The area bounded by

Question: The area bounded by the curves $y=\cos x$ and $y=\sin x$ between the ordinates $x=0$ and $x=$ $\frac{3 \pi}{2}$ is :-$4 \sqrt{2}-2$$4 \sqrt{2}+2$$4 \sqrt{2}-1$$4 \sqrt{2}+1$Correct Option: 1 Solution:...

Solve the equation

Question: If $\mathrm{a} \in \mathrm{R}$ and the equation $-3(\mathrm{x}-[\mathrm{x}])^{2}+2(\mathrm{x}-[\mathrm{x}])+\mathrm{a}^{2}=0$ (where $[\mathrm{x}]$ deontes the greatest integer $\leq x)$ has no integral solution, then all possible values of a lie in the interval:$(-1,0) \cup(0,1)$$(1,2)$$(-2,-1)$$(-\infty,-2) \cup(2, \infty)$Correct Option: Solution:...

Let f be a function defined by

Question: Let $\mathrm{f}$ be a function defined by $\mathrm{f}(\mathrm{x})=(\mathrm{x}-1)^{2}+1,(\mathrm{x} \geq 1)$ Statement - 1 : The set $\left\{x: f(x)=f^{-1}(x)\right\}=\{1,2\}$ Statement - 2 : $f$ is bijection and $\mathrm{f}^{-1}(\mathrm{x})=1+\sqrt{\mathrm{x}-1}, \mathrm{x} \geq 1$Statement1 is true, Statement2 is false.Statement1 is false, Statement2 is true.Statement1 is true, Statement2 is true ; Statement2 is a correct explanation for Statement 1.Statement1 is true, Statement2 is t...

The area of the region bounded

Question: The area of the region bounded by the parabola $(y-2)^{2}=x-1$, the tangent to the parabola at the point $(2,3)$ and the $x$-axis is :-91236Correct Option: 1 Solution:...

The domain of the function

Question: The domain of the function $f(x)=\frac{1}{\sqrt{|x|-x}}$ is :-$(-\infty, 0)$$(-\infty, \infty)-\{0\}$$(-\infty, \infty)$$(0, \infty)$Correct Option: 1 Solution: $f(x)=\frac{1}{\sqrt{|x|-x}}$...

Solve the equation

Question: For real $x$, let $f(x)=x^{3}+5 x+1$, then :-f is one-one and onto Ris neither one-one nor onto Rf is one-one but not onto Rf is onto R but not one-oneCorrect Option: 1 Solution:...

Statement-1 : The point A(1,0,7) is the mirror image

Question: Statement-1 : The point $\mathrm{A}(1,0,7)$ is the mirror image of the point $\mathrm{B}(1,6,3)$ in the line : $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$ Statement-2 : The line : $\frac{\mathrm{x}}{1}=\frac{\mathrm{y}-1}{2}=\frac{\mathrm{z}-2}{3}$ bisects the line segment joining $\mathrm{A}(1,0,7)$ and $\mathrm{B}(1,6,3)$Statement- 1 is true, Statement- 2 is false.Statement- 1 is false, Statement-2 is trueStatement- 1 is true, Statement- 2 is true; Statement- 2 is a correct explanation...

If the angle between the line

Question: If the angle between the line $x=\frac{y-1}{2}=\frac{z-3}{\lambda}$ and the plane $x+2 y+3 z=4$ is $\cos ^{-1}\left(\sqrt{\frac{5}{14}}\right)$, then $\lambda$ equals:-$\frac{2}{5}$$\frac{5}{3}$$\frac{2}{3}$$\frac{3}{2}$Correct Option: Solution:...

Question: Statement-1 : The point $A(3,1,6)$ is the mirror image of the point $B(1,3,4)$ in the plane $x-y+z=5$ Statement-2 : The plane $x-y+z=5$ bisects the line segment joining $A(3,1,6)$ and $B(1,3,4)$Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement$1 .$Statement-1 is true, Statement $-2$ is true ; Statement-2 is not a correct explanation for statement$1 .$Statement-1 is true, $n$ Statement-2 is false.Statement-1 is false, Statement-2 is true.Correc...

The strongest acid

Question: The strongest acid amongst the following compounds is ?$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}(\mathrm{Cl}) \mathrm{CO}_{2} \mathrm{H}$$\mathrm{ClCH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COOH}$$\mathrm{CH}_{3} \mathrm{COOH}$$\mathrm{HCOOH}$Correct Option: 1 Solution:...

Tangent and normal are drawn at

Question: Tangent and normal are drawn at $\mathrm{P}(16,16)$ on the parabola $\mathrm{y}^{2}=16 \mathrm{x}$, which intersect the axis of the parabola at $A$ and $B$, respectively. If $C$ is the centre of the circle through the points $\mathrm{P}, \mathrm{A}$ and $\mathrm{B}$ and $\angle \mathrm{CPB}=\theta$, then a value of $\tan \theta$ is-23$\frac{4}{3}$$\frac{1}{2}$Correct Option: 1 Solution:...

The correct order of increasing basicity

Question: The correct order of increasing basicity of the given conjugate base $\left(\mathrm{R}=\mathrm{CH}_{3}\right)$ is :-$\mathrm{RCO} \overline{\mathrm{O}}\mathrm{HC} \equiv \overline{\mathrm{C}}\overline{\mathrm{NH}_{2}}\overline{\mathrm{R}}$$\mathrm{RCO} \overline{\mathrm{O}}\mathrm{HC} \equiv \overline{\mathrm{C}}\overline{\mathrm{R}}\overline{\mathrm{N}} \mathrm{H}_{2}$$\overline{\mathrm{R}}\mathrm{HC} \equiv \overline{\mathrm{C}}\mathrm{RCO} \overline{\mathrm{O}}\overline{\mathrm{N}} ...

