Solve this following
Question: Let $\mathrm{R}$ be the set of real numbers. Statement-1: $A=\{(x, y) \in R \quad R: y-x$ is an integer $\}$ is an equivalence relation on $R$. Statement-2: $B=\{(x, y) \in R \quad R: x=\alpha y$ for some rational number $\alpha\}$ is an equivalence relation on $\mathrm{R}$. 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 for Statement- 1Statement- 1 is true, Stateme...
Read More →Solve this following Question
Question: The integral $\int_{2}^{4} \frac{\log x^{2}}{\log x^{2}+\log \left(36-12 x+x^{2}\right)} d x$ is equal to :1624Correct Option: 1 Solution:...
Read More →Solve the equation
Question: Let $\alpha$ and $\beta$ be the roots of equation $\mathrm{px}^{2}+\mathrm{qx}+\mathrm{r}=0, \mathrm{p} \neq 0$. If $\mathrm{p}, \mathrm{q}, \mathrm{r}$ are in A.P. and $\frac{1}{\alpha}+\frac{1}{\beta}=4$, then the value of $|\alpha-\beta|$ is:$\frac{\sqrt{61}}{9}$$\frac{2 \sqrt{17}}{9}$$\frac{\sqrt{34}}{9}$$\frac{2 \sqrt{13}}{9}$Correct Option: , 4 Solution:...
Read More →Consider the reaction:
Question: Consider the reaction: $\mathrm{Cl}_{2}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{~S}(\mathrm{aq}) \rightarrow \mathrm{S}(\mathrm{s})+2 \mathrm{H}^{+}(\mathrm{aq})+2 \mathrm{Cl}^{-}(\mathrm{aq})$ The rate equation for this reaction is rate $=\mathrm{k}\left[\mathrm{Cl}_{2}\right]\left[\mathrm{H}_{2} \mathrm{~S}\right]$ Which of these mechanisms is/are consistent with this rate equation? A. $\mathrm{Cl}_{2}+\mathrm{H}_{2} \mathrm{~S} \rightarrow \mathrm{H}^{+}+\mathrm{Cl}^{-}+\mathrm{Cl}^{+}+...
Read More →The eccentricity of an ellipse whose centre is at the origin
Question: The eccentricity of an ellipse whose centre is at the origin is $\frac{1}{2}$. If one of its directices is $x=-4$, then the equation of the normal to it at $\left(1, \frac{3}{2}\right)$ is :-x + 2y = 42y x = 24x 2y = 14x + 2y = 7Correct Option: , 3 Solution:...
Read More →Consider the following relations :-
Question: Consider the following relations :- $\mathrm{R}=\{(\mathrm{x}, \mathrm{y}) \mid \mathrm{x}, \mathrm{y}$ are real numbers and $\mathrm{x}=$ wy for some rational number $\mathrm{w}\}$; $\mathrm{S}=\left\{\left(\frac{\mathrm{m}}{\mathrm{n}}, \frac{\mathrm{p}}{\mathrm{q}}\right) \mid \mathrm{m}, \mathrm{n}, \mathrm{p}\right.$ and $\mathrm{q}$ are integers such that $\mathrm{n}, \mathrm{q} \neq 0$ and $\left.\mathrm{qm}=\mathrm{pn}\right\}$ Then : $\mathrm{R}$ is an equivalence relation but...
Read More →Solve this following Question
Question: The integral $\int_{0}^{\pi} \sqrt{1+4 \sin ^{2} \frac{x}{2}-4 \sin \frac{x}{2}} d x$ equals :$\pi-4$$\frac{2 \pi}{3}-4-4 \sqrt{3}$$4 \sqrt{3}-4$$4 \sqrt{3}-4-\frac{\pi}{3}$Correct Option: , 4 Solution:...
Read More →The sum of first 20 terms of the sequence
Question: The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, ......, is :$\frac{7}{81}\left(179-10^{-20}\right)$$\frac{7}{9}\left(99-10^{-20}\right)$$\frac{7}{81}\left(179+10^{-20}\right)$$\frac{7}{9}\left(99-10^{-20}\right)$Correct Option: , 3 Solution:...
