The area of the region given by \(\left\{(x, y): x y \leq 8,1 \leq y \leq x^2\right\}\) is :
The sum of the absolute maximum and minimum values of the function \(f(x)=\left|x^2-5 x+6\right|-3 x+2\)in the interval \([-1,3]\) is equal to :
As shown in figure, a $70 kg$ garden roller is pushed with a force of $\vec{F}=200 N$ at an angle of $30^{\circ}$ with horizontal. The normal reaction on the roller is (Given $g=10 m s ^{-2}$ )
An organic compound 'A' with emperical formula $C _6 H _6 O$ gives sooty flame on burning Its reaction with bromine solution in low polarity solvent results in high yield of $B .B$ is
Choose the correct set of reagents for the following conversion trans $\left( Ph - CH = CH - CH _3\right) \rightarrow \operatorname{cis}\left( Ph - CH = CH - CH _3\right)$
Consider the following reaction
The correct statement for product $B$ is It is
$H _2 O _2$ acts as a reducing agent in
Cobalt chloride when dissolved in water forms pink colored complex $X$ which has octahedral geometry. This solution on treating with cone $HCl$ forms deep blue complex, $\underline{Y}$ which has a $\underline{Z}$ geometry $X, Y$ and $Z$, respectively, are
Match List I with List II
Choose the correct answer from the options given below :
The correct order of melting points of dichlorobenzenes is
The correct increasing order of the ionic radii is
If the domain of the function $f(x)=\frac{[x]}{1+x^2}$, where $[x]$ is greatest integer $\leq x$, is $[2,6)$, then its range is
Let a circle $C_1$ be obtained on rolling the circle $x^2+y^2-4 x-6 y+11=0$ upwards 4 units on the tangent $T$ to it at the point $(3,2)$ Let $C_2$ be the image of $C_1$ in $T$ Let $A$ and $B$ be the centers of circles $C_1$ and $C_2$ respectively, and $M$ and $N$ be respectively the feet of perpendiculars drawn from $A$ and $B$ on the $x$-axis. Then the area of the trapezium AMNB is:
Cyclohexylamine when treated with nitrous acid yields (P) On treating (P) with $PCC$ results in (Q) When $(Q)$ is heated with dil. $NaOH$ we get $(R)$ The final product $(R)$ is :
In the following halogenated organic compounds the one with maximum number of chlorine atoms in its structure is :
A hydrocarbon ' $X$ ' with formula $C _6 H _8$ uses two moles of $H _2$ on catalytic hydrogenation of its one mole On ozonolysis, ' $X$ ' yields two moles of methane dicarbaldehyde The hydrocarbon ' $X$ ' is :
Let the mean and standard deviation of marks of class A of $100$ students be respectively $40$ and $\alpha$ (> 0 ), and the mean and standard deviation of marks of class B of $n$ students be respectively $55$ and 30 $-\alpha$. If the mean and variance of the marks of the combined class of $100+ n$ students are respectively $50$ and $350$ , then the sum of variances of classes $A$ and $B$ is :
