DPP - Daily Practice Problems

Name : Date :

Start Time : End Time :

SYLLABUS : Vectors
05
Max. Marks : 116 Time : 60 min.
GENERAL INSTRUCTIONS
• The Daily Practice Problem Sheet contains 29 MCQ's. For each question only one option is correct. Darken the correct
circle/ bubble in the Response Grid provided on each page.
• You have to evaluate your Response Grids yourself with the help of solution booklet.
• Each correct answer will get you 4 marks and 1 mark shall be deduced for each incorrect answer. No mark will be given/
deducted if no bubble is filled. Keep a timer in front of you and stop immediately at the end of 60 min.
• The sheet follows a particular syllabus. Do not attempt the sheet before you have completed your preparation for that
syllabus. Refer syllabus sheet in the starting of the book for the syllabus of all the DPP sheets.
• After completing the sheet check your answers with the solution booklet and complete the Result Grid. Finally spend time
to analyse your performance and revise the areas which emerge out as weak in your evaluation.

DIRECTIONS (Q.1-Q.21) : There are 21 multiple choice 1

(a) zero (b) m/s 2 N-W
questions. Each question has 4 choices (a), (b), (c) and (d), out 2
of which ONLY ONE choice is correct. 1 1
Q.1 The length of second’s hand in watch is 1 cm. The change
(c) m/s2 N-E (d) m/s 2S-W
2 2
in velocity of its tip in 15 seconds is ur
ˆ ˆ
Q.3 A force F = - K ( yi + xj ) (where K is a positive constant)
p
(a) zero (b) cm/sec acts on a particle moving in the x-y plane. Starting from
30 2 the origin, the particle is taken along the positive x-axis to
p the point (a, 0) and then parallel to the y-axis to the point
p 2 ur
(c) cm/sec (d) cm/sec
30 30 (a, a). The total work done by the forces F on the particle
Q.2 A particle moves towards east with velocity 5 m/s. After is
10 seconds its direction changes towards north with same (a) – 2 Ka2 (b) 2 Ka2
(c) – Ka 2 (d) Ka2
velocity. The average acceleration of the particle is

RESPONSE GRID 1. 2. 3.
Space for Rough Work
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Q.4 A metal sphere is hung by a string fixed to a wall. The
A
sphere is pushed away from the wall by a stick. The forces
acting on the sphere are shown in the second diagram. 30°
Which of the following statements is wrong? 30 N
O

W
q

q (a) 30 3,30 (b) 30 3, 60

(c) 60 3,30 (d) None of these
P
W
Q.9 A boat is moving with a velocity 3iˆ + 4 ˆj with respect to
r r r
(a) P = W tan q (b) T + P + W = 0 ground. The water in the river is moving with a velocity
(c) T 2 = P 2 + W 2 (d) T = P + W – 3iˆ - 4 ˆj with respect to ground. The relative velocity of
Q.5 The speed of a boat is 5km/h in still water. It crosses a
the boat with respect to water is
river of width 1 km along the shortest possible path in 15
minutes. The velocity of the river water is (a) 8 ˆj (b) -6iˆ - 8 ˆj (c) 6iˆ + 8 ˆj (d) 5 2 iˆ
(a) 1 km/h (b) 3 km/h Q.10 A person aiming to reach the exactly opposite point on the
(c) 4 km/h (d) 5 km/h bank of a stream is swimming with a speed of 0.5 m/s at an
Q.6 A man crosses a 320 m wide river perpendicular to the angle of 120° with the direction of flow of water. The speed
current in 4 minutes. If in still water he can swim with a of water in the stream is
speed 5/3 times that of the current, then the speed of the (a) 1 m/s (b) 0.5 m/s (c) 0.25 m/s(d) 0.433 m/s
current in m/min is Q.11 A man can swim with velocity v relative to water. He has to
(a) 30 (b) 40 cross a river of width d flowing with a velocity u (u > v).
(c) 50 (d) 60 The distance through which he is carried down stream by
Q.7 P, Q and R are three coplanar forces acting at a point and the river is x. Which of the following statements is correct?
are in equilibrium. Given P = 1.9318 kg wt, sin q1 = 0.9659,
the value of R is (in kg wt) (a) If he crosses the river in minimum time x = du
v
150°
P Q
(b) x cannot be less than du
v
q2 q1
(c) For x to be minimum he has to swim in a direction making
R
ο Êvˆ
an angle of , sin,1 ÁÁ ˜˜˜ with the direction of the
2 ÁË u ¯
(a) 0.9659 (b) 2 flow of water.
1 (d) x will be maximum if he swims in a direction making
(c) 1 (d) p
2 ævö
an angle of + sin -1 ç ÷ with direction of the flow of
Q.8 As shown in figure the tension in the horizontal cord is 30 2 èuø
N. The weight W and tension in the string OA in newton are water.

