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NIMCET Previous Year Questions (PYQs)

NIMCET Vector PYQ


NIMCET PYQ 2023
If a=ˆiˆk, b=xˆi+ˆj+(1x)ˆk and c=yˆi+xˆj+(1+xy)ˆk, then [abc] depends on





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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

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NIMCET PYQ 2023
If a,b are unit vectors such that 2a+b=3 then which of the following statement is true?





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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

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NIMCET PYQ 2023
θ=cos1(310) is the angle between a=ˆi2xˆj+2yˆk & b=xˆi+ˆj+yˆk then possible values of (x,y) that lie on the locus





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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

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NIMCET PYQ 2023
If a vector having magnitude of 5 units, makes equal angle with each of the three mutually perpendicular axes,then the sum of the magnitude of the projections on each of the axis is





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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

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NIMCET PYQ 2019
The value of non-zero scalars α and  β such that for all vectors  and  such that  is





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NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

Solution


NIMCET PYQ 2019

A force of 78 grams acts at the point (2,3,5). The direction ratios of the line of action being 2,2,1 . The magnitude of its moment about the line joining the origin to the point (12,3,4) is






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NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

Solution


NIMCET PYQ 2019
The position vectors of the vertices





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NIMCET Previous Year PYQNIMCET NIMCET 2019 PYQ

Solution



NIMCET PYQ 2022
Let a,b,c be distinct non-negative numbers. If the vectors aˆi+aˆj+cˆk , ˆi+ˆk and cˆi+cˆj+bˆk lie in a plane, then c is





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

Solution

a=aˆi+aˆj+cˆk,b=ˆi+ˆk&c=cˆi+cˆj+bˆk are coplanar.

|aac101ccb|=0

acab+ac+c2=0

c2=ab

NIMCET PYQ 2024
The value of m for which volume of the parallelepiped is 4 cubic units whose three edges are represented by a = mi + j + k, b = i – j + k, c = i + 2j –k is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2024
The number of distinct real values of λ for which the vectors λ2ˆi+ˆj+ˆk,ˆi+λ2ˆj+j and ˆi+ˆj+λ2ˆk are coplanar is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
If the volume of the parallelepiped whose adjacent edges are a=2ˆi+3ˆj+4ˆk, b=ˆi+αˆj+2ˆk and c=ˆi+2ˆj+αˆk is 15, then α is equal to





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
If F|= 40N (Newtons), |D| = 3m, and θ=60, then the work done by F acting
from P to Q is





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
Let a=2ˆi+2ˆj+ˆk and b be another vector such that a.b=14 and a×b=3ˆi+ˆj8ˆk the vector b =





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
A man starts at the origin O and walks a distance of 3 units in the north- east direction and then walks a distance of 4 units in the north-west direction to reach the point P. then OP is equal to





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
If a=λˆi+ˆj2ˆk , b=ˆi+λˆj2ˆk and c=ˆi+ˆj+ˆk and [abc]=7, then the values of the λ are





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2024
How much work does it take to slide a crate for a distance of 25m along a loading dock by pulling on it with a 180 N force where the dock is at an angle of 45° from the horizontal?





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NIMCET Previous Year PYQNIMCET NIMCET 2024 PYQ

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NIMCET PYQ 2022
If (a×b)×c=a×(b×c), then





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NIMCET Previous Year PYQNIMCET NIMCET 2022 PYQ

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NIMCET PYQ 2021
Let a=2ˆi+ˆj+2ˆk , b=ˆiˆj+2ˆk and c=ˆi+ˆj2ˆk are are three vectors. Then, a vector in the plane of a and c whose projection on b is of magnitude 16 is





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

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NIMCET PYQ 2021
If the position vector of A and B relative to O be ˆi4ˆj+3ˆk and ˆi+2ˆjˆk respectively, then the median through O of ΔABC is:





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

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NIMCET PYQ 2021
The area of the triangle formed by the vertices whose position vectors are 3ˆi+ˆj5ˆi+2ˆj+ˆk , ˆi2ˆj+3ˆk is





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

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NIMCET PYQ 2021
If the vectors aˆi+ˆj+ˆk,ˆi+bˆj+ˆk,ˆi+ˆj+cˆk(a,b,c1) are coplanar, then 11a+11b+11c=





