A multiple choice examination has 5 questions.
Question: A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is :$\frac{17}{3^{5}}$$\frac{13}{3^{5}}$$\frac{11}{3^{5}}$$\frac{10}{3^{5}}$Correct Option: , 3 Solution:...
Read More →Three numbers are chosen at random without replacement from
Question: Three numbers are chosen at random without replacement from $\{1,2,3, \ldots . .8\}$. The probability that their minimum is 3 , given that their maximum is 6 , is: $\frac{2}{5}$$\frac{3}{8}$$\frac{1}{5}$$\frac{1}{4}$Correct Option: , 3 Solution:...
Read More →If the equations
Question: If the equations $x^{2}+2 x+3=0$ and $a x^{2}+b x+c=0, a, b, c \in R$, have a common root, then $\mathrm{a}: \mathrm{b}: \mathrm{c}$ is :1 : 2 : 33 : 2 : 11 : 3 : 23 : 1 : 2Correct Option: 1 Solution:...
Read More →The time for half life period
Question: The time for half life period of a certain reaction $\mathrm{A} \longrightarrow$ Products is 1 hour, when the initial concentration of the reactant 'A' is $2.0 \mathrm{~mol} \mathrm{~L}-1$, 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 \mathrm{~h}$$4 \mathrm{~h}$$0.5 \mathrm{~h}$$0.29$.Correct Option: , 4 Solution:...
Read More →Tangents are drawn to the hyperbola
Question: Tangents are drawn to the hyperbola $4 x^{2}-y^{2}=36$ at the point $P$ and $Q$. If these tangents intersect at the point $T(0,3)$ then the area (in sq. units) of $\triangle P T Q$ is -$54 \sqrt{3}$$60 \sqrt{3}$$36 \sqrt{5}$$45 \sqrt{5}$Correct Option: , 4 Solution:...
Read More →The magnetic moment (spin only)
Question: The magnetic moment (spin only) of $\left[\mathrm{NiCl}_{4}\right]^{2-}$ is :-$2.82 \mathrm{BM}$$1.41 \mathrm{BM}$$1.82 \mathrm{BM}$$5.46 \mathrm{BM}$Correct Option: 1 Solution: Solution not required...
Read More →The magnetic moment (spin only)
Question: The magnetic moment (spin only) of $\left[\mathrm{NiCl}_{4}\right]^{2-}$ is :-$2.82 \mathrm{BM}$$1.41 \mathrm{BM}$$1.82 \mathrm{BM}$$5.46 \mathrm{BM}$Correct Option: 1 Solution: Solution not required...
Read More →he area bounded by the curves
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$$4 \sqrt{2}+1$Correct Option: 1 Solution:...
Read More →The half life period of a
Question: The half life period of a first order chemical reaction is $6.93$ minutes. The time required for the completion of $99 \%$ of the chemical reaction will be $(\log 2=0.301):-$$46.06$ minutes$460.6$ minutes$230.3$ minutes$23.03$ minutesCorrect Option: 1 Solution:...
Read More →The equation
Question: The equation $e^{\sin x}-e^{-\sin x}-4=0$ has :exactly four real roots.infinite number of real roots.no real roots.exactly one real root.Correct Option: , 3 Solution:...
Read More →Solve this following
Question: Let $A, B, C$ be pairwise independent events with $P(C)0$ and $P(A \cap B \cap C)=0$. Then $\mathrm{P}\left(\mathrm{A}^{\mathrm{c}} \cap \mathrm{B}^{\mathrm{c}} \mid \mathrm{C}\right)$ is equal to: $P\left(A^{c}\right)-P(B)$$\mathrm{P}(\mathrm{A})-\mathrm{P}\left(\mathrm{B}^{\mathrm{c}}\right)$$P\left(A^{c}\right)+P\left(B^{c}\right)$$P\left(A^{c}\right)-P\left(B^{c}\right) S$Correct Option: 1 Solution:...
Read More →Which of the following facts about the complex
Question: Which of the following facts about the complex $\left[\mathrm{Cr}\left(\mathrm{NH}_{3}\right)_{6}\right] \mathrm{Cl}_{3}$ is wrong ?The complex is an outer orbital complexThe complex gives white precipitate with silver nitrate solutionThe complex involves $\mathrm{d}^{2} \mathrm{sp}^{3}$ hybridisation and is octahedral in shapeThe complex is paramagneticCorrect Option: 1 Solution: Solution not required...
Read More →A hyperbola passes through the point
Question: A hyperbola passes through the point $P(\sqrt{2}, \sqrt{3})$ and has foci at $(\pm 2,0)$. Then the tangent to this hyperbola at $P$ also passes through the point :$(-\sqrt{2},-\sqrt{3})$$(3 \sqrt{2}, 2 \sqrt{3})$$(2 \sqrt{2}, 3 \sqrt{3})$$(\sqrt{3}, \sqrt{2})$Correct Option: , 3 Solution:...
Read More →Sachin and Rahul attempted to solve a quadratic equation.
