MCQ
The area bounded by the curves $y=\log _e x$ and $y=\left(\log _e x\right)^2$ is
- A$3- e$
- B$e-3$
- C$\frac{1}{2}(3- e )$
- D$\frac{1}{2}(e-3)$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The function $\text{f}(\text{x})=\sum_{\text{r}=1}^5(\text{x}-\text{r})^{2}$ assume minimum value at $x =$
→If $\bar{a}, \bar{b}, \bar{c}$ are non-zero, non-collinear vectors, then the vectors $\bar{a}$ - $\bar{b}$ + $\bar{c}$, 4$\bar{a}$ - 7$\bar{b}$ - $\bar{c}$ and 3$\bar{a}$ + 6$\bar{b}$ + 6$\bar{c}$ are
→$\int_0^3[x] d x=\ldots$, where $[x]$ is greatest integer function.
→If the plane passing through the points (1,2,3), (2,3,1) and (3,1,2) is $a x+b y+c z=d$ then $a+2 b+3 c=$
→The p.d.f. of a continuous random variable $X$ is
$\begin{aligned}\mathrm{f}(x) & =\frac{x^2}{3}, & & -1<x<2 \\& =0, & & \text { otherwise }\end{aligned}$
Then the c.d.f. of X is given by
→$\begin{aligned}\mathrm{f}(x) & =\frac{x^2}{3}, & & -1<x<2 \\& =0, & & \text { otherwise }\end{aligned}$
Then the c.d.f. of X is given by
For the system of equations:
$x + 2y + 3z = 1$
$2x + y + 3z = 2$
$5x + 5y + 9z = 4$
→$x + 2y + 3z = 1$
$2x + y + 3z = 2$
$5x + 5y + 9z = 4$
$A$ and $B$ are two events such that $P(A) = 0.25$ and $P(B) = 0.50.$ The probability pf both happening together is $0.14.$ The probability of both $A$ and $B$ hot happening is.
→The upper triangular matrix of the matrix $\left[\begin{array}{ccc}1 & -1 & 2 \\ 2 & 1 & 3 \\ 3 & 2 & 4\end{array}\right]$ is
→For the following probability distribution:
The value of $E(X)$ is:
→| $X:$ | $-4$ | $-3$ | $-2$ | $-1$ | $0$ |
| $P(X):$ | $0.1$ | $0.2$ | $0.3$ | $0.2$ | $0.2$ |
The projection of the vector $\hat{i}-2 \hat{j}+\hat{k}$ on the vector $4 \hat{i}-4 \hat{j}+7 \hat{k}$ is
→