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

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NIMCET PYQ 2017
The direction cosines of the vector a = (- 2i + j – 5k) are





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution


NIMCET PYQ 2021
Let a=ˆi+ˆj and  b=2ˆiˆk, the point of intersection of the lines r×a=b×a  and  r×b=a×b  is





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

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NIMCET PYQ 2017
If ab and c are vectors such that a+b+c = 0 and |a| =7, b=5,  |c| = 3, then the angle between the vectors b and c





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution


NIMCET PYQ 2017
If  ,  and 
 , (a ≠ b ≠ c ≠ 1) are co-planar, then the value of  is





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution


NIMCET PYQ 2017
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 between a and c is





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution


NIMCET PYQ 2017
Let  and  be three vector such that || = 2, || = 3, || = 5 and ++ = 0. The value of .+.+. is





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

Solution


NIMCET PYQ 2018
If , and  are unit vectors, then  does not exceeds





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

Solution


NIMCET PYQ 2017
If = (i + 2j - 3k) and =(3i -j + 2k), then the angle between ( + ) and ( - )





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

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NIMCET PYQ 2018
The vector  lies in the plane of the vector  and  and bisects the angle between  and . Then which of the following gives possible values of  and ?





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

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NIMCET PYQ 2018
A bird is flying in a straight line with velocity vector 10i+6j+k, measured in km/hr. If the starting point is (1,2,3), how much time does it to take to reach a point in space that is 13m high from the ground?





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NIMCET Previous Year PYQNIMCET NIMCET 2018 PYQ

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NIMCET PYQ 2021
Angle between a and  b is 120. If |b|=2|a| and the vectors , a+xb ,   ab are at right angle, then x=





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

Solution


NIMCET PYQ 2021
If e1=(1,1,1) and e2=(1,1,1) and a and b  and two vectors such that e2=a+2b , then angle between a and b





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NIMCET Previous Year PYQNIMCET NIMCET 2021 PYQ

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NIMCET PYQ 2017
A cube is made up of 125 one cm. square cubes placed on a table. How many squares are visible only on three sides?





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NIMCET Previous Year PYQNIMCET NIMCET 2017 PYQ

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NIMCET PYQ 2020
If  are three non-coplanar vectors, then 





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

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NIMCET PYQ 2020
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 values of θ for which the resultant force is equal to 





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

Solution


NIMCET PYQ 2020
If  are four vectors such that is collinear with  and is collinear with  then  =





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

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NIMCET PYQ 2020
Forces of magnitude 5, 3, 1 units act in the directions 6i + 2j + 3k, 3i - 2j + 6k, 2i - 3j - 6k respectively on a particle which is displaced from the point (2, −1, −3) to (5, −1, 1). The total work done by the force is





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

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NIMCET PYQ 2020
The position vectors of points A and B are  and  . Then the position vector of point p dividing AB in the ratio m : n is





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

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NIMCET PYQ 2020
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 is collinear with a , then | a + 2b + 6c | will be equal to





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

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NIMCET PYQ 2020
Vertices of the vectors i - 2j + 2k , 2i + j - k and 3i - j + 2k form a triangle. This triangle is





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

Solution


NIMCET PYQ 2020
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 =





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NIMCET Previous Year PYQNIMCET NIMCET 2020 PYQ

Solution


NIMCET PYQ 2023
If a and b are vectors in space, given by a=ˆi2ˆj5 and b=2ˆi+ˆj+3ˆk14, then the value of(2\vec{a} + \vec{b}).[(\vec{a} × \vec{b}) × (\vec{a} – 2\vec{b})] is





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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

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NIMCET PYQ 2023
Let \vec{A} = 2\hat{i} + \hat{j} – 2\hat{k} and \vec{B} = \hat{i} + \hat{j}, If \vec{C} is a vector such that |\vec{C} – \vec{A}| = 3 and the angle between A × B and C is {30^{\circ}}, then |(\vec{A} × \vec{B}) × \vec{C}| = 3 then the value of \vec{A}.\vec{C} is equal to





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NIMCET Previous Year PYQNIMCET NIMCET 2023 PYQ

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