MCQ
What is the value of $\int\limits_{-1}^{1} \sin^3\text{x}\cos^2\text{x  dx} :$
  • $0$
  • B
    $1$
  • C
    $\frac{1}{2}$
  • D
    $2$

Answer

Correct option: A.
$0$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

If $X$ and $Y$ are two independent binomial variates, satisfying $B\left( {10,\frac{1}{2}} \right)$ and $B\left( {8,\frac{1}{2}} \right)$ respectively, then probability $P\left( {X + Y = 2} \right)$ is
Consider the objective function Z = 40x + 50y The minimum number of constraints that are required to maximize Z are:
The system of equations:
x + y + z = 5
x + 2y + 3z = 9
x + 3y + λz = µ
has a unique solution, if
The differential equation of all circles passing through the origin and having their centres on the $x-$axis is
$\int_0^{\pi /4} {{{\sec }^7}\theta {{\sin }^3}\theta } \,d\theta = $
Suppose $A$ is $3 \times 3$ matrix consisting of integer entries that are chosen at random from the set $\{-1000,-999, \ldots 999,1000\}$. Let $P$ be the probability that either $A^2=-I$ or $A$ is diagonal, where $I$ is the $3 \times 3$ identity matrix. Then,
$f\left( x \right) = \int {\frac{{dx}}{{{{\sin }^6}\,x}}} $ is a polynomial of degree 
If $f(x) = \left\{ {\begin{array}{*{20}{c}}
{x\left[ x \right],\,\,\,\,\,\,\,\,\,\,\,\,\,}&{0 \le x < 2}\\
{\left( {x - 1} \right)\left[ x \right]\,,\,\,\,}&{2 \le x \le 4}
\end{array}} \right.,$ where $[.]$ denotes greatest integer function, then
A fair coin is tossed $99$ times. If $X$ is the number of times head appears, then $P(X = r)$ is maximum when $r$ is:
A special lottery is to be held to select a student who will live in the only deluxe room in a hostel. There are 100 Year-III, 150 Year-II and 200 Year-I students who applied. Each Year-III's name is placed in the lottery 3 times; each Year-II's name, 2 times and Year-I's name, 1 time. What is the probability that a Year-III's name will be chosen?