St. R. C CONVENT SCHOOL JHINJHANA
UT-1 EXAM 2024
CLASS-12 SUBJECT- MATHS. M.M 10
NOTE: ALL QUESTIONS ARE COMPULSORY:
Q.1 . Find the derivatives with respect to x of cosx½
Q.2. If y = A sinx + B cosx, then prove that d²y /dx² + y = 0
Q.3. If x.(1+y)½ + y.( 1+x)½ = 0 , then prove that dy/dx = - 1/ (1+x)²
Q.4. The volume of a cube is Increasing at the rate of 9 cubic centimetres per second. How fast is the surface area Increasing when the length of an edge is 10 centimetres.?
Q.5 . Show that the function f given by f(x) = x³ - 3x² + 4x, is Increasing on R
Q.6 . Find the intervals in which the function f given by f(x) = 4x³- 6x² - 72x + 30. Is
(a) Increasing (b) Decreasing
Q.7 . Find the absolute maximum and minimum values of a function f given by f(x) = 2x³ - 15 x² + 36x + 1 on the interval [1 ,5].
Q.8 .Find two numbers whose sum is 24 and whose product is large as possible.
Q.9. Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to the diameter of the base.
Q.10. Find the derivatives of log log log log x, with respect to x.
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