Class XI

Which of the following algebraic operations on vectors not permissible?
  1. adding any two vectors
  2. multiplying any vector by any scalar,
  3. adding a scalar component of the vector to the same vector
  4. multiplying the sum of vectors A and B by a scalar
A house has well-insulated walls. It contains a volume of 100 m3m3 of air at 300 K. If the energy required to lift an object of mass m through a height of 2.00 m equals the energy required to increase the temperature of this air by 1.00∘∘C., what is the value of m? (CP=72R)
  1. 6.18 ×× 103103 kg
  2. 6.03 ×× 103103 kg
  3. 5.87 ×× 103103 kg
  4. 6.67 ×× 103103 kg
Two vectors are equal if
  1. the two vectors have opposite directions
  2. the direction is the same for both
  3. the magnitude is the same for both
  4. the magnitude and direction are the same for both
An arbitrary vector v can be expressed as
  1. a sum of three mutually perpendicular unit vectors each multiplied scalar constant equal to 1
  2. a sum of three mutually perpendicular unit vectors each multiplied scalar constant equal to -1
  3. a sum of three mutually perpendicular unit vectors each multiplied by the same scalar constant
  4. a sum of three mutually perpendicular unit vectors each multiplied by a some scalar constant
A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude and direction of acceleration of the stone ?
  1. 11.9 m s−2s−2 , along the radius at every point away from the center
  2. 10.2 m s−2s−2 , along the radius at every point towards the center
  3. 9.9 m s−2s−2 , along the radius at every point away from the center
  4. 9.9 m s−2s−2, along the radius at every point towards the center
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