A certain vector in the xy-plane has an x-component of \(4\) m and a y-component of \(10\) m. It is then rotated in the xy-plane so that its x-component is doubled. Then, its new y-component will be: (approximately)
1. \(20\) m
2. \(7.2\) m
3. \(5.0\) m
4. \(4.5\) m

Subtopic:  Resolution of Vectors |
 52%
From NCERT
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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

Subtopic:  Integration |
 58%
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The acceleration of a particle starting from rest varies with time according to relation, a=α t+β. The velocity of the particle at time instant t is: (\(Here, a=\frac{dv}{dt}\))

1. αt2+βt

2. αt2+βt2

3. αt22+βt

4. 2αt2+βt

Subtopic:  Integration |
 85%
From NCERT
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The displacement of the particle is zero at t=0 and at t=t it is x. It starts moving in the x-direction with a velocity that varies as v=kx, where k is constant. The velocity will : (Here, \(v=\frac{dx}{dt}\))

1. vary with time.

2. be independent of time.

3. be inversely proportional to time.

4. be inversely proportional to acceleration.

Subtopic:  Integration |
 51%
From NCERT
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The acceleration of a particle is given by a=3t  at t=0, v=0, x=0. The velocity and displacement at t = 2 sec will be: (\(Here, a=\frac{dv}{dt}~ and~v=\frac{dx}{dt}\))

1. 6 m/s, 4 m

2. 4 m/s, 6 m

3. 3 m/s, 2 m

4. 2 m/s, 3 m

Subtopic:  Integration |
 85%
From NCERT
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At what angle must the two forces (x + y) and (x y) act so that the resultant comes out to be x2+y2 ?

1. cos-1-x2+y22(x2-y2)

2. cos-1-2(x2-y2)x2+y2

3. cos-1-x2+y2x2-y2

4. cos-1-x2-y2x2+y2

Subtopic:  Resultant of Vectors |
 65%
From NCERT
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Component of 3i^+4j^ perpendicular to i^+j^ and in the same plane as that of 3i^+4j^ is:

1.  12j^-i^

2.  32j^-i^

3.  52j^-i^

4.  72j^-i^

Subtopic:  Scalar Product |
 50%
From NCERT
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A particle is moving along the x-axis. The velocity v of this particle varies with its position x as v=1x. Find the velocity of the particle as a function of time t given that at t=0, x=1 and v=dxdt.

1.  v=2t+1

2.  v=12t+1

3.  v=1t

4.  None of these

Subtopic:  Differentiation |
 56%
From NCERT
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A and B are two vectors and θ is the angle between them. If A×B=3A.B, then the value of θ will be:

1. 60o

2. 45o

3. 30o

4. 90o

Subtopic:  Scalar Product | Vector Product |
 80%
From NCERT
AIPMT - 2007
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Temperature of a body varies with time as T=T0+at2+b sintK, where T0 is the temperature in Kelvin at t=0 sec & a=2/π K/s2 & b=-K, then the rate of change of temperature dTdt at t=π sec is:

1.  8 K

2.  80 K

3.  8 K/sec

4.  80 K/sec

Subtopic:  Differentiation |
 57%
From NCERT
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