| 2024-01-22 | Area of the region bounded by \( [x]^{2}=[y]^{2} \),
if \( x \in[1,5] \), where [ ] denotes the .... | 4:15 | 0 | |
|
| 2024-01-22 | The axis divides the region bounded by the
parabolas \( y=4 x-x^{2} \) and \( y=x^{2}-x \) in th.... | 6:19 | 0 | |
|
| 2024-01-22 | Passage
For \( j=0,1,2, \ldots n \) let \( S_{j} \) be the area of region bounded by
the \( x \).... | 6:44 | 4 | |
|
| 2024-01-22 | Passage
For \( j=0,1,2, \ldots n \) let \( S_{j} \) be the area of region bounded by the \( x \).... | 3:40 | 2 | |
|
| 2024-01-22 | Area enclosed by the curves \( y=x^{2}+1 \) and a normal
drawn to it with gradient -1 ; is equal.... | 6:10 | 3 | |
|
| 2024-01-22 | The area defined by \( |y| \leq e^{-|x|}-\frac{1}{2} \) in cartesian co-
ordinate system, is:.... | 5:27 | 7 | |
|
| 2024-01-22 | If \( f(x)=\max \left\{\sin x, \cos x, \frac{1}{2}\right\} \) then the area of the
region bounde.... | 6:03 | 0 | |
|
| 2024-01-22 | The triangle formed by the tangent to the curve \( f(x) \)
\( =x^{2}+b x-b \) at the point \( (1.... | 4:55 | 0 | |
|
| 2024-01-22 | The area of region enclosed by the curves \( y=x^{2} \) and
\( y=\sqrt{|x|} \) is:.... | 2:10 | 0 | |
|
| 2024-01-22 | The area bounded by the curves \( y=\ln x, y=\ln |x|, y \)
\( =|\ln x| \) and \( y=|\ln | x|| \).... | 3:27 | 2 | |
|
| 2024-01-22 | The area bounded by the curve \( y=|x|-1 \) and \( y=- \) \( |x|+1 \) is:.... | 3:57 | 0 | |
|
| 2024-01-22 | The area of the figure bounded by two branches of the curve \( (y-x)^{2}=x^{3} \) and the straig.... | 2:57 | 3 | |
|
| 2024-01-22 | Let \( f(x) \) be a continuous function such that the area
bounded by the curve \( v=f(x) \), th.... | 2:25 | 2 | |
|
| 2024-01-22 | List-I contains the function and List-II contains their derivatives at \( x=0 \)
\begin{tabular}.... | 6:14 | 1 | |
|
| 2024-01-22 | The area bounded by \( y=x e^{|x|} \) and lines. \( |x|=1, y=0 \)
is
W).... | 3:07 | 3 | |
|
| 2024-01-22 | The value of \( c \) for which the area of the figure
bounded by the curve \( y=8 x^{2}-x^{5} \).... | 4:08 | 1 | |
|
| 2024-01-22 | The area of the figure bounded by the curves \( y=\mid x- \)
\( 1 \mid \) and \( y=3-|x| \) is
W.... | 7:12 | 4 | |
|
| 2024-01-22 | The area of the region bounded by \( 1-y^{2}=|x| \) and \( |x| \)
\( +|y|=1 \) is
W).... | 4:36 | 1 | |
|
| 2024-01-22 | The slope of the tangent to a curve \( y=f(x) \) at \( (x, f(x)) \)
is \( 2 x+1 \). If the curve.... | 2:11 | 0 | |
|
| 2024-01-22 | Let \( f(x) \) be a differentiable function in \( [-1, \infty) \) and \( f(0)=1 \) such that
\[
.... | 3:55 | 2 | |
|
| 2024-01-22 | Let \( f(x)=\min [x+1, \sqrt{(1-x)}] \). Then area bounded
by \( f(x) \) and \( x \)-axis is.... | 2:56 | 1 | |
|
| 2024-01-22 | The area between the curve \( y=2 x^{4}-x^{2} \), the \( x \)-axis
and the ordinates of two mini.... | 4:32 | 1 | |
|
| 2024-01-22 | A differentiable function satisfy the relation \( \ln (f(x+y))=\ln (f(x)) . \ln (f(y)) \forall x.... | 4:31 | 1 | |
|
| 2024-01-22 | If \( y=e^{\sqrt{x}} \) then the value of \( \left[4 \cdot y^{\prime}(4)\right] \) (where \( [\c.... | 1:15 | 0 | |
|
| 2024-01-22 | Let \( f(x)=\cos ^{-1}\left(2 x^{2}-1\right) \) then.... | 3:21 | 0 | |
|
| 2024-01-22 | If \( f(\theta)=\tan \left(\sin ^{-1} \sqrt{\frac{2}{3+\cos 2 \theta}}\right) \) then :.... | 2:14 | 1 | |
|
