Revision Quiz on Increasing, Decreasing Function & Maxima-Minima for JEE & BITSAT Exams

Question 1

Let

and

be a constant such that

for all

real and

Then the least possible value of

is

Question 2

An ellipse inscribed in a semi-circle touches the circular arc at two distinct points and also touches the bounding diameter. Its major axis is parallel to the bounding diameter. When the ellipse has the maximum possible area, its eccentricity is

Question 3

Let P(x) = a₀+a₁x² + a₂x⁴ + a₃x⁶ + .... + a_nx²ⁿ be a polynomial in a real variable x with 0< a₀< a₁ < a₂ <....<a_n. The function P(x) has

Question 4

Let f(x) = sinx + 2cos²x, $Description: E:\WBJEE\2013\2013_Mathematics_files\image026.png$ ≤ x ≤ $Description: E:\WBJEE\2013\2013_Mathematics_files\image232.png$ . Then f attains its

Question 5

If f(x) = x + cos x – a then

Question 6

The adjacent side of a rectangle with given parameter as 200 cm and enclosing maximum area are

Question 7

Let p(x) be a polynomial with real coefficients and a,b ε R with a<b, be two consecutive roots of p (x) = 0. Then if there exist ‘c’ in (a,b) then which of the following hold true:

Question 8

On which of the following intervals is the function f(x) = 2x² – log |x|, x ≠ 0 increasing 2.

Question 9

If f is a real – valued differentiable function such that f(x)f’(x)< 0 for all real x, then

Question 10

The minimum value of $Description: Description: Vitjee-2014-Maths_files\image035.png$ is

Question 11

In a regular triangular prism the distance from the centre of one base to one of the vertices of the other base is l. The altitude of the prism for which the volume is greatest.