Maths Question Paper Cbse

1. If a line y = x + 1 is a tangent to the curve y2= 4x ,find the point the of contact ? 2. Find the point on the curve y = 2x2– 6x – 4 at which the tangent is parallel to the x – axis 3. Find the slope of tangent for y = tan x + sec x at x = π/4 4. Show that the function f(x) == x3– 6x2 +12x -99 is increasing for all x. 5. Find the maximum and minimum values, if any of 6. For the curve y = 3x² + 4x, find the slope of the tangent to the curve at the point x = -2. 7. Find a point on the curve y = x2– 4x -32 at which tangent is parallel to x-axis. 8. Find a, for which f(x) = a(x+sinx)+a is increasing . 9. The side of a square is increasing at 4 cm/minute. At what rate is the area increasing when the side is 8 cm long? 10. Find the point on the curve y =x2-7x+12, where the tangent is parallel to x-axis. 11. Find the intevals in which the function f(x) = 2log(x-2) - x2 + 4x + 1is increasing or decreasing. 12. Find the intervals in which the function f ( x ) = x3 - 6x2 + 9x + 15 is
(i) increasing
(ii) decreasing. 13. Find the equation of the tangent line to the curve x = θ + sinθ, y = 1+cosθ a=π/4 14. Prove that is increasing in [o, π/2] 15. Prove that curves y² = 4ax and xy = c² cut at right angles If c4 = 32 a4 16. A water tank has the shape of an inverted right circular cone with its axis vertical and vertex lower most. Its semi vertical angle is . Water is poured into it at a constant rate of 5 cubic meter per minute. Find the rate at which the level of the water is rising at the instant when the depth of water in the tank is 10m. Find the point on the curve y =x²-7x+12, where the tangent is parallel to x-axis. 17. Discuss applicability Rolle’s Theorem for the function f(x) = cosx + sinx in [0,2π ] and hence find a point at which tangent is parallel to X axis. 18. Verify Lagrange’s mean value theorem for the function f(x) = x + 1/x in [1,3]. 19. Find the intervals in which f(x) = sinx +