If  ,  and 

 , (a ≠ b ≠ c ≠ 1) are co-planar, then the value of  is

1

If $\vec{a}$, $\vec{b}$ and $\vec{c}$ are vectors such that $\vec{a}$+$\vec{b}$+$\vec{c}$…

Topic: NIMCET 2017

2

The equation of the hyperbola with centre at the region, length of the transverse axis is 6 and one focus (0, 4) is

Topic: NIMCET 2017

3

The direction cosines of the vector a = (- 2i + j – 5k) are

Topic: NIMCET 2017

4

If the graph of y = (x – 2)2 – 3 is shifted by 5 units up along y-axis and 2 units to the right along the x-axis, then …

Topic: NIMCET 2017

5

The equation of the tangent line to the curve y = 2x sin x at the point (π/2, π), is

Topic: NIMCET 2017

6

If x2 + 3xy + 2y2 – x – 4y – 6 = 0 represents a pair of straight lines, their point of intersection is

Topic: NIMCET 2017

7

In a triangle ABC, let angle C = π/2. If R is the inradius and R is circumradius of the triangle ABC, then 2(r + R) equ…

Topic: NIMCET 2017

8

If the lines x + (a – 1)y + 1 = 0 and 2x + a2y – 1 = 0 are perpendicular, then the condition satisfies by a is

Topic: NIMCET 2017

9

If non-zero numbers a, b, c are in A.P., then the straight line ax + by + c = 0 always passes through a fixed point, th…

Topic: NIMCET 2017

10

Express (cos 5x – cos7x) as a product of sines or cosines or sines and cosines,

Topic: NIMCET 2017

1

Let a, b and c be three vectors having magnitudes 1, 1 and 2 respectively. If a x (a x c) - b = 0, then the acute angle…

Topic: NIMCET 2017

2

Let ,  and  be three vector such that || = 2, || = 3, || = 5 and ++ = 0. The value o…

Topic: NIMCET 2017

3

If = (i + 2j - 3k) and =(3i -j + 2k), then the angle between ( + ) and ( - )

Topic: NIMCET 2017

4

The number of elements in the power set P(S) of the set S = {2, (1, 4)} is

Topic: NIMCET 2017

5

If (1 - x + x2 )n = a + a1x + a2x2 + ... + a2nx2n , then a0 + a2 + a4 + ... + a2n is

Topic: NIMCET 2017

6

m distinct animals of a circus have to be placed in m cages, one is each cage. There are n small cages and p large anim…

Topic: NIMCET 2017

7

Let A and B two sets containing four and two elements respectively. The number of subsets of the A × B, each having at …

Topic: NIMCET 2017

8

The slope of the function \[ f(x) = \begin{cases} x^2 \sin\!\left(\dfrac{1}{x}\right), & \text{if } x \ne 0, \…

Topic: NIMCET 2017

9

What is the largest area of an isosceles triangle with two edges of length 3?

Topic: NIMCET 2017

10

The value of $\int_{0}^{\pi}x^3 \sin x dx$

Topic: NIMCET 2017