Step 1: Vector Components. The vector represents a 3-dimensional vector with components along the , , and directions. The angle made by the vector with the y-axis is the angle between the vector and the y-axis unit vector . Step 2: Using the dot product formula. The cosine of the angle between the vector and the y-axis is given by:
Since is a unit vector, . The dot product is simply the coefficient of , which is 2. The magnitude of is:
Thus, the cosine of the angle is:
So, the angle is . Step 3: Conclusion. The correct answer is , which is option (D).
02
PYQ 2020
medium
physicsID: mht-cet-
A body performing simple harmonic motion has potential energy at displacement . Its potential energy is at displacement . The potential energy at displacement is
1
2
3
4
Official Solution
Correct Option:
(4)
Step 1: Potential energy in SHM. Potential energy is proportional to the square of displacement: Step 2: Expressing energies.
Step 3: Energy at displacement .
Step 4: Conclusion. The correct expression is .
03
PYQ 2020
medium
physicsID: mht-cet-
If and are perpendicular to each other, then what will be the value of ?
1
0.5
2
-0.5
3
1
4
-1
Official Solution
Correct Option:
(1)
Step 1: Using the condition for perpendicular vectors. For two vectors and to be perpendicular, their dot product must be zero: Step 2: Finding the dot product. The dot product of and is: Step 3: Solving for . Simplifying: Thus, the correct answer is (A) 0.5.
04
PYQ 2020
medium
physicsID: mht-cet-
The displacement of the particle at a distance from the origin is given by , where is the angular velocity and is the linear velocity. The dimensions of are
1
2
3
4
Official Solution
Correct Option:
(1)
Step 1: Argument of sine function. The argument of a trigonometric function must be dimensionless. Step 2: Dimensions of .
Step 3: Role of constant . Since must have same dimensions,
Step 4: Conclusion.
05
PYQ 2020
medium
physicsID: mht-cet-
The given circuit is a balanced Wheatstone’s bridge. The value of resistance is
1
2
3
4
Official Solution
Correct Option:
(1)
Step 1: Condition for balanced Wheatstone bridge. For a balanced Wheatstone bridge,
Step 2: Substituting values from the circuit. From the given figure,
Step 3: Solving for .
Step 4: Conclusion. The value of resistance is .
06
PYQ 2020
medium
physicsID: mht-cet-
In meter-bridge experiment a resistance of is connected in left gap and unknown resistance is connected in right gap. The null point is obtained at from left end. If unknown resistance is replaced by , the null point is obtained at . The unknown resistance is
1
2
3
4
Official Solution
Correct Option:
(3)
Step 1: Balance condition for meter bridge.
Step 2: Second balance condition. When resistance becomes , Step 3: Solving the equations. From both equations, solving gives Step 4: Conclusion. The unknown resistance is .
07
PYQ 2020
medium
physicsID: mht-cet-
A fixed number of spherical drops of a liquid of radius coalesce to form a large drop of radius and volume . If is the surface tension, then the energy
1
is neither released nor absorbed.
2
is released.
3
is released.
4
is absorbed.
Official Solution
Correct Option:
(2)
Step 1: Surface energy of a spherical drop. Surface energy of a drop is:
Step 2: Number of small drops. Let the number of drops be . Using volume conservation:
Step 3: Initial surface energy.
Step 4: Final surface energy.
Step 5: Energy released. Using :
Step 6: Conclusion. Energy is released.
08
PYQ 2020
medium
physicsID: mht-cet-
For an ideal gas, if the ratio of molar specific heats , then the specific heat at constant pressure , specific heat at constant volume and corresponding molecule are respectively
1
monoatomic.
2
polyatomic.
3
non-rigid diatomic.
4
rigid diatomic.
Official Solution
Correct Option:
(4)
Step 1: Use the definition of .
Step 2: Substitute given value.
Step 3: Identify type of gas. For a rigid diatomic gas:
Step 4: Verify ratio.
Step 5: Conclusion. The gas is rigid diatomic with and .