Question: Sachin and Rahul attempted to solve a quadratic equation. Sachin made a mistake in writing down the constant term and ended up in roots (4, 3). Rahul made a mistake in writing down coefficient of x to get roots (3, 2). The correct roots of equation are:4, 36, 14, 36, 1Correct Option: , 2 Solution:...
Read More →Consider 5 independent Bernoulli's trials each with probability of success
Question: Consider 5 independent Bernoulli's trials each with probability of success $\mathrm{p}$. If the probability of at least one failure is greater than or equal to $\frac{31}{32}$, then $\mathrm{p}$ lies in the interval :-$\left[0, \frac{1}{2}\right]$$\left(\frac{11}{12}, 1\right]$$\left(\frac{1}{2}, \frac{3}{4}\right]$$\left(\frac{3}{4}, \frac{11}{12}\right]$Correct Option: 1 Solution:...
Read More →For the decomposition of the compound,
Question: For the decomposition of the compound, represented as $\mathrm{NH}_{2} \mathrm{COONH}_{4}(\mathrm{~s}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g})+\mathrm{CO}_{2}(\mathrm{~g})$ the $\mathrm{K}_{\mathrm{P}}=2.9 \times 10^{-5} \mathrm{~atm}^{3}$. If the reaction is started with $1 \mathrm{~mol}$ of the compound, the total pressure at equilibrium would be$38.8 \times 10^{-2} \mathrm{~atm}$$1.94 \times 10^{-2} \mathrm{~atm}$$5.82 \times 10^{-2} \mathrm{~atm}$$7.66 \times 10^{-2} \mat...
Read More →The eccentricity of the hyperbola whose length of the latus
Question: The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is :$\sqrt{3}$$\frac{4}{3}$$\frac{4}{\sqrt{3}}$$\frac{2}{\sqrt{3}}$Correct Option: , 4 Solution:...
Read More →The area of the region bounded by the parabola
Question: The area of the region bounded by the parabola $(\mathrm{y}-2)^{2}=\mathrm{x}-1$, the tangent to the parabola at the point $(2,3)$ and the $x$-axis is :-91236Correct Option: 1 Solution:...
Read More →Solve the equation
Question: Let for $a \neq a_{1} \neq 0, f(x)=a x^{2}+b x+c, g(x)=a_{1} x^{2}+b_{1} x+c_{1}$ and $p(x)=f(x)-g(x)$. If $\mathrm{p}(\mathrm{x})=0$ only for $\mathrm{x}=-1$ and $\mathrm{p}(-2)=2$, then the value of $\mathrm{p}(2)$ is18396Correct Option: 1 Solution:...
Read More →A solution containing 2.675 g
Question: A solution containing $2.675 \mathrm{~g}$ of $\mathrm{CoCl}_{3} .6 \mathrm{NH}_{3}\left(\right.$ molar mass $=267.5 \mathrm{~g} \mathrm{~mol}^{-1}$ ) is passed through a cation exchanger. The chloride ions obtained in solution were treated with excess of $\mathrm{AgNO}_{3}$ to give $4.78 \mathrm{~g}$ of $\mathrm{AgCl}$ (molar mass $=143.5 \mathrm{~g} \mathrm{~mol}^{-1}$ ). The formula of the complex is :-$\left[\mathrm{CoCl}\left(\mathrm{NH}_{3}\right)_{5}\right] \mathrm{Cl}_{2}$$\left...
Read More →Solve the equation
Question: If $\alpha$ and $\beta$ are the roots of the equation $x^{2}-x+1=0$, then $\alpha^{2009}+\beta^{2009}=$2112Correct Option: , 3 Solution:...
Read More →A common tangent to the conics
Question: A common tangent to the conics $x^{2}=6 y$ and $2 x^{2}-4 y^{2}=9$ is :$x+y=\frac{9}{2}$$x+y=1$$x-y=\frac{3}{2}$x-y=1Correct Option: , 3 Solution:...
Read More →Which one of the following has an optical isomer ?
Question: Which one of the following has an optical isomer ?$\left[\mathrm{Zn}(\mathrm{en})_{2}\right]^{2+}$$\left[\mathrm{Zn}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2}\right]^{2+}$$\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}$$\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}(\mathrm{en})\right]^{3+}(\mathrm{en}=$ ethylenediamine)Correct Option: , 3 Solution: Solution not required...
Read More →If the roots of the equation
Question: If the roots of the equation $b x^{2}+c x+a=0$ be imaginary, then for all real values of $x$, the expression $3 b^{2} x^{2}+6 b c x+2 c^{2}$ is :-Greater than $-4 a b$Less than $-4 a b$Greater than $4 a b$Less than $4 a b$Correct Option: 1 Solution:...
Read More →The equilibrium constants
Question: The equilibrium constants at $298 \mathrm{~K}$ for a reaction $\mathrm{A}+\mathrm{B} \rightleftharpoons \mathrm{C}+\mathrm{D}$ is 100 . If the initial concentration of all the four species were $1 \mathrm{M}$ each, then equilibrium concentration of $\mathrm{D}$ (in $\mathrm{mol} \mathrm{L}^{-1}$ ) will be :$1.182$$0.182$$0.818$$1.818$Correct Option: , 4 Solution:...
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