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

1

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

2

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

Topic: NIMCET 2016

3

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

4

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

Topic: NIMCET 2016

5

 is equal to 

Topic: NIMCET 2016

6

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

7

The solution set of equation logx2 log2x 2 = log4x 2 is

Topic: NIMCET 2016

8

The number of 5 people groups that can be selected from 9 people when two particular persons are not to be in the same …

Topic: NIMCET 2016

9

The average marks of boys in class is 52 and that of

Topic: NIMCET 2016

10

If C is the midpoint of AB and P is any point outside AB, then

Topic: NIMCET 2016

1

Which of the following statements is False ?

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

The vector perpendicular to the plane passing through $(1,-1,0),; (2,1,-1)$ and $(-1,1,2)$ 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 area of region bounded by the lines $y = |x - 1|$ and $y = 3 - |x|$ is

Topic: NIMCET 2016

6

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

7

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

Topic: NIMCET 2016

8

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

9

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

10

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