09
PYQ 2020
medium
physicsID: mht-cet-
Which one of the following is a unit vector?
1
2
3
4
Official Solution
Correct Option:
(1)
Step 1: Definition of a Unit Vector. A unit vector is a vector that has a magnitude of 1. To verify if a given vector is a unit vector, we compute its magnitude and check if it equals 1. The magnitude of the vector is:
Thus, the vector is a unit vector. Step 2: Final Answer. Thus, the unit vector is .
10
PYQ 2020
medium
physicsID: mht-cet-
A vector has components along X and Y axis having magnitude 2 units and 4 units respectively. A vector along negative X-axis, has magnitude 6 units. Then vector is:
1
2
3
4
Official Solution
Correct Option:
(3)
Step 1: Vector Components. The vector has components . The vector is along the negative X-axis, so its components are . To find , subtract the components:
Thus, the resulting vector is . Step 2: Final Answer. Thus, .
11
PYQ 2020
medium
physicsID: mht-cet-
A vector is a unit vector along the positive direction of x-axis and is of magnitude 4. If the vector product of and is zero, then is
1
2
3
4
Official Solution
Correct Option:
(3)
Step 1: Understanding the vector product. The vector product of two vectors and is zero when the vectors are parallel. That is, and must be parallel. Step 2: Analyzing the given vectors. The vector is a unit vector along the positive x-axis, so . The vector must have components in both and -directions to be parallel to , and its magnitude must be 4. The correct vector that satisfies this condition is: Step 3: Conclusion. Thus, is , corresponding to option (C).
12
PYQ 2020
medium
physicsID: mht-cet-
Two vectors and have equal magnitudes. If and , then the angle between and is
1
2
3
4
Official Solution
Correct Option:
(1)
Step 1: Using the law of cosines. The magnitudes of the vectors and are given, so we can use the law of cosines. For , we have: where is the angle between the vectors. Since , this simplifies to: Similarly, for , we have: Step 2: Solving for . From the two equations, we solve for and find: Step 3: Conclusion. Thus, the angle between and is , corresponding to option (A).
13
PYQ 2020
medium
physicsID: mht-cet-
Forces and have resultant whose magnitude is . makes an angle with as well as . The magnitude of is
1
2
3
4
Official Solution
Correct Option:
(3)
Step 1: Use parallelogram law of forces. If resultant makes equal angles with and , then . Step 2: Use relation for resultant of two equal forces. Step 3: Substitute given values. Step 4: Simplify.
14
PYQ 2020
medium
physicsID: mht-cet-
For three non-zero vectors , and , and , then the angle between and will be
1
2
3
4
Official Solution
Correct Option:
(1)
Step 1: Use vector identity. Step 2: Compare with given condition. Given: Step 3: Substitute and simplify. Step 4: Find angle.
15
PYQ 2020
medium
physicsID: mht-cet-
Three vectors , and are such that , then is parallel to
1
2
3
4
Official Solution
Correct Option:
(2)
Step 1: Interpret dot product conditions. Given and , hence is perpendicular to both and .
Step 2: Direction perpendicular to both vectors. The vector perpendicular to both and is given by their cross product .
Step 3: Conclusion. Therefore, is parallel to .
16
PYQ 2020
medium
physicsID: mht-cet-
Let the two forces have equal magnitude . If the magnitude of the resultant is , then the angle between those two forces is}
1
2
3
4
Official Solution
Correct Option:
(2)
Step 1: Resultant of two equal forces.
Step 2: Substituting given resultant.
Step 3: Solving for .
Step 4: Conclusion.
17
PYQ 2020
medium
physicsID: mht-cet-
The extension in a wire obeying Hooke’s law is . The speed of sound in the stretched wire is . If the extension in the wire is increased to , then the speed of sound in the wire is
1
2
3
4
Official Solution
Correct Option:
(3)
Step 1: Formula for the speed of sound in a stretched wire. The speed of sound in a wire depends on the tension in the wire and the mass per unit length. The relationship is given by:
where is the tension and is the mass per unit length. Step 2: Relationship between extension and tension. Since the tension is directly proportional to the extension , if the extension is increased to , the tension will also increase by a factor of 4. Therefore, the speed of sound will increase by a factor of . Step 3: Conclusion. Thus, the new speed of sound is (C) .
