One ticket is selected at random from 50 tickets numbered
Question: One ticket is selected at random from 50 tickets numbered $00,01,02, \ldots . ., 49$. Then the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals$\frac{5}{14}$$\frac{1}{50}$$\frac{1}{14}$$\frac{1}{7}$Correct Option: , 2 Solution:...
Read More →For any three positive real numbers a, b and c,
Question: For any three positive real numbers $a, b$ and $c, 9\left(25 a^{2}+b^{2}\right)+25\left(c^{2}-3 a c\right)=15 b(3 a+c)$. Then :a, b and c are in G.P.b, c and a are in G.P.b, c and a are in A.P.a, b and c are in A.P.Correct Option: , 3 Solution:...
Read More →Define F(x) as the product of two real functions
Question: Define $\mathrm{F}(\mathrm{x})$ as the product of two real functions $f_{1}(x)=x, x \in \mathbb{R}$, and $f_{2}(x)=\left\{\begin{array}{ccc}\sin \frac{1}{x}, \text { if } x \neq 0 \\ 0, \text { if } x=0\end{array}\right.$ as follows : $F(x)=\left\{\begin{array}{cll}f_{1}(x) \cdot f_{2}(x) \text { if } x \neq 0 \\ 0, \text { if } x=0\end{array}\right.$ Statement-1 : $F(x)$ is continuous on $\mathbb{R}$. Statement-2 : $\mathrm{f}_{1}(\mathrm{x})$ and $\mathrm{f}_{2}(\mathrm{x})$ are cont...
Read More →For a first order reaction,
Question: For a first order reaction, (A) $\rightarrow$ products, the concentration of A changes from $0.1 \mathrm{M}$ to $0.025 \mathrm{M}$ in 40 minutes. The rate of reaction when the concentration of $\mathrm{A}$ is $0.01 \mathrm{M}$ is :$1.73 \times 10^{-4} \mathrm{M} / \mathrm{min}$$1.73 \times 10^{-5} \mathrm{M} / \mathrm{min}$$3.47 \times 10^{-4} \mathrm{M} / \mathrm{min}$$3.47 \times 10^{-5} \mathrm{M} / \mathrm{m}$Correct Option: Solution: solution not required...
Read More →The equilibrium constant
Question: The equilibrium constant $\left(\mathrm{K}_{\mathrm{C}}\right)$ for the reaction $\mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NO}(\mathrm{g})$ at temperature $\mathrm{T}$ is $4 \times 10^{-4}$. The value of $\mathrm{K}_{\mathrm{C}}$ for the reaction. $\mathrm{NO}(\mathrm{g}) \longrightarrow 1 / 2 \mathrm{~N}_{2}(\mathrm{~g})+1 / 2 \mathrm{O}_{2}(\mathrm{~g})$ at the same temperature is :-$50.0$$0.02$$2.5 \times 10^{2}$$4 \times 10^{-4}$Correct Opti...
Read More →If the angles of elevation of the top of a tower
Question: If the angles of elevation of the top of a tower from three collinear points $A, B$ and $C$, on a line leading to the foot of the tower, are $30^{\circ}, 45^{\circ}$ and $60^{\circ}$ respectively, then the ratio, $\mathrm{AB}$ : $B C$, is:$1: \sqrt{3}$2: 3$\sqrt{3}: 1$$\sqrt{3}: \sqrt{2}$Correct Option: , 3 Solution:...
Read More →If, for a positive integer n, the quadratic equation,
Question: If, for a positive integer n, the quadratic equation, $x(x+1)+(x+1)(x+2)+\ldots .+(x+n-1)(x+n)=10 n$ has two consecutive integral solutions, then $\mathrm{n}$ is equal to :1112910Correct Option: 1 Solution:...
Read More →A vessel at
Question: A vessel at $1000 \mathrm{~K}$ contains $\mathrm{CO}_{2}$ with a pressure of $0.5$ atm. Some of the $\mathrm{CO}_{2}$ is converted into $\mathrm{CO}$ on the addition of graphite. If the total pressure at equilibrium is $0.8 \mathrm{~atm}$, the value of $\mathrm{K}$ is :-$0.3 \mathrm{~atm}$$0.18 \mathrm{~atm}$$1.8 \mathrm{~atm}$$3 \mathrm{~atm}$Correct Option: , 3 Solution:...