RESPONSE 4. 5. 6. 7. 8.
GRID 9. 10. 11.

Space for Rough Work

DPP/ P 05 3
Q.12 A 120 m long train is moving towards west with a speed of r r
Q.20 Two forces F1 = 5iˆ + 10 ˆj - 20kˆ and F2 = 10iˆ - 5 ˆj - 15kˆ
10 m/s. A bird flying towards east with a speed of 5 m/s
r r
crosses the train. The time taken by the bird to cross the act on a single point. The angle between F1 and F2 is nearly
train will be
(a) 30° (b) 45°
(a) 16 sec (b) 12 sec (c) 10 sec (d) 8 sec
ur (c) 60° (d) 90°
Q.13 What is the value of linear velocity, if w = 3$i - 4 $j + k$ and Q.21 With respect to a rectangular cartesian coordinate system,
r three vectors are expressed as
r = 5i$ - 6 $j + 6k$ r
r
(a) 6$i - 2 $j + 3k$ (b) 6$i - 2 $j + 8k$ a = 4iˆ - ˆj, b = -3iˆ + 2 ˆj , and cr = - kˆ

(c) 4$i - 13 $j + 6k$ (d) -18$i - 13 $j + 2k$ where iˆ, ˆj , kˆ are unit vectors, along the X, Y and Z-axis
ur ur ur ur ur ur
Q.14 If | A ´ B | = 3 A . B, then the value of | A + B | is respectively. The unit vectors r̂ along the direction of sum
1/ 2 of these vector is
æ 2 2 AB ö
(a) çè A + B + ÷ (b) A + B 1 ˆ ˆ ˆ 1 ˆ ˆ ˆ
3ø (a) rˆ = (i + j - k ) (b) rˆ = (i + j - k )
3 2
(c) ( A2 + B 2 + 3 AB )1/ 2 (d) ( A2 + B 2 + AB )1/ 2 1 1 ˆ ˆ ˆ
ur (c) rˆ = (iˆ - ˆj + kˆ) (d) rˆ = (i + j + k )
Q.15 Find the torque of a force F = -3$i + $j + 5k$ acting at a point 3 2
r
r = 7$i + 3 $j + k$ DIRECTIONS (Q.22-Q.24) : In the following questions,
(a) 14$i - 38 $j + 16k$ (b) 4$i + 4 $j + 6k$ more than one of the answers given are correct. Select
the correct answers and mark it according to the following
(c) 21i$ + 4 $j + 4k$ (d) -14$i + 34 $j - 16k$ codes:
ur ur ur ur ur ur
Q.16 If | A ´ B | = | A . B |, then angle between A and B will be Codes :
(a) 30° (b) 45° (c) 60° (d) 90° (a) 1, 2 and 3 are correct (b) 1 and 2 are correct
ur ur (c) 2 and 4 are correct (d) 1 and 3 are correct
Q.17 The vector P = ai + a j + 3k and Q = ai$ - 2 $j - k$ are
$ $ $
Q.22 A boy walks uniformally along the sides of a rectangular
perpendicular to each other. The positive value of a is
(a) 3 (b) 4 park of size 400 m × 300 m, starting from one corner to
(c) 9 (d) 13 the other corner diagonally opposite. Which of the
following statements is correct?
Q.18 A particle moves from position 3$i + 2 $j - 6k$ to (1) He has travelled a distance of 700 m
14$i + 13 $j + 9k$ due to a uniform force of (4$i + $j + 3k$ ) N . (2) His displacement is 500 m
If the displacement in metres then work done will be (3) His velocity is not uniform throughout the walk
(a) 100 J (b) 200 J (c) 300 J d) 250 J (4) His displacement is 700 m
ur ur r r
Q.19 The three vectors A = 3iˆ - 2 ˆj + kˆ, B = iˆ - 3 ˆj + 5kˆ and Q.23 The three vectors A = 3iˆ - 2jˆ - k, ˆ B = iˆ - 3jˆ + 5kˆ and
ur r
C = 2iˆ + ˆj - 4kˆ form C = 2iˆ – ˆj - 4kˆ does not form
(a) an equilateral triangle (b) isosceles triangle (1) an equilateral triangle (2) isosceles triangle
(c) a right angled triangle (d) no triangle (3) a right angled triangle (4) no triangle

