Solve this following
Question: If for $x \in\left(0, \frac{1}{4}\right)$, the derivative of $\tan ^{-1}\left(\frac{6 x \sqrt{x}}{1-9 x^{3}}\right)$ is $\sqrt{x} \cdot g(x)$, then $g(x)$ equals$\frac{3}{1+9 x^{3}}$$\frac{9}{1+9 x^{3}}$$\frac{3 x \sqrt{x}}{1-9 x^{3}}$$\frac{3 x}{1-9 x^{3}}$Correct Option: , 2 Solution:...
Read More →If the lines
Question: If the lines $\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}$ and $\frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}$ are coplanar, then $k$ can have :any valueexactly one valueexactly two valuesexactly three values.Correct Option: , 3 Solution:...
Read More →The area (in sq. units) of the region
Question: The area (in sq. units) of the region $\left\{(x, y\}: x \geq 0, x+y \leq 3, x^{2} \leq 4 y\right.$ and $\left.y \leq 1+\sqrt{x}\right\}$ is :$\frac{5}{2}$$\frac{59}{12}$$\frac{3}{2}$$\frac{7}{3}$Correct Option: 1 Solution: Solution not required...
Read More →Distance between two parallel planes
Question: Distance between two parallel planes $2 \mathrm{x}+\mathrm{y}+2 \mathrm{z}=8$ and $4 \mathrm{x}+2 \mathrm{y}+4 \mathrm{z}+5=0$ is :-$\frac{3}{2}$$\frac{5}{2}$$\frac{7}{2}$$\frac{9}{2}$Correct Option: , 3 Solution:...
Read More →If the integral
Question: If the integral $\int \frac{5 \tan x}{\tan x-2} d x=x+a \ln |\sin x-2 \cos x|+k$ then a is equal to :2- 1- 21Correct Option: 1 Solution:...
Read More →Solve this following
Question: If $\mathrm{g}$ is the inverse of a function $f$ and $f^{\prime}(\mathrm{x})=\frac{1}{1+\mathrm{x}^{5}}$, then $\mathrm{g}^{\prime}(\mathrm{x})$ is equal to : $1+x^{5}$$5 x^{4}$$\frac{1}{1+\{g(x)\}^{5}}$$1+\{g(x)\}^{5}$Correct Option: , 4 Solution:...
Read More →The area (in sq.units)
Question: The area (in sq.units) of the region $\left\{(x, y): y^{2} \geq 2 x\right.$ and $\left.x^{2}+y^{2} \leq 4 x, x \geq 0, y \geq 0\right\}$ is :-$\frac{\pi}{2}-\frac{2 \sqrt{2}}{3}$$\pi-\frac{4}{3}$$\pi-\frac{8}{3}$$\pi-\frac{4 \sqrt{2}}{3}$Correct Option: , 3 Solution:...
Read More →Solve this following
Question: If $y=\sec \left(\tan ^{-1} x\right)$, then $\frac{d y}{d x}$ at $x=1$ is equal to :$\frac{1}{\sqrt{2}}$$\frac{1}{2}$1$\sqrt{2}$Correct Option: , 4 Solution:...
Read More →The area of the region
Question: The area of the region described by $A=\left\{(x, y): x^{2}+y^{2} \leq 1\right.$ and $\left.y^{2} \leq 1-x\right\}$ is:$\frac{\pi}{2}+\frac{4}{3}$$\frac{\pi}{2}-\frac{4}{3}$$\frac{\pi}{2}-\frac{2}{3}$$\frac{\pi}{2}+\frac{2}{3}$Correct Option: 1 Solution:...
Read More →Solve this
Question: Let $f:[-2,3] \rightarrow[0, \infty)$ be a continuous function such that $\mathrm{f}(1-\mathrm{x})=f(\mathrm{x})$ for all $\mathrm{x} \in[-2,3]$. If $R_{1}$ is the numerical value of the area of the region bounded by $y=f(x), x=-2, x=3$ and the axis of $\mathrm{x}$ and $\mathrm{R}_{2}=\int_{-2}^{3} x f(x) d x$, then :$2 R_{1}=3 R_{2}$$\mathrm{R}_{1}=\mathrm{R}_{2}$$3 R_{1}=2 R_{2}$$\mathrm{R}_{1}=2 \mathrm{R}_{2}$Correct Option: , 4 Solution:...
Read More →If the lines
Question: If the lines $\frac{\mathrm{x}-1}{2}=\frac{\mathrm{y}+1}{3}=\frac{\mathrm{z}-1}{4}$ and $\frac{\mathrm{x}-3}{1}=\frac{\mathrm{y}-\mathrm{k}}{2}=\frac{\mathrm{z}}{1}$ intersect, then $\mathrm{k}$ is equal to :0$-1$$\frac{2}{9}$$\frac{9}{2}$Correct Option: , 4 Solution:...