18
PYQ 2020
medium
physicsID: mht-cet-
The mass of the earth is 81 times the mass of the moon and the distance between their centres is . The distance from the centre of the earth where gravitational force will be zero is
1
2
3
4
Official Solution
Correct Option:
(1)
Step 1: Understanding the force equilibrium.
The point where the gravitational forces due to the earth and moon balance each other can be found using the formula:
where is the gravitational constant, and are the masses of the earth and moon, respectively, is the distance from the earth, and is the distance between the earth and the moon.
Step 2: Solving the equation.
Given that , the equation becomes:
Simplifying this yields:
Step 3: Conclusion.
The correct answer is (A) .
19
PYQ 2020
medium
physicsID: mht-cet-
A simple pendulum of length has a bob of mass . It executes S.H.M. of small amplitude . The maximum tension in the string is
1
2
3
4
Official Solution
Correct Option:
(4)
Step 1: Understanding the forces involved.
The maximum tension in the string occurs at the lowest point of the pendulum's swing, when both the gravitational force and the centripetal force act together. Step 2: Maximum tension expression.
At the lowest point, the maximum tension is:
where is the maximum velocity. For small amplitude oscillations, , so:
Step 3: Conclusion.
The maximum tension is , so the correct answer is (D).
20
PYQ 2020
medium
physicsID: mht-cet-
The magnetic susceptibility of a paramagnetic material at is . Its value at will be
1
2
3
4
Official Solution
Correct Option:
(3)
Step 1: Curie’s Law.
The magnetic susceptibility of a paramagnetic material is inversely proportional to the temperature, according to Curie's law:
where is the Curie constant and is the absolute temperature. Step 2: Applying Curie’s law.
Using the values at and , the temperature in Kelvin is:
Thus, the ratio of the magnetic susceptibility is:
Hence, . Step 3: Conclusion.
The magnetic susceptibility at is , so the correct answer is (C).
21
PYQ 2020
medium
physicsID: mht-cet-
If three vectors have equal magnitude i.e. , then the angle between and is . If , then the angle between and is , then is}
1
2
3
4
Official Solution
Correct Option:
(3)
Step 1: Case of three equal vectors. When three vectors of equal magnitude form a closed triangle, the angle between any two vectors is . Hence, .
Step 2: Given condition .} This represents equilibrium of three equal vectors. Therefore, the angle between each pair of vectors is . Hence, .
Step 3: Ratio calculation.
Step 4: Conclusion. The required ratio is .
22
PYQ 2020
medium
physicsID: mht-cet-
In a parallelogram shown below,
1
2
3
4
Official Solution
Correct Option:
(3)
Step 1: Understanding the problem. In the given parallelogram, we need to find the sum of the squares of the sides and , i.e., , using the diagonals and . Step 2: Relation between sides and diagonals. For any parallelogram, the relation between the sides , and the diagonals , is given by the following formula:
Step 3: Conclusion. Thus, the sum of the squares of the sides of the parallelogram is , which corresponds to option (C).
23
PYQ 2020
medium
physicsID: mht-cet-
For any two vectors and if , the magnitude of is (given , )
1
2
3
4
Official Solution
Correct Option:
(1)
Step 1: Using the formula for the magnitude of the sum of two vectors. The magnitude of the sum of two vectors and is given by: Step 2: Substituting the given values. We are given , so: Thus, the correct answer is (A) .
24
PYQ 2020
medium
physicsID: mht-cet-
The sum of the magnitudes of two vectors and is and magnitude of the resultant is . If the resultant vector is perpendicular to any one vector, then the magnitudes of the two vectors and are}
1
2
3
4
Official Solution
Correct Option:
(1)
Step 1: Vector addition. Let magnitudes of vectors and be and respectively. From the given information: Resultant magnitude of perpendicular vectors:
Step 2: Solving the system of equations. We now solve the system: By solving, we get and .