12. 13. 14. 15. 16.

RESPONSE 17. 18. 19. 20. 21.
GRID
22. 23.

Space for Rough Work

 EBD_7
4 DPP/ P 05
r r r r
Q.24 If for two vectors A and B, A ¥ B < 0, which of the following DIRECTIONS (Q.28-Q.29) : Each of these questions contains two
is not correct? statements: Statement-1 (Assertion) and Statement-2 (Reason).
(1) They are perpendicular to each other Each of these questions has four alternative choices, only one of
(2) They act at an angle of 60° which is the correct answer. You have to select the correct choice.
(3) They act at an angle of 30°
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a
(4) They are parallel to each other
correct explanation for Statement-1.
DIRECTIONS (Q.25-Q.27) : Read the passage given below (b) Statement-1 is True, Statement-2 is True; Statement-2 is
and answer the questions that follows : NOT a correct explanation for Statement-1.
r r
A = 2iˆ + ˆj + kˆ and B = iˆ + ˆj + kˆ are two vectors. (c) Statement -1 is False, Statement-2 is True.
r (d) Statement -1 is True, Statement-2 is False.
Q.25 The unit vector perpendicular to A is
r r r r r
- ˆj + kˆ - ˆj - kˆ iˆ + kˆ iˆ - kˆ Q.28 Statement-1:If A + B = A - B , then angle between A
(a) (b) (c) (d)
2 2 2 2 r
r and B is 90°
Q.26 The unit vector parallel to A is r r r r
2iˆ - ˆj + 3kˆ 2iˆ + ˆj + kˆ Statement-2 : A + B = B + A
(a) (b) Q.29 Statement-1 : The sum of two vectors can be zero.
2 6
ˆ ˆ
2i - j - k ˆ 2i + ˆj - 2kˆ
ˆ Statement-2 : Two vectors cancel each other, when they
(c) (d) are equal and opposite.
5 6
r
Q.27 The unit vector perpendicular to B is
- ˆj - kˆ - ˆj + kˆ iˆ - kˆ iˆ + kˆ
(a) (b) (c) (d)
3 2 3 2

RESPONSE 24. 25. 26. 27. 28.

GRID 29.

DAILY PRACTICE PROBLEM SHEET 5 - PHYSICS

Total Questions 29 Total Marks 116
Attempted Correct
Incorrect N et Score
Cut-off Score 30 Qualifying Score 44
Success Gap = Net Score – Qualifying Score
Net Score = (Correct × 4) – (Incorrect × 1)

Space for Rough Work