Read More →The rate of a chemical reaction doubles for every
Question: The rate of a chemical reaction doubles for every 10C rise of temperature. If the temperature is raised by 50C, the rate of the reaction increases by about :-32 times64 times10 times24 timesCorrect Option: , 3 Solution:...
Read More →If the sum of the first ten terms of the series
Question: If the sum of the first ten terms of the series $\left(1 \frac{3}{5}\right)^{2}+\left(2 \frac{2}{5}\right)^{2}+\left(3 \frac{1}{5}\right)^{2}+4^{2}+\left(4 \frac{4}{5}\right)^{2}+\ldots$, is $\frac{16}{5} \mathrm{~m}$, then $\mathrm{m}$ is equal to :-99102101100Correct Option: , 3 Solution:...
Read More →The values of p and q for which the function
Question: The values of $p$ and $q$ for which the function $f(x)=$ $f(x)= \begin{cases}\frac{\sin (p+1) x+\sin x}{x}, x0 \\ q , x=0 \text { is continuous for } \\ \frac{\sqrt{x+x^{2}}-\sqrt{x}}{x^{\frac{3}{2}}}, x0\end{cases}$ all $x$ in $R$, are :-$\mathrm{p}=-\frac{3}{2}, \mathrm{q}=\frac{1}{2}$$\mathrm{p}=\frac{1}{2}, \mathrm{q}=\frac{3}{2}$$\mathrm{p}=\frac{1}{2}, \mathrm{q}=-\frac{3}{2}$$\mathrm{p}=\frac{5}{2}, \mathrm{q}=\frac{1}{2}$Correct Option: 1 Solution:...
Read More →Which of the following compounds
Question: Which of the following compounds contain(s) no covalent bond(s)?] $\mathrm{KCl}, \mathrm{PH}_{3}, \mathrm{O}_{2}, \mathrm{~B}_{2} \mathrm{H}_{6}, \mathrm{H}_{2} \mathrm{SO}_{4}$$\mathrm{KCl}, \mathrm{H}_{2} \mathrm{SO}_{4}$$\mathrm{KCl}$$\mathrm{KCl}, \mathrm{B}_{2} \mathrm{H}_{6}$$\mathrm{KCl}, \mathrm{B}_{2} \mathrm{H}_{6}, \mathrm{PH}_{3}$Correct Option: , 2 Solution:...
Read More →Solve the equation
Question: If the $2^{\text {nd }}, 5^{\text {th }}$ and $9^{\text {th }}$ terms of a non-constant A.P. are in G.P., then the common ratio of this G.P.is$\frac{7}{4}$$\frac{8}{5}$$\frac{4}{3}$1Correct Option: Solution:...
Read More →ABCD is a trapezium such that AB and CD are parallel
Question: $\mathrm{ABCD}$ is a trapezium such that $\mathrm{AB}$ and $\mathrm{CD}$ are parallel and $\mathrm{BC} \perp \mathrm{CD}$. If $\angle \mathrm{ADB}=\theta, \mathrm{BC}=$ $p$ and $C D=q$, then $A B$ is equal to$\frac{\left(p^{2}+q^{2}\right) \sin \theta}{p \cos \theta+q \sin \theta}$$\frac{p^{2}+q^{2} \cos \theta}{p \cos \theta+q \sin \theta}$$\frac{p^{2}+q^{2}}{p^{2} \cos \theta+q^{2} \sin \theta}$$\frac{\left(p^{2}+q^{2}\right) \sin \theta}{(p \cos \theta+q \sin \theta)^{2}}$Correct Op...
Read More →According to molecular
Question: According to molecular orbital theory, which of the following will not be a viable molecule ?$\mathrm{He}_{2}^{+}$$\mathrm{H}_{2}^{-}$$\mathrm{H}_{2}^{2-}$$\mathrm{He}_{2}^{2+}$Correct Option: , 3 Solution:...
