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Mathematical tools - 30 September 2020 Contact Number: 9667591930 / 8527521718
Mathematical tools - 30 September 2020 Contact Number: 9667591930 / 8527521718
1.

A particle moves in the XY plane and at time t is at the point whose coordinates are (t2, . Then at what instant of time, will its velocity and acceleration vectors be perpendicular to each other?
(1)  1/3 sec
(2)  2/3 sec
(3)  3/2 sec
(4)  never



2.

The maximum value of the function 7 + 6 x - 9 x^{2} is:
1. 8
2. -8
3. 4
4. -4



3.

A motor boat of mass m moving along a lake with velocity V0. At t=0, the engine of the boat is shut down. Magnitude of resistance force offered to the boat is equal to rV. (V is instantaneous speed). What is the total distance covered till it stops completely? Hint: Fx=mVdVdx=-rV
(1)  mV0/r
(2)  3 mV0/2r
(3)  mV0/2r
(4)  2mV0/r



4.

If a curve is governed by the equation y = sinx, then the area enclosed by the curve and x-axis between x = 0 and x = π is (shaded region):
              
1. 1 unit
2. 2 units
3. 3 units
4. 4 units



5.

The dimension of uvmvdv is
(1) M1L-2T-2
(2) M1L2T-2
(3) [M1L1T-1]
(4) None of these



6.

Component of 3i^+4j^ perpendicular to i^+j^ and in the same plane as that of 3i^+4j^ is:
1. 12(j^-i^)
2. 32(j^-i^)
3. 52(j^-i^)
4. 72(j^-i^)



7.

If two force vectors A and B of the same magnitude are arranged in the following manner, the magnitude of resultant is maximum for?
                    
(1) (I)
(2) (II)
(3) Both (II) & (III)
(4) Both (I) & (II)



8.

If vector P, Q and R have magnitude 5, 12 and 13 units and P+Q=R, then the angle between Q and R will be:
1.  cos-1 512
2.  cos-1 513
3.  cos-1 1213
4.  cos-1 213



9.

A particle travels with speed 50 m/s from the point (3,7) in a direction 7\hat i -24 \hat j. Find its position vector after 3 seconds.
1. 151\hat i+45\hat j
2. 45\hat i-137\hat j
3. 151\hat i-45\hat j
4. 4.5\hat i-151\hat j



10.

Two forces A and B have a resultant R1. If B is doubled, the new resultant R2 is perpendicular to A. Then
1. R1=A
2. R1=B
3. R2=A
4. R2=B




Mathematical tools - 30 September 2020 Contact Number: 9667591930 / 8527521718
11.

Which of the sets given below may represent the magnitude of resultant of three vectors adding to zero?
(1)  2, 4, 8
(2)  4, 8, 16
(3)  1, 2, 1
(4)  0.5, 1, 2



12.

The angle that the vector A=2i^+3j^ makes with the y-axis is:
(1)  tan-1 3/2
(2)  tan-1 2/3
(3)  sin-1 2/3
(4)  cos-1 3/2



13.

Two constant forces F1=2i^-3j^+3k^ N and F2=i^+j^-2k^ N act on a body and displace it from the position r1=i^+2j^-2k^ m to the position r2=7i^+10j^+5k^ m. What is the work done W? [Given : W =F.r]
(A)  9 Joule
(B)  41 Joule
(C)  -3 Joule
(D)  None of these



14.

The linear velocity of a rotating body is given by v=ω×r, where ω is the angular velocity and r is the radius vector. The angular velocity of a body, ω=i^-2j^+2k^ and their radius vector is  r=4j^-3k^, then value of |v| will be:
1. 29 units
2. 31 units
3. 37 units
4. 41 units



15.

If θ is the angle between vectors A and B, then which of the following is the unit vector perpendicular to A and B?
1. A^ × B^AB sin θ
2. A × BAB cos θ
3. A×BAB sin θ
4. A × BAB 



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