JEE Maths - Monotonicity

Buy JEE Main Engineering Entrance Exam (Pro) Practice test pack

Question - 1

Function f(x) = x3+ 6x2 +(9+ 2k) x + 1 \(\forall x \in R\) is strictly increasing function if  k > \(\lambda\) then find \(\lambda\).

  • A 1.50
  • B 1.60
  • C 1.70
  • D 1.80

Question - 2

The function f(x) = \(\frac{a \sin x+2 \cos x}{\sin x+\cos x}\) is increasing for x \(\in\) R where a >  \(\lambda\) then find \(\lambda\).

  • A 1.00
  • B 2.00
  • C 3.00
  • D 4.00

Question - 3

Let \(\phi\) (x) = f(x) + f(2a - x) and f '' (x) > 0; \(\forall \mathrm{x} \in[0, \mathrm{a}]\). If \(\phi\)(x) is decreasing  in [0, \(\lambda\)a] then find \(\lambda\).

  • A 1.00
  • B 2.00
  • C 3.00
  • D 4.00

Question - 4

Function f(x) = 2x3 - 9x2+ 12x + 29 is decreasing when x \(\in\) (a, b) then find value of a + b.

  • A 3.00
  • B 6.00
  • C 9.00
  • D 12.00

Question - 5

The interval in which 2x3 + 5 increases less rapidly than 9x2 - 12x, is (a, b) then find a + b.

  • A 3.00
  • B 6.00
  • C 9.00
  • D 12.00

Question - 6

If the function f: R \(\rightarrow\) R given by f(x) = x3 + ax2 + 5x + sin 2x is invertible and a \(\in\) (-3, 1) then find \(\lambda\).

  • A 1.00
  • B 2.00
  • C 3.00
  • D 4.00

Question - 7

If f(x) = x3 + 4x2 + \(\lambda\)x + 1 is monotonically decreasing function of x in the largest possible interval
(-2, - 2/3): then find \(\lambda\).

  • A 1.00
  • B 2.00
  • C 3.00
  • D 4.00

Question - 8

If the complete set of values of x in which f(x) = 2 loge (x - 2) - x2 + 4x + l increases, is (a + b) then
find a + b.

  • A 1.00
  • B 5.00
  • C 3.00
  • D 7.00

Question - 9

If f(x) =Kx3 - 9x2 + 9x + 3 is monotonically increasing \(\forall \mathrm{x} \in R\)  and k \(\in(\lambda, \infty)\) then find value of \(\lambda\).

  • A 1.00
  • B 2.00
  • C 3.00
  • D 4.00

Question - 10

If f(x) = x - 2 sin x, 0 \(\leq\) x \(\leq\) 2\(\pi\) is increasing in the interval [a\(\pi\), b\(\pi\)], then find value of a+ b.

  • A 1.00
  • B 2.00
  • C 3.00
  • D 4.00
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next
Previous Next