Read More →Total number of lone
Question: Total number of lone pair of electrons in $\mathrm{I}_{3}^{-}$ion is69123Correct Option: , 2 Solution:...
Read More →If m is the A.M. of two distinct real numbers l and n(l, n > 1) a
Question: If $\mathrm{m}$ is the A.M. of two distinct real numbers $l$ and $n(1, n1)$ and $G_{1}, G_{2}$ and $G_{3}$ are three geometric means between 1 and $n$, then $G_{1}^{4}+2 G_{2}^{4}+G_{3}^{4}$ equals -$4 \operatorname{lmn}^{2}$$41^{2} m^{2} n^{2}$$4 l^{2} \mathrm{mn}$$4 \operatorname{lm}^{2} n$Correct Option: , 4 Solution:...
Read More →A reactant (A) forms two products :
Question: A reactant (A) forms two products : $\mathrm{A} \stackrel{\mathrm{k}_{1}}{\longrightarrow} \mathrm{B}$, Activation Energy $\mathrm{Ea}_{1}$ $\mathrm{A} \stackrel{\mathrm{k}_{1}}{\longrightarrow} \mathrm{C}$, Activation Energy $\mathrm{Ea}_{2}$ If $\mathrm{Ea}_{2}=2 \mathrm{Ea}_{1}$, then $\mathrm{k}_{1}$ and $\mathrm{k}_{2}$ are related as :-$\mathrm{k}_{1}=2 \mathrm{k}_{2} \mathrm{e}^{\mathrm{Ea}_{2} / \mathrm{RT}}$$\mathrm{k}_{1}=\mathrm{k}_{2} \mathrm{e}^{\mathrm{Ea}_{1} / \mathrm{R...
Read More →The value of
Question: The value of $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\sin ^{2} x}{1+2^{x}} d x$ is :$\frac{\pi}{2}$$4 \pi$$\frac{\pi}{4}$$\frac{\pi}{8}$Correct Option: , 3 Solution:...
Read More →Which of the following species is not paramagnetic :-
Question: Which of the following species is not paramagnetic :-$\mathrm{NO}$$\mathrm{CO}$$\mathrm{O}_{2}$$B_{2}$Correct Option: , 2 Solution:...
Read More →Solve the equation
Question: If $(10)^{9}+2(11)^{1}(10)^{8}+3(11)^{2}(10)^{7}+\ldots \ldots+10(11)^{9}=\mathrm{k}(10)^{9}$, then $\mathrm{k}$ is equal to :$\frac{121}{10}$$\frac{441}{100}$100110Correct Option: , 3 Solution:...
Read More →The species in which
Question: The species in which the $\mathrm{N}$ atom is in a state of sp hybridization is :-$\mathrm{NO}_{2}$$\mathrm{NO}_{2}^{+}$$\mathrm{NO}_{2}^{-}$$\mathrm{NO}_{3}^{-}$Correct Option: , 2 Solution:...
Read More →Solve this following Question
Question: The integral $\int_{\frac{\pi}{4}}^{\frac{3 \pi}{4}} \frac{d x}{1+\cos x}$ is equal to :--1-224Correct Option: , 3 Solution:...
Read More →Amongst
Question: Amongst $\mathrm{LiCl}, \mathrm{RbCl}, \mathrm{BeCl}_{2}$ and $\mathrm{MgCl}_{2}$ the compounds with the greatest and the least ionic character, respectively are :$\mathrm{RbCl}$ and $\mathrm{MgCl}_{2}$$\mathrm{LiCl}$ and $\mathrm{RbCl}$$\mathrm{MgCl}_{2}$ and $\mathrm{BeCl}_{2}$$\mathrm{RbCl}$ and $\mathrm{BeCl}_{2}$Correct Option: , 4 Solution:...
Read More →Three positive numbers form an increasing G.P.
Question: Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is :$\sqrt{2}+\sqrt{3}$$3+\sqrt{2}$$2-\sqrt{3}$$2+\sqrt{3}$Correct Option: Solution:...
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