The projections of a vector on the three coordinate

Question: The projections of a vector on the three coordinate axis are $6,-3,2$ respectively. The direction cosines of the vector are :-$\frac{6}{7}, \frac{-3}{7}, \frac{2}{7}$$\frac{-6}{7}, \frac{-3}{7}, \frac{2}{7}$$6,-3,2$$\frac{6}{5}, \frac{-3}{5}, \frac{2}{5}$Correct Option: 1 Solution:...

The radius of a circle, having minimum area,

Question: The radius of a circle, having minimum area, which touches the curve $y=4-x^{2}$ and the lines, $y=|x|$ is :-$4(\sqrt{2}+1)$$2(\sqrt{2}+1)$$2(\sqrt{2}-1)$None of theseCorrect Option: Solution: which is not in options therefore it must be bonus. But according to history of JEE-Mains it seems they had following line of thinking. Given curves are $y=4-x^{2}$ and $y=|x|$...

For which of the following molecule

Question: For which of the following molecule significant $\mu^{1} 0$ Only (3)(3) and (4)Only (1)(1) and (2)Correct Option: , 2 Solution:...

Solve this following Question

Question: Let the line $\frac{\mathrm{x}-2}{3}=\frac{\mathrm{y}-1}{-5}=\frac{\mathrm{z}+2}{2}$ lie in the plane $\mathrm{x}+3 \mathrm{y}-\alpha \mathrm{z}+\beta=0$. Then $(\alpha, \beta)$ equals$(5,-15)$$(-5,5)$$(6,-17)$$(-6,7)$Correct Option: 1 Solution:...

Which of the following name formula

Question: Which of the following name formula combinations is not correct? Solution: (3) $\left[\mathrm{Mn}(\mathrm{CN})_{5}\right]^{2-}$ Pentacyanomagnate (II) ion...

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary

Question: From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is-less than 500at least 500 but less than 750at least 750 but less than 1000at least 1000Correct Option: , 4 Solution:...

The order of stability of the following carbocations

Question: The order of stability of the following carbocations $\mathrm{III}\mathrm{II}\mathrm{I}$II III II II IIIIII I IICorrect Option: , 4 Solution: Solution not required...

Let P be the point on the parabola,

Question: Let $\mathrm{P}$ be the point on the parabola, $\mathrm{y}^{2}=8 \mathrm{x}$ which is at a minimum distance from the cente $\mathrm{C}$ of the circle, $\mathrm{x}^{2}+(\mathrm{y}+6)^{2}=1$. Then the equation of the circle, passing through $\mathrm{C}$ and having its centre at $\mathrm{P}$ is :$x^{2}+y^{2}-4 x+9 y+18=0$$x^{2}+y^{2}-4 x+8 y+12=0$$x^{2}+y^{2}-x+4 y-12=0$$x^{2}+y^{2}-\frac{x}{4}+2 y-24=0$Correct Option: , 2 Solution:...

A man X has 7 friends, 4 of them are ladies and 3 are men.

Question: A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is :484485468469Correct Option: , 2 Solution:...

Solve this following

Question: A player $\mathrm{X}$ has a biased coin whose probability of showing heads is $\mathrm{p}$ and a player $\mathrm{Y}$ has a fair coin. They start playing a game with their own coins and play atlernately. The player who throws a head first is a winner. If X starts the game, and the probability of winning the game by both the players is equal, then the value of ' $p$ ' is :-$\frac{1}{3}$$\frac{2}{5}$$\frac{1}{4}$$\frac{1}{5}$Correct Option: 1 Solution: Solution not required...

Let O be the vertex and Q be any point on the parabola,

Question: Let $\mathrm{O}$ be the vertex and $\mathrm{Q}$ be any point on the parabola, $\mathrm{x}^{2}=8 \mathrm{y}$. If the point $\mathrm{P}$ divides the line segment $\mathrm{OQ}$ internally in the ratio $1: 3$, then the locus of $\mathrm{P}$ is :-$y^{2}=2 x$$x^{2}=2 y$$x^{2}=y$$y^{2}=x$Correct Option: Solution: Let P(h, k) divides segment...

Among the following the

Question: Among the following the molecule with the lowest dipole moment is :-$\mathrm{CHCl}_{3}$$\mathrm{CH}_{2} \mathrm{Cl}_{2}$$\mathrm{CCl}_{4}$$\mathrm{CH}_{3} \mathrm{Cl}$Correct Option: , 3 Solution: Solution not required...

Solve this following Question

Question: Let $g(x)=\cos x^{2}, f(x)=\sqrt{x}$ and $\alpha, \beta(\alpha\beta)$ be the roots of the quadratic equation $18 x^{2}-9 \pi x+\pi^{2}=0$. Then the area (in sq. units) bounded by the curve $y=(g o f)(x)$ and the lines $x=\alpha, x=\beta$ and $y=0$ is-$\frac{1}{2}(\sqrt{3}+1)$$\frac{1}{2}(\sqrt{3}-\sqrt{2})$$\frac{1}{2}(\sqrt{2}-1)$$\frac{1}{2}(\sqrt{3}-1)$Correct Option: , 4 Solution:...