Step 3: Conclusion. The magnitudes of the two vectors are and .
25
PYQ 2020
medium
physicsID: mht-cet-
Resultant of two vectors and is of magnitude . If the direction of is reversed, the resultant is of magnitude . The value of is
1
2
3
4
Official Solution
Correct Option:
(2)
Step 1: Using the law of cosines. The magnitude of the resultant vector is given by the law of cosines: Similarly, when the direction of is reversed, the magnitude of the resultant is: Step 2: Adding the equations. Adding and , we get: Step 3: Conclusion. Thus, the value of is , which is option (B).
26
PYQ 2020
medium
physicsID: mht-cet-
The unit vector is perpendicular to . The value of 'b' is
1
2
3
4
Official Solution
Correct Option:
(4)
Step 1: Understanding the condition. We are told that the unit vector is perpendicular to . The condition for perpendicular vectors is that their dot product is zero.
Step 2: Dot product calculation. The dot product of and is given by: For the vectors to be perpendicular, we must have . Thus, .
Step 3: Normalizing the vector. Since the vector is a unit vector, we have: Substituting , we get: Thus, . The correct answer is .
27
PYQ 2020
medium
physicsID: mht-cet-
and are two non-zero vectors inclined at an angle . and are unit vectors along and respectively. The component of in the direction of is
1
2
3
4
Official Solution
Correct Option:
(4)
Step 1: Definition of component of a vector. The component of vector along direction of is given by the dot product of with unit vector along .
Step 2: Write mathematical expression.
Step 3: Final conclusion. Thus, the correct expression is .
28
PYQ 2020
medium
physicsID: mht-cet-
If , and form a right angled triangle, then out of the following which one is satisfied?
1
2
3
4
Official Solution
Correct Option:
(4)
Step 1: Use condition for right angled triangle. If vectors form a right angled triangle, then the square of the hypotenuse equals the sum of squares of the other two sides.
Step 2: Check vector addition.
Step 3: Verify magnitude relation. Thus the given condition is satisfied.
29
PYQ 2020
medium
physicsID: mht-cet-
Two unit vectors and are inclined to each other at an angle . If , then the value of is
1
2
2
3
1
4
Official Solution
Correct Option:
(4)
Step 1: Using the given condition. We are given that the magnitude of . Squaring both sides:
This gives:
Expanding this dot product:
Since and are unit vectors, and , so we have:
Simplifying:
Step 2: Finding the desired dot product. Now, we need to calculate . Expanding this dot product:
Simplifying the terms:
Step 3: Conclusion. Thus, the value of is , which is option (D).
30
PYQ 2020
medium
physicsID: mht-cet-
If and are perpendicular to each other, then
1
2
3
4
Official Solution
Correct Option:
(4)
Step 1: Using the perpendicularity condition. When two vectors are perpendicular, their dot product is zero. The dot product of and is given by: This implies: Step 2: Solving for the ratio. Rearranging the equation, we get: Step 3: Conclusion. Thus, the correct answer is (D), .
31
PYQ 2020
medium
physicsID: mht-cet-
A vector when added to the sum of the vectors and gives a unit vector along y-axis. The magnitude of vector is
1
2
3
4
Official Solution
Correct Option:
(2)
Step 1: Add the given vectors.
Step 2: Resultant including vector .
Step 3: Find vector .
Step 4: Find magnitude of .
Step 5: Conclusion. The magnitude of vector is .
32
PYQ 2020
medium
physicsID: mht-cet-
The angle between two forces of equal magnitude , if the magnitude of their resultant is , is
1
2
3
4
Official Solution
Correct Option:
(1)
Step 1: Write formula for resultant of two forces. For two equal forces making an angle between them, resultant is Step 2: Substitute given resultant.
Step 3: Square both sides.
Step 4: Simplify.
Step 5: Conclusion.
33
PYQ 2025
medium
physicsID: mht-cet-
Initially identical capacitors are joined in parallel and are charged to potential V. Now they are separated and joined in series. Then}
1
potential difference and total energy remain the same.
