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  4. The maximum value of 3 cos θ + 4 sin θ is

Q. The maximum value of is

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Solution:

Maximum value of is
Given,
Here,
Maximum value
Alternative Let
On differentiating w.r.t. , we get

For maximum or minimum put


Again differentiating, we get


ve, maximum
Maximum value of is

Questions from UPSEE 2007

1. The vector is rotated through an angle and doubled in magnitude, then it becomes . The value of is

2. A ball of mass moving with a velocity of collides with another ball of mass moving with velocity in the opposite direction. If the first ball comes to rest after the impact and , then is in , is

3. Three forces of magnitude , and acting at a point are in equilibrium. If the angle between the first two is , the value of is

4. Let and be two equal vectors inclined at an angle , then is equal to

5. The solution of the equation is

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