** Directions :** Each of these questions contain two statements, Assertion and Reason. Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes (a), (b), (c) and (d) given below.

(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.

(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion

(c) Assertion is correct, reason is incorrect

(d) Assertion is incorrect, reason is correct.

**Q.1. Assertion :** If dot product and cross product of **A** and **B** are zero, it implies that one of the vector **A** and **B** must be a null vector**Reason : **Null vector is a vector with zero magnitude.

## Answer

Answer: (c)**Q.2. Assertion : **The scalar product of two vectors can be zero.**Reason : **If two vectors are perpendicular to each other, their scalar product will be zero.

## Answer

Answer: (b)**Q.3. Assertion: **A physical quantity cannot be called as a vector if its magnitude is zero.**Reason: **A vector has both magnitude and direction.

## Answer

Answer: (d) If a vector quantity has zero magnitude then it is called a null vector. That quantity may have some direction even if its magnitude is zero.**Q.4. Assertion : **Minimum number of non-equal vectors in a plane required to give zero resultant is three.**Reason : **If sum of vectors **A+B+C=0** , then they must lie in one plane.

## Answer

Answer: (c)**Q.5. Assertion : **If ** A.B**=

**, then**

*B.C***may not always be equal to C.**

*A***Reason :**The dot product of two vectors involves cosine of the angle between the two vectors.

## Answer

Answer: (b)**Q.6. Assertion :** If a body of mass m is projected upwards with a speed V making an angle with the vertical, than the change in the momentum of the body along X–axis is zero.**Reason : **Mass of the body remains constant along X–axis

## Answer

Answer: (b) When a body is projected up making an angle the velocity component along-axis remains constant.Therefore, Momentum along x-axis is constant. Along horizontal, mass and velocity both are constant.

**Q.7. Assertion :** The magnitude of velocity of two boats relative to river is same. Both boats start simultaneously from same point on one bank may reach opposite bank simultaneously moving along different paths.**Reason : **For boats to cross the river in same time. The component of their velocity relative to river in direction normal to flow should be same.

## Answer

Answer: (b)**Q.8. Assertion : **Two balls of different masses are thrown vertically upward with same speed. They will pass through their point of projection in the downward direction with the same speed.**Reason : **The maximum height and downward velocity attained at the point of projection are independent of the mass of the ball.

## Answer

Answer: (b)**Q.9. Assertion : τ=r x F** and

*τ=F x r***Reason :**Cross product of vectors is commutative.

## Answer

Answer: (d)**Q.10. Assertion : **If there were no gravitational force, the path of the projected body always be a straight line.**Reason : **Gravitational force makes the path of projected body always parabolic.