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

1

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

2

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

Topic: NIMCET 2017

3

The value of sin36o is

Topic: NIMCET 2017

4

If cosθ = 4/5 and cosϕ = 12/13, θ and ϕ both in the fourth quadrant, the value of cos( θ + ϕ )is

Topic: NIMCET 2017

5

Find the principal value of  is

Topic: NIMCET 2017

6

If tan x = - 3/4 and 3π/2 < x < 2π, then the value of sin2x is

Topic: NIMCET 2017

7

The value of A that satisfies the equation asinA + bcosA = c is equal to

Topic: NIMCET 2017

8

If  +  =  , then 

Topic: NIMCET 2017

9

Three positive number whose sum is 21 are in arithmetic progression. If 2, 2, 14 are added to them respectively then re…

Topic: NIMCET 2017

10

The equation $(x-a)^3+(x-b)^3+(x-c)^3=0$ has

Topic: NIMCET 2017

1

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

2

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

Topic: NIMCET 2017

3

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

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

Topic: NIMCET 2017

6

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

7

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

Topic: NIMCET 2017

8

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

Topic: NIMCET 2017

9

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

10

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

Topic: NIMCET 2017