2
potential difference remains the same and energy increases n times.
3
potential difference becomes nV and energy remains the same.
4
potential difference is nV and energy increases n times.
Official Solution
Correct Option:
(3)
Step 1: Parallel Connection
Each capacitor has charge and potential . Total energy . Step 2: Series Connection
The potential differences add up: . Step 3: Energy Conservation
Since the capacitors are isolated after charging, the total work/energy stored in the electric fields remains conserved. . Final Answer: (C)
34
PYQ 2025
medium
physicsID: mht-cet-
Which of the following molecules contains maximum number of electrons in antibonding molecular orbitals?
1
Li
2
N
3
O
4
F
Official Solution
Correct Option:
(4)
Step 1: Electronic Configuration
Antibonding electrons ( ):
- (Total 6e): .
- (Total 14e): .
- (Total 16e): .
- (Total 18e): . Step 2: Conclusion
has the most electrons in antibonding orbitals. Final Answer: (D)
35
PYQ 2025
hard
physicsID: mht-cet-
If and are the vectors such that is perpendicular to , then the value of is:
1
6
2
8
3
-6
4
-8
Official Solution
Correct Option:
(2)
Given vectors:
Let
Since , their dot product is zero:
Compute the dot product:
Simplify:
Final Answer:
36
PYQ 2025
easy
physicsID: mht-cet-
If the volume of the tetrahedron, whose vertices are and , is cubic units, then the value of is:
1
3
2
-2
3
4
4
-1
Official Solution
Correct Option:
(1)
The volume of a tetrahedron formed by four vertices is given by the formula: Substituting the coordinates of the points into the above matrix: Now, calculate the determinant of the matrix and solve for . Upon solving, we find that .
37
PYQ 2025
medium
physicsID: mht-cet-
If the angle between the line and the plane is , then the value of is:
1
2
3
4
Official Solution
Correct Option:
(3)
We are given the line equation: The direction ratios for the line are: The equation of the plane is: The normal vector for the plane is: The angle between the line and the plane is given by: Given that the angle between the line and the plane is , we know: Now, substituting the values and solving the equation, we get the value of : Thus, the correct answer is .
38
PYQ 2025
easy
physicsID: mht-cet-
If cos(12/13) + sin(P), then the value of P is:
1
2
3
4
Official Solution
Correct Option:
(1)
We are given the equation: Let us denote the angles corresponding to the inverse trigonometric functions as follows: Let and , so the equation becomes: We know that: Now, we can find and using the Pythagorean identity. From , we get: Similarly, from , we get: Now, we use the sum identity for sine: Substituting the values of , , , and : Thus, . Therefore, the correct answer is:
39
PYQ 2025
medium
physicsID: mht-cet-
Approximate value of is:
1
2
3
4
Official Solution
Correct Option:
(2)
To find the approximate value of , Among the given options, the closest value to 0.515 is:
40
PYQ 2025
medium
physicsID: mht-cet-
Four particles each of mass are placed at the corners of a square of side . The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is
1
2
3
4
Official Solution
Correct Option:
(4)
Concept:
Radius of gyration:
where = moment of inertia, = radius of gyration. Step 1: Find distance of each mass from centre. For a square of side , distance of corner from centre: Step 2: Calculate moment of inertia. Each mass contributes:
For 4 masses:
Step 3: Find radius of gyration. Total mass = Step 4: Conclusion.
About Vectors - MHT-CET
Vectors is a vital chapter for MHT-CET aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.
By rigorously practicing the previous year questions associated with this chapter, you can identify high-yield topics, understand the examiner's perspective, and boost your confidence during the actual exam.
Frequently Asked Questions
Why focus on Vectors PYQs?
Analyzing PYQs for this specific chapter reveals the most frequently tested concepts and the typical complexity of questions, allowing you to tailor your study plan efficiently.
How to best use this analysis?
Review the topic breakdown to see which sub-topics within Vectors carry the most weight. Then, tackle the questions iteratively to solidify your understanding.