Read More →The time for half life period of a certain reaction
Question: The time for half life period of a certain reaction A $\longrightarrow$ Products is 1 hour, when the initial concentration of the reactant ' $\mathrm{A}^{\prime}$ is $2.0 \mathrm{~mol} \mathrm{} \mathrm{L}^{-1}$, How much time does it take for its concentration to come from $0.50$ to $0.25 \mathrm{~mol} \mathrm{} \mathrm{L}^{-1}$ if it is a zero order reaction?1 h4 h0.5 h0.29Correct Option: , 4 Solution: For zero order reaction...
Read More →The area (in sq. units) of the quadrilateral
Question: The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse $\frac{x^{2}}{9}+\frac{y^{2}}{5}=1$ is :$\frac{27}{2}$27$\frac{27}{4}$18Correct Option: , 2 Solution:...
Read More →If 100 times the 100 term of an A.P.
Question: If 100 times the $100^{\text {th }}$ term of an A.P. with non-zero common difference equals the 50 times its $50^{\text {th }}$ term, then the $150^{\text {th }}$ term of this A.P. is :zero150150 times its $50^{\text {th }}$ term150Correct Option: 1 Solution:...
Read More →Statement-I : The value of the integral
Question: Statement-I : The value of the integral $\int_{\pi / 6}^{\pi / 3} \frac{\mathrm{dx}}{1+\sqrt{\tan x}}$ is equal to $\frac{\pi}{6}$. Statement-II : $\int_{a}^{b} f(x) d x=\int_{a}^{b} f(a+b-x) d x$.Statement-I is true, Statement-II is true; Statement-II is a correct explanation for Statement-I.Statement-I is true, Statement-II is true; Statement-II is not a correct explanation for Statement-I.Statement-I is true, Statement-II is false.Statement-I is false, Statement-II is true.Correct O...
Read More →The half life period of a first order chemical reaction
Question: The half life period of a first order chemical reaction is 6.93 minutes. The time required for the completion of 99% of the chemical reaction will be (log 2 = 0.301) :-46.06 minutes460.6 minutes230.3 minutes23.03 minutesCorrect Option: , 2 Solution: $\mathrm{k}=\frac{0.693}{\mathrm{t}_{1 / 2}}=\frac{0.693}{6.93}=0.1 \mathrm{~min}^{-1}$...
Read More →The locus of the foot of perpendicular drawn from the centre
Question: The locus of the foot of perpendicular drawn from the centre of the ellipse $x^{2}+3 y^{2}=6$ on any tangent to it is :-$\left(x^{2}-y^{2}\right)^{2}=6 x^{2}+2 y^{2}$$\left(x^{2}-y^{2}\right)^{2}=6 x^{2}-2 y^{2}$$\left(x^{2}+y^{2}\right)^{2}=6 x^{2}+2 y^{2}$$\left(x^{2}+y^{2}\right)^{2}=6 x^{2}-2 y^{2}$Correct Option: , 3 Solution:...
Read More →Statement-1 : The sum of the series
Question: Statement-1 : The sum of the series $1+(1+2+4)+(4+6+9)+(9+12+16)$ $+\ldots \ldots .+(361+380+400)$ is $8000 .$ Statement-2 : $\sum_{\mathrm{k}=1}^{\mathrm{n}}\left(\mathrm{k}^{3}-(\mathrm{k}-1)^{3}\right)=\mathrm{n}^{3}$, for any natural number $\mathrm{n}$.Statement1 is true, Statement2 is false.Statement1 is false, Statement2 is true.Statement1 is true, Statement2 is true ; Statement2 is a correct explanation for Statement1.Statement1 is true, Statement2 is true ; Statement2 is not a...
Read More →The correct order of bond
Question: The correct order of bond dissociation energy among $\mathrm{N}_{2}, \mathrm{O}_{2}, \mathrm{O}_{2}$-is shown in which of the following arrangements?$\mathrm{N}_{2}\mathrm{O}_{2}\mathrm{O}_{2}^{-}$$\mathrm{O}_{2}\mathrm{O}_{2}^{-}\mathrm{N}_{2}$$\mathrm{N}_{2}\mathrm{O}_{2}^{-}\mathrm{O}_{2}$$\mathrm{O}_{2}^{-}\mathrm{O}_{2}\mathrm{N}_{2}$Correct Option: 1 Solution:...
