MCQ
Consider the following statements:Statement $I:\ $ The area bounded by the curve, $\text{y}=\sin\text{x}$ between $\text{x}=0$ and $x = 2p$ is $2\ sq.$ units.Statement $II:\ $ The area bounded by the curve, $\text{y}=2\cos\text{x}$ and the $x-$axis from $\text{x}=0$ to $x = 2p$ is $8\ sq.$ units.
  • A
    Statement $I$ is true
  • Statement $II$ is true
  • C
    Both statements are true
  • D
    Both statements are false

Answer

Correct option: B.
Statement $II$ is true

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

Which of the following groups are not the direction cosines of a line?
Let $f(x)=\int \frac{d x}{\left(3+4 x^2\right) \sqrt{4-3 x^2}},|x| < \frac{2}{\sqrt{3}}$. If $f(0)=0$ and $f(1)=\frac{1}{\alpha \beta} \tan ^{-1}\left(\frac{\alpha}{\beta}\right), \alpha, \beta > 0$, then $\alpha^2+\beta^2$ is equal to $.........$.
The value of objective function is maximum under linear constraints
If vertices of a triangle are $A(1,\, - 1,\,2),\,B(2,\,0,\, - 1)$ and $C(0,\,2,\,1),$ then the area of a triangle is
The area enclosed between the curves $y = \sin x ,\, y = \cos x \, \&$ the $x-$ axis if $0 \le x \le \frac{\pi }{2}$ is :
Let $\mathrm{a}$ and $\mathrm{b}$ be real constants such that the function $f$ defined by $f(x)=\left\{\begin{array}{cc}x^2+3 x+a & x \leq 1 \\ b x+2, & x>1\end{array}\right.$ be differentiable on $R$. Then, the value of $\int_{-2}^2 f(x) d x$ equals
If the function $f(x) = \left\{ \begin{array}{l}{(\cos x)^{1/x}},\;x \ne 0\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,k,\,x = 0\end{array} \right.$ is continuous at $x = 0$, then the value of $k$ is
A natural number is selected at random from the set $\{1 \leq  x \leq  100\}.$ The probatility that number satisfies the inequation $x^2 -13x \leq  30$ is :-
Let $\mathrm{p}$ be an odd prime number and $\mathrm{T}_{\mathrm{p}}$ be the following set of $2 \times 2$ matrices :

$T_p=\left\{A=\left[\begin{array}{ll}\mathrm{a} & \mathrm{b} \\ \mathrm{c} & \mathrm{a}\end{array}\right]: \mathrm{a}, \mathrm{b}, \mathrm{c} \in\{0,1, \ldots ., \mathrm{p}-1\}\right\}$

$1.$ The number of $A$ in $T_p$ such that $A$ is either symmetric or skew-symmetric or both, and $\operatorname{det}(\mathrm{A})$ divisible by $\mathrm{p}$ is

$(A)$ $(\mathrm{p}-1)^2$  $(B)$ $2(\mathrm{p}-1)$

$(C)$ $(\mathrm{p}-1)^2+1$  $(D)$ $2 \mathrm{p}-1$

$2.$ The number of $A$ in $T_p$ such that the trace of $A$ is not divisible by $p$ but det $(A)$ is divisible by $p$ is [Note: The trace of a matrix is the sum of its diagonal entries.]

$(A)$ $(\mathrm{p}-1)\left(\mathrm{p}^2-\mathrm{p}+1\right)$ $(B)$ $\mathrm{p}^3-(\mathrm{p}-1)^2$

$(C)$ $(\mathrm{p}-1)^2$ $(D)$ $(p-1)\left(p^2-2\right)$

$3.$ The number of $A$ in $T_p$ such that det $(A)$ is not divisible by $p$ is

$(A)$ $2 \mathrm{p}^2$ $(B)$ $p^3-5 p$ $(C)$ $p^3-3 p$ $(D)$ $p^3-p^2$

Give the answer question $1,2$ and $3.$

The solution of differential equation, $(x\,\cot \,y + \ln \,(\cos \,x))dy\, + \,(\ln \,(\sin \,y) - y\,\tan \,x)dx = 0$ is (where $C$ denotes constant of integration)