\sqrt{1}+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{4}}+\cdot…

Topic: NIMCET 2016

7

Consider the function $f$ defined by $f(x)=\begin{cases} x^2-1, & x

Topic: NIMCET 2016

8

Three house are available in a locality. Three persons apply for the houses. Each applies for one house without consult…

Topic: NIMCET 2016

9

Five horse are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A select…

Topic: NIMCET 2016

10

If $3^x = 4^{x-1}$, then $x=$

Topic: NIMCET 2016