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**Ques 31: Which one is a vector quantity?(a) Time (b) Temperature(c) Flux density (d) Magnetic field intensity**

Option (d) is correct.

âˆ´ Angle between

Option (b) is correct.

Let Q

Thus, Eq. (i) takes the form

P

or 2PQcos Î¸ = 0

or cosÎ¸ = 0

or Î¸ = 90Â°

âˆ´ Angle between

âˆ´

or

or P

or 2PR cos Ï† = Q

or 2PR cos Ï† = - R

or 2P cos Ï† = - R

or 2P cos Ï† = - P

or

âˆ´ Ï† = 135Â°

âˆ´ Angle between

Option (a) is correct.**Ques 35: The angle between ****(a) 90Â° **

**(b) between 0Â° and 180Â°(c) 180Â° only (d) None of these**

Angle Ï† between

This implies that angle between and will vary from 0 to Ï€.

Option (b) is correct

for R = P = Q

P

or

or Î¸ = 120Â°

Option (b) is correct.

= 25 J

Option (b) is correct.

Other value is - ive.

Option (d) is correct.

cos

âˆ´ Option (a) is correct.

âˆ´

Option (b) is correct.

âˆ´ Vectors will be coplanar if their scalar triple product is zero i.e.,

or 65 - 4n + 7 = 0

or n = 18

Option (a) is correct.**Ques 42: Which one of the following statement is false? ****(a) A vector has only magnitude, whereas a scalar has both magnitude and direction ****(b) Distance is a scalar quantity but displacement is a vector quantity ****(c) Momentum, force, torque are vector quantities ****(d) Mass, speed and energy are scalar quantities****Ans: **A vector has only magnitude, whereas a scalar has both magnitude and direction**Ques 43: are two vectors then the value of ****Ans:****Sol:**

Option (a) is correct.**Ques 44: The angle between the two vectors ****(a) 60Â° ****(b) 0Â° ****(c) 90Â° ****(d) None of these****Ans:** 90Â°**Sol:**

= 0

â‡’ Î¸ = 90Â°

Option (c) is correct.**Ques 45: Maximum and minimum values of the resultant of two forces acting at a point are 7 N and 3 N respectively. The smaller force will be equal to ****(a) 5 N ****(b) 4 N ****(c) 2 N ****(d) 1 N****Ans: **2 N**Sol: **A + B = 7

A - B = 3

âˆ´ B = 2 N

Option (c) is correct.**Ques 46: The component of vector along the vector****(a) 5/âˆš2****(b) 10/âˆš2****(c) 5 âˆš2****(d) 5****Ans: **5/âˆš2**Sol:** Angle between

and

Component of

Option (a) is correct.**Ques 47: The resultant of two forces 3P and 2P is R. If the first force is doubled then the resultant is also doubled. The angle between the two forces is ****(a) 60Â° ****(b) 120Â° ****(c) 70Â° ****(d) 180Â°****Ans: **120Â°**Sol:**

Option (b) is correct.**Ques 48: The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is ****(a) 120Â° ****(b) 60Â° ****(c) 90Â° ****(d) 150Â°****Ans: **120Â°**Sol: **

As Î¸ = 90Â°, tan Î± = âˆž

âˆ´ P + Q cos Î± = 0

i.e.,

âˆ´ Î± = 120Â°

Option (a) is correct.**Ques 49: Three vectors satisfy the relation is parallel to****Ans:****Sol: **

â‡’ â€¦(i)

â‡’ â€¦(ii)

From Eq. (i) and Eq. (ii), we conclude that is perpendicular to the plane containing

This implies that is perpendicular to

Option (c) is correct.**Ques 50: The sum of two forces at a point is 16 N. If their resultant is normal to the smaller force and has a magnitude of 8 N. Then two forces are ****(a) 6N, 10N ****(b) 8 N, 8 N ****(c) 4 N, 12N ****(d) 2 N, 14N****Ans: **6N, 10N**Sol: ** P^{2} + Q^{2} + 2PQ cos Î± = R^{2}

or P^{2} + Q^{2} + 2PQ cos Î± = 8^{2}

or P^{2} + Q^{2} + 2PQ + 2PQ cos Î± - 2PQ = 64

or (P + Q)^{2} + 2 PQ (cos Î± - 1) = 64

or (16)^{2} + 2 PQ (cos Î± - 1) = 64

or 2 PQ (cos Î± - 1) = - 192

or PQ cos Î± - PQ = - 96 â€¦(i)

(as Î¸ = 90Â°)

âˆ´ P + Q cos Î± = 0

Qcos Î± = -P â€¦(ii)

Using Eq. (ii) and Eq. (i),

P (- P) - PQ = - 96

or - P (P + Q) = - 96

or

P = + 6 N

âˆ´ Q = 10 N

Option (a) is correct.**Ques 51: then the value of ****(a) (A ^{2} + B^{2} + AB)^{1/2}**

(c) (A + B)

Sol:

â‡’ tan Î¸ = âˆš3

â‡’ Î¸ = 60Â°

= A

= A

(a) BA

(b) BA

(c) BA

(d) zero

âˆ´

or

Option (d) is correct.

âˆ´

Option (c) is correct.

Option (c) is correct.

A

or A

or

or A

or A

â‡’ A = B

Option (a) is correct.

__Match the Columns__

**Ques 1: Column-I shows some vector equations. Match coloumn I with the value of angle between A and B given in column II.**

Column I | Column II |

(p) zero | |

(q) Ï€/2 | |

(r) Ï€/4 | |

(s) 3Ï€/4 |

**Sol:**

or

or

â‡’

Thus, (a) â†’ (r) (s).

(given)

or

or

or sin Î¸ = - sin Î¸

or 2 sin Î¸ = 0

â‡’ Î¸ = 0 rad

or

or

â‡’

or

or

or

or

â‡’

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