| 2024-01-22 | A differentiable function satisfy the relation \( \ln (f(x+y))=\ln (f(x)) . \ln (f(y)) \forall x.... | 1:15 | 0 | |
|
| 2024-01-22 | \( \frac{d^{2} x}{d y^{2}} \) equals :
(1) \( \quad-\left(\frac{d^{2} y}{d x^{2}}\right)^{-1}\le.... | 1:24 | 0 | |
|
| 2024-01-22 | The derivative of \( e^{\sin ^{-1}(x)} \) with respect to ' \( \sqrt{1-x^{2}} \),
at \( x=1 \) i.... | 1:27 | 0 | |
|
| 2024-01-22 | If \( y=x \sin x \) then the value of \( y^{i v}(0) \) is.... | 2:22 | 0 | |
|
| 2024-01-22 | If \( y=(\sin x)^{\tan x} \), then \( \frac{d y}{d x} \) is equal to :.... | 1:10 | 2 | |
|
| 2024-01-22 | If \( x=e^{t} \cos t \) and \( y=e^{t} \sin t \) then the value of \( \frac{d y}{d x} \) at
\( t.... | 1:04 | 0 | |
|
| 2024-01-22 | Let \( f(x)=\left|\begin{array}{ccc}x^{3} & 2 x^{2} & -x \\ 2 x & 1 & 0 \\ x & 0 & 3\end{array}\.... | 1:03 | 1 | |
|
| 2024-01-22 | If \( y=1+x+\frac{x^{2}}{2 !}+\frac{x^{3}}{3 !}+\ldots .+\frac{x^{n}}{n !}+\ldots . . \infty \) .... | 1:35 | 5 | |
|
| 2024-01-22 | If \( y=\tan ^{-1}\left(\frac{x}{2}\right)+\sin ^{-1}\left(\frac{2}{\sqrt{4+x^{2}}}\right) \) th.... | 2:35 | 3 | |
|
| 2024-01-22 | Derivative of ' \( y \) ' if \( y=\frac{1}{\sec x-\tan x} \).... | 1:05 | 1 | |
|
| 2024-01-22 | If \( \frac{d y}{d x}=\frac{d}{d x}\left(\frac{\sin ^{4} x+\sin ^{2} x+1}{\sin ^{2} x-\sin x+1}\.... | 1:41 | 1 | |
|
| 2024-01-22 | If \( f(x)=\left\{\begin{array}{cc}x^{2}\left(\frac{e^{1 / x}-e^{-1 / x}}{e^{1 / x}+e^{-1 / x}}\.... | 2:32 | 0 | |
|
| 2024-01-22 | Let \( f(x)=\lim _{n \rightarrow \infty}(\sin x)^{2 n} \), then \( f \) is:.... | 2:45 | 1 | |
|
| 2024-01-22 | If \( 3 x^{2}-10 x y+5 y^{2}=0 \) then \( \frac{d y}{d x} \) is equal to :.... | 2:19 | 2 | |
|
| 2024-01-22 | Statement-1: If \( f(x)=\frac{2}{\pi} \cot ^{-1}\left(\frac{3 x^{2}+1}{(x-1)(x-2)}\right) \),
th.... | 2:20 | 0 | |
|
| 2024-01-22 | The derivative of ' \( \sec ^{2} x \) ' with respect to ' \( \tan x \) ' is.... | 0:46 | 0 | |
|
| 2024-01-22 | The derivative of an odd function is.... | 1:08 | 0 | |
|
| 2024-01-22 | The number of points of non differentiability of the
function \( f(x)=|\sin x|+\sin |x| \) in \(.... | 3:28 | 0 | |
|
| 2024-01-22 | If \( y=x^{x^{2}} \), find \( \frac{d y}{d x} \).... | 1:41 | 0 | |
|
| 2024-01-22 | Let \( f^{\prime \prime}(x) \) be continuous at \( x=0 \) and \( f^{\prime \prime}(0)=4 \) then
.... | 1:42 | 0 | |
|
| 2024-01-22 | Statement-1: \( \lim _{x \rightarrow \infty}\left(\frac{1}{x^{2}}+\frac{2}{x^{2}}+\frac{3}{x^{2}.... | 1:20 | 0 | |
|
| 2024-01-22 | If \( \lim _{n \rightarrow \infty} \frac{n^{98}}{n^{x}-(n-1)^{x}}=\frac{1}{99} \), then the valu.... | 1:47 | 1 | |
|
| 2024-01-22 | Consider \( f(x)=\frac{\sin x+a e^{x}+b e^{-x}+c \ln (1+x)}{x^{3}} \), where
\( a, b, c \) are r.... | 3:19 | 1 | |
|
| 2024-01-22 | Consider \( f(x)=\frac{\sin x+a e^{x}+b e^{-x}+c \ln (1+x)}{x^{3}} \), where
\( a, b, c \) are r.... | 1:55 | 1 | |
|
| 2024-01-22 | Consider \( f(x)=\frac{\sin x+a e^{x}+b e^{-x}+c \ln (1+x)}{x^{3}} \), where
\( a, b, c \) are r.... | 2:37 | 0 | |
|
| 2024-01-22 | Statement-1: \( \lim _{x \rightarrow 0}\left[\frac{\sin x}{x}\right]=0 \)
Statement - 2: \( \lim.... | 0:38 | 1 | |
|
| 2024-01-22 | The function \( f(x)=\sin ^{-1}(\cos x) \) is:.... | 2:58 | 1 | |
|
| 2024-01-22 | Let \( f(x)=\left\{\begin{array}{cc}x \sin \left(\frac{1}{x}\right)+\sin \left(\frac{1}{x^{2}}\r.... | 1:22 | 0 | |
