Important Questions

CBSE Guess > Papers > Important Questions > Class XII > 2010 > Maths > Mathematics By Mr. Kalpesh

CBSE CLASS XII

Q. 1. Show that the normal at any point  to the curve   is at a constant distance from the origin.

Q. 2. Find the intervals in which the function given by  is ,    

  1. increasing 
  2. decreasing .

Q. 3. A large window has a shape of a rectangle surmounted by an equilateral triangle. If the perimeter of the window is 12 m ,find the dimensions of the rectangle that will produce the largest area of the window

Q. 4. Show that the maximum value of is .

Q. 5. Find the maximum and minimum values if any, of the following function given by 

  1.  
  2.  .

Q. 6. The time  of a complete oscillation of a simple pendulum of length   is given by the equation ,where  is constant. What is the approximate error in  when  is increased by 2 %  ?

Q. 7. Prove that the curves and cut at right angles if .

Q. 8. The surface area of a spherical bubble is increasing at the rate of  . When the radius is, at what rate is the volume of the bubble increasing .

Q. 9. Discuss the continuity of the (Greatest integer function).

Q. 10. Find the values of  and  such that the function defined by

 is a continuous function .

Q. 11. Find  in the  .

Q. 12. Differentiate the function  .

Q. 13. Find  of  the function if   prove that

.

Q. 14. Find

 .

Q. 15. Using MVT, find a point on the curve  defined on the interval ,where the tangent is parallel to the chord joining the end point of the curve .

Paper By Mr. Kalpesh
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