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

1

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

Topic: NIMCET 2016

2

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

Topic: NIMCET 2016

3

Which of the following statements is False ?

Topic: NIMCET 2016

4

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

Topic: NIMCET 2016

5

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

6

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

Topic: NIMCET 2016

7

A box contains 2 blue caps, 4 red caps, 5 green caps and 1 yellow cap. If four caps are picked at random, the probabili…

Topic: NIMCET 2016

8

If  ,  , and  +  are vectors of magnitude α then the magnitude of the vect…

Topic: NIMCET 2016

9

 is equal to 

Topic: NIMCET 2016

10

The equation of a circle with diameters are 2x – 3y + 12 = 0 and x + 4y – 5 = 0 and area of 154 sq. units is

Topic: NIMCET 2016

1

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

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

Topic: NIMCET 2016

4

An experiment has $10$ equally likely outcomes. Let $A$ and $B$ be two non-empty events of the experiment. If $A$ consi…

Topic: NIMCET 2016

5

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

6

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

7

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

8

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

9

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

10

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