|
| 2024-01-22 | The value of \( \lim _{x \rightarrow 0} x^{2}\left[\frac{1}{x^{2}}\right] \) is (where [.] denot.... | 1:00 | 0 | |
|
| 2024-01-22 | If \( f(x)=x \sin \left(\frac{\pi}{2}(x+2[x])\right) \), then \( f(x) \) is \( \{ \) where
[.] d.... | 3:58 | 1 | |
|
| 2024-01-22 | If \( f(x)=\frac{x}{\sqrt{x+1}-\sqrt{x}} \) be a real valued function,
then.... | 2:05 | 6 | |
|
| 2024-01-22 | A function \( f(x) \) is defined as below
\( f(x)=\frac{\cos (\sin x)-\cos x}{x^{2}}, x \neq 0 \.... | 2:03 | 1 | |
|
| 2024-01-22 | The number of points of local extremum of \( f(x)=|\sin x| \) over the interval \( (0,2 \pi) \) .... | 4:11 | 1 | |
|
| 2024-01-22 | \( \lim _{x \rightarrow 0} \frac{x \cos x-\log (1+x)}{x^{2}} \) equals:.... | 1:16 | 0 | Vlog |
|
| 2024-01-22 | Match the following:
\begin{tabular}{|l|l|l|l|}
\hline & \multicolumn{1}{|c|}{ List -I } & & \mu.... | 7:20 | 1 | |
|
| 2024-01-22 | Evaluate \( \lim _{x \rightarrow 2} \frac{\sqrt{x^{2}+x-3}-\sqrt{x+1}}{x-2} \).... | 2:03 | 0 | |
|
| 2024-01-22 | Evaluate \( \lim _{x \rightarrow \infty} \frac{\sqrt{x^{2}+1}-\sqrt[3]{x^{2}+1}}{\sqrt[4]{x^{4}+.... | 1:43 | 1 | |
|
| 2024-01-22 | Evaluate \( \lim _{x \rightarrow a} \frac{x^{3 / 5}-a^{3 / 5}}{x^{1 / 3}-a^{1 / 3}} \).... | 1:18 | 0 | |
|
| 2024-01-22 | If \( f(x)=\frac{\sin \left(e^{x-2}-1\right)}{\log (x-1)} \), then \( \lim _{x \rightarrow 2} f(.... | 1:01 | 1 | Vlog |
|
| 2024-01-22 | Match the following:
\begin{tabular}{|l|l|l|l|}
\hline & \multicolumn{1}{|c|}{ List -I } & & Lis.... | 6:51 | 1 | |
|
| 2024-01-22 | Match the following:
\begin{tabular}{|l|l|l|l|}
\hline & \multicolumn{1}{|c|}{ List - I } & & Li.... | 4:15 | 1 | |
|
| 2024-01-22 | Evaluate \( \lim _{x \rightarrow 2} \frac{x^{6}-24 x-16}{x^{3}+2 x-12} \).... | 1:06 | 1 | |
|
| 2024-01-22 | If the absolute maximum value of \( f(x)=\cot ^{-1}(x) \) over
the interval \( [-1,1] \) is of t.... | 2:08 | 4 | |
|
| 2024-01-22 | For which of the following functions Rolle's theorem
is applicable?.... | 4:14 | 4 | |
|
| 2024-01-22 | The function \( f(x)=\left(x^{2}+1\right) e^{-x} \) is decreasing in the
interval.... | 2:39 | 1 | |
|
| 2024-01-22 | A body moves along a straight line, so that the distance (in metres) travelled in ' \( t \) ' se.... | 1:23 | 3 | |
|
| 2024-01-22 | A body moves along a straight line, so that the distance (in metres) travelled in ' \( t \) ' se.... | 1:34 | 2 | |
|
| 2024-01-22 | Let \( h(x)=(f(x))^{3}+(f(x))^{2}+f(x) \) for every real
number ' \( x \) '. Then.... | 3:20 | 4 | |
|
| 2024-01-22 | The point on the curve \( 2 y^{4}+3 x^{2}-9=0 \) where the
tangent is vertical is.... | 3:30 | 0 | |
|
| 2024-01-22 | The equation of tangent to the curve
\( y=3 x^{3}+4 x^{2}+5 x+6 \) at \( x=-1 \) is.... | 2:46 | 2 | |
|
| 2024-01-22 | The interval in which \( f(x)=x^{1 / x} \) is increasing?.... | 2:24 | 1 | |
|
| 2024-01-22 | A circular disc of radius \( 4 \mathrm{~cm} \) is being heated. Due to
expansion, its radius inc.... | 1:48 | 3 | |
|
| 2024-01-22 | A ladder \( 10 \mathrm{~cm} \) long is leaning against a wall. The
bottom of the ladder is pulle.... | 4:16 | 3 | |
|
| 2024-01-22 | The interval in which the function ' \( f \) ' given by
\( f(x)=e^{x}\left(x^{2}-3\right) \) is .... | 2:50 | 0 | |
|
| 2024-01-22 | A particle moves along the curve \( 2 y=3 x^{2}+4 x \).
