If the volume of a parallelepiped whose adjacent edges are 

a = 2i + 3j + 4k,

b = i + αj + 2k

c = i + 2k + αk

is 15, then α =

1

Vertices of the vectors i - 2j + 2k , 2i + j - k and 3i - j + 2k form a triangle. This triangle is

Topic: NIMCET 2020

2

If a, b, c are three non-zero vectors with no two of which are collinear, a + 2b  is collinear with c and b + 3c i…

Topic: NIMCET 2020

3

The position vectors of points A and B are  and  . Then the position vector of point p dividing AB …

Topic: NIMCET 2020

4

Forces of magnitude 5, 3, 1 units act in the directions 6i + 2j + 3k, 3i - 2j + 6k, 2i - 3j - 6k respectively on a part…

Topic: NIMCET 2020

5

If  are four vectors such that is collinear with  and is collinear with  then &…

Topic: NIMCET 2020

6

Two forces F1 and F2 are used to pull a car, which met an accident. The angle between the two forces is θ . Find the va…

Topic: NIMCET 2020

7

If  are three non-coplanar vectors, then 

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8

Find the area bounded by the line y = 3 - x, the parabola y = x2 - 9 and 

Topic: NIMCET 2020

9

The value of  depends on the

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10

If  where n is a positive integer, then the relation between In and In-1 is

Topic: NIMCET 2020

1

Solve the equation sin2 x - sinx - 2 = 0 for for x on the interval 0 ≤ x < 2π

Topic: NIMCET 2020

2

If $\frac{tanx}{2}=\frac{tanx}{3}=\frac{tanx}{5}$ and x + y + z = π, then the value of tan2x + tan2y + tan2z is

Topic: NIMCET 2020

3

Find the value of sin 12°sin 48°sin 54°

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4

If cos x = tan y , cot y = tan z and cot z = tan x, then sinx&nb…

Topic: NIMCET 2020

5

The value of  is

Topic: NIMCET 2020

6

The value of sin 10°sin 50°sin 70° is

Topic: NIMCET 2020

7

The expression  $\frac{tanA}{1-cotA}+\frac{cotA}{1-tanA}$ can be written as 

Topic: NIMCET 2020

8

Angle of elevation of the top of the tower from 3 points (collinear) A, B and C on a road leading to the foot of the to…

Topic: NIMCET 2020

9

The area enclosed between the curves y2 = x and y = |x| is

Topic: NIMCET 2020

10

Test the continuity of the function at x = 2 $f(x)= \begin{cases} \frac{5}{2}-x & \text{ if } x<2 \\ 1 &amp…

Topic: NIMCET 2020