Read More →Solve this following
Question: $\frac{d^{2} x}{d y^{2}}$ equals :$\left(\frac{d^{2} y}{d x^{2}}\right)\left(\frac{d y}{d x}\right)^{-2}$$-\left(\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right)\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{-3}$$\left(\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right)^{-1}$$-\left(\frac{d^{2} y}{d x^{2}}\right)^{-1}\left(\frac{d y}{d x}\right)^{-3}$Correct Option: , 2 Solution:...
Read More →The area under the
Question: The area under the curve $y=|\cos x-\sin x|, 0 \leq x \leq \frac{\pi}{2}$, and above $x$-axis is :$2 \sqrt{2}$$2 \sqrt{2}+2$0$2 \sqrt{2}-2$Correct Option: , 4 Solution: The area under the...
Read More →The area of the region
Question: The area of the region (in sq. units), in the first quadrant, bounded by the parabola $y=9 x^{2}$ and the lines $x=0, y=1$ and $y=4$, is :-$7 / 9$$14 / 3$$14 / 9$$7 / 3$Correct Option: , 3 Solution:...
Read More →The area bounded by
Question: The area bounded by the curve $\mathrm{y}=\ln (x)$ and the lines $y=0, y=\ln (3)$ and $x=0$ is equal to :$3 \ln (3)-2$32$3 \ln (3)+2$Correct Option: , 3 Solution:...
Read More →The area
Question: The area (in square units) bounded by the curves $y=\sqrt{x}, 2 y-x+3=0$, $x$-axis and lying in the first quadrant is :93618$\frac{27}{4}$Correct Option: 1 Solution:...
Read More →The area bounded between
Question: The area bounded between the parabolas $x^{2}=\frac{y}{4}$ and $x^{2}=9 y$, and the straight line $y=2$ is :$10 \sqrt{2}$$20 \sqrt{2}$$\frac{10 \sqrt{2}}{3}$$\frac{20 \sqrt{2}}{3}$Correct Option: , 4 Solution:...
Read More →Solve this following
Question: Let $\mathrm{f}:(-1,1) \rightarrow \mathrm{R}$ be a differentiable function with $\mathrm{f}(0)=-1$ and $\mathrm{f}^{\prime}(0)=1$. Let $\mathrm{g}(\mathrm{x})=[\mathrm{f}(2 \mathrm{f}(\mathrm{x})+$ 2)] $]^{2}$. Then $g^{\prime}(0)$ :4$-4$0$-2$Correct Option: , 2 Solution:...
Read More →An equation of a plane parallel to the plane
Question: An equation of a plane parallel to the plane $x-2 y+2 z-5=0$ and at a unit distance from the origin is:$x-2 y+2 z+5=0$$x-2 y+2 z-3=0$$x-2 y+2 z+1=0$$x-2 y+2 z-1=0$Correct Option: , 2 Solution:...
Read More →The area bounded
Question: The area bounded by the curves $y^{2}=4 x$ and $x^{2}=4 y$ is :-0$\frac{32}{3}$$\frac{16}{3}$$\frac{8}{3}$Correct Option: , 3 Solution:...
Read More →The function f : R
Question: The function $\mathrm{f}: \mathrm{R} \rightarrow\left[-\frac{1}{2}, \frac{1}{2}\right]$ defined as $\mathrm{f}(\mathrm{x})=\frac{\mathrm{x}}{1+\mathrm{x}^{2}}$, is :neither injective nor surjective.invertibleinjective but not surjective.surjective but not injectiveCorrect Option: , 4 Solution:...
Read More →The area of the region
Question: The area of the region enclosed by the curves $y=x, x=e, y=\frac{1}{x}$ and the positive $x$-axis is:-$\frac{3}{2}$ square units$\frac{5}{2}$ square units$\frac{1}{2}$ square units1 square unitsCorrect Option: 1 Solution:...
Read More →Solve the equation
Question: If $f(x)+2 f\left(\frac{1}{x}\right)=3 x, x \neq 0$, and $S=\{x \in R: f(x)=f(-x)\} ;$ then $S:$contains more than two elements. (2) (3) c (4)is an empty set.contains exactly one elementcontains exactly two elementsCorrect Option: , 4 Solution:...
Read More →Solve this following
Question: Let $y$ be an implicit function of $x$ defined by $x^{2 x}-2 x^{x} \cot y-1=0$. Then $y^{\prime}(1)$ equals : $\log 2$$-\log 2$$-1$1Correct Option: , 3 Solution:...
Read More →The distance of the point (1,-5,9) from the plane
Question: The distance of the point $(1,-5,9)$ from the plane $x-y+z=5$ measured along a straight from the origin is :$3 \sqrt{5}$$10 \sqrt{3}$$5 \sqrt{3}$$3 \sqrt{10}$Correct Option: , 2 Solution:...
Read More →