The point on the curve at which the \( y.... | 2:27 | 1 | |
|
| 2024-01-22 | Consider a matrix \( A=\left[a_{i j}\right] \) of order \( 3 \times 3 \) such that \( a_{i j}=(k.... | 4:34 | 1 | |
|
| 2024-01-22 | The total revenue in Rupees received from the sale of
' \( x \) ' units of a product is given by.... | 1:55 | 2 | |
|
| 2024-01-22 | \( A=\left[\begin{array}{ll}0 & 1 \\ 3 & 0\end{array}\right] \) and \( \left(A^{8}+A^{6}+A^{4}+A.... | 3:22 | 0 | |
|
| 2024-01-22 | Match of following lists:
\begin{tabular}{|l|l|l|l|}
\hline & \begin{tabular}{l} List I (A, B, C.... | 4:08 | 3 | |
|
| 2024-01-22 | The length ' \( a \) ' of a rectangle is decreasing at the rate
\( 8 \mathrm{~cm} / \mathrm{s} \.... | 1:50 | 3 | |
|
| 2024-01-22 | If \( \left[\begin{array}{cc}a & b \\ c & 1-a\end{array}\right] \) is an idempotent matrix and \.... | 2:25 | 0 | |
|
| 2024-01-22 | The area of circle is decreasing at a rate \( 10 \mathrm{~cm}^{2} / \mathrm{s} \).
How fast is t.... | 2:23 | 1 | |
|
| 2024-01-22 | If \( A=\left[\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right] \), the.... | 4:39 | 1 | |
|
| 2024-01-22 | The volume of a sphere is increasing at a rate \( 16 \mathrm{~m}^{3} / \mathrm{s} \).
How fast i.... | 2:28 | 0 | |
|
| 2024-01-22 | Which of the following is true?.... | 0:48 | 1 | |
|
| 2024-01-22 | Find the rate of change of the area of a square per
second with respect to its edge ' \( a \) ' .... | 1:34 | 0 | |
|
| 2024-01-22 | Let \( A \) be a matrix of order \( 2 \times 2 \) such that \( A^{2}=0 \).
\[
(I+A)^{100}=
\]
W..... | 1:56 | 0 | |
|
| 2024-01-22 | Let \( A \) be a matrix of order \( 2 \times 2 \) such that \( A^{2}=0 \).
\( A^{2}-(a+d) A+(a d.... | 2:56 | 0 | |
|
| 2024-01-22 | Let \( A \) be a matrix of order \( 2 \times 2 \) such that \( A^{2}=0 \).
\( \operatorname{tr}(.... | 1:53 | 0 | |
|
| 2024-01-22 | Which of the following determinant(s) vanish(es)?.... | 8:10 | 0 | |
|
| 2024-01-22 | If \( \left(\begin{array}{cc}1 & -\tan \theta \\ \tan \theta & 1\end{array}\right)\left(\begin{a.... | 1:51 | 0 | |
|
| 2024-01-22 | If \( \left[\begin{array}{cc}\cos \frac{2 \pi}{7} & -\sin \frac{2 \pi}{7} \\ \sin \frac{2 \pi}{7.... | 3:28 | 1 | |
|
| 2024-01-22 | If \( Z \) is an idempotent matrix, then \( (I+Z)^{n} \).... | 1:47 | 0 | |
|
| 2024-01-22 | If \( A \) and \( B \) are squares matrices such that \( A^{2006}=O \)
is \( A B=A+B \). then \(.... | 1:36 | 1 | |
|