Read More →At 518°C, the rate of decomposition of a sample
Question: At $518^{\circ} \mathrm{C}$, the rate of decomposition of a sample of gaseous acetaldehyde, initially at a pressure of 363 Torr, was $1.00$ Torr $\mathrm{s}^{-1}$ when $5 \%$ had reacted and $0.5$ Torr $^{-1}$ when $33 \%$ had reacted. The order of the reaction is :3102Correct Option: , 4 Solution:...
Read More →Solve this following Question
Question: If $g(x)=\int_{0}^{x} \cos 4 t d t$, then $g(x+\pi)$ equals :$\mathrm{g}(\mathrm{x}) \cdot \mathrm{g}(\pi)$$\frac{g(x)}{g(\pi)}$$g(x)+g(\pi)$$g(x)-g(\pi)$Correct Option: 3, 4, Solution:...
Read More →A point on the ellipse,
Question: A point on the ellipse, $4 x^{2}+9 y^{2}=36$, where the normal is parallel to the line, $4 x-2 y-5$ $=0$, is :-$\left(\frac{8}{5},-\frac{9}{5}\right)$$\left(-\frac{9}{5}, \frac{8}{5}\right)$$\left(\frac{8}{5}, \frac{9}{5}\right)$$\left(\frac{9}{5}, \frac{8}{5}\right)$Correct Option: , 4 Solution:...
Read More →Solve the equation
Question: Let $a_{n}$ be the $n^{\text {th }}$ term of an A.P. If $\sum_{r=1}^{100} a_{2 r}=\alpha$ and $\sum_{r=1}^{100} a_{2 r-1}=\beta$, then the common difference of the A.P. is :$\frac{\alpha-\beta}{200}$$\alpha-\beta$$\frac{\alpha-\beta}{100}$$\beta-\alpha$Correct Option: , 3 Solution: $\frac{100}{2}[\mathrm{a}+\mathrm{a}+198 \mathrm{~d}]=\beta \Rightarrow 50(2 \mathrm{a}+198 \mathrm{~d})=\beta \ldots \ldots(2)$ (1) $-(2) \quad \alpha-\beta=50(2 \mathrm{~d})=\mathrm{d}=\frac{\alpha-\beta}{...
Read More →Shapes of certain
Question: Shapes of certain interhalogen compounds are stated below. Which one of them is not correctly stated?$\mathrm{IF}_{7}$ : Pentagonal bipyramid$\mathrm{BrF}_{5}$ : Trigonal bipyramid$\mathrm{ICl}_{3}$ : Planar dimeric$\mathrm{BrF}_{3}$ : Planar T-shapedCorrect Option: , 2 Solution:...
Read More →Solve this following
Question: Let $\mathrm{S}=\{\mathrm{x} \in \mathrm{R}: \mathrm{x} \geq 0$ and $2|\sqrt{\mathrm{x}}-3|+\sqrt{\mathrm{x}}(\sqrt{\mathrm{x}}-6)+6=0\}$. Then $\mathrm{S}$ :contains exactly one element.contains exactly two elements.contains exactly four elements.is an empty set.Correct Option: , 2 Solution:...
Read More →A man saves Rs. 200 in each of the first three months of his service.
Question: .A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after :-20 months21 months18 months19 monthsCorrect Option: , 2 Solution:...
Read More →Two reactions
Question: Two reactions $R_{1}$ and $R_{2}$ have identical pre-exponential factors. Activation energy of $R_{1}$ exceeds that of $\mathrm{R}_{2}$ by $10 \mathrm{~kJ} \mathrm{~mol}^{-1}$. If $\mathrm{k}_{1}$ and $\mathrm{k}_{2}$ are rate constants for reactions $\mathrm{R}_{1}$ and $\mathrm{R}_{2}$ respectively at $300 \mathrm{~K}$, then $\ln \left(\mathrm{k}_{2} / \mathrm{k}_{1}\right)$ is equal to :- $\left(\mathrm{R}=8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right)$81264Correct Opt...
Read More →If the curves
Question: If the curves $\frac{x^{2}}{\alpha}+\frac{y^{2}}{4}=1$ and $y^{3}=16 x$ intersect at right angles, then a value of $\alpha$ is :$\frac{4}{3}$$\frac{3}{4}$$\frac{1}{2}$2Correct Option: 1 Solution:...
Read More →