The integral
Question: The integral $\int \frac{d x}{(x+4)^{\frac{8}{7}}(x-3)^{\frac{6}{7}}}$ is equal to : (where $\mathrm{C}$ is a constant of integration)$\left(\frac{x-3}{x+4}\right)^{\frac{1}{7}}+C$$-\left(\frac{x-3}{x+4}\right)^{\frac{1}{7}}+C$$\frac{1}{2}\left(\frac{x-3}{x+4}\right)^{\frac{3}{7}}+C$$-\frac{1}{13}\left(\frac{x-3}{x+4}\right)^{-\frac{13}{7}}+C$Correct Option: 1 Solution:...
Read More →Solve this following
Question: $10.30 \mathrm{mg}$ of $\mathrm{O}_{2}$ is dissolved into a liter of sea water of density $1.03 \mathrm{~g} / \mathrm{mL}$. The concentration of $\mathrm{O}_{2}$ in ppm is Solution: $\mathrm{ppm}=\frac{10.3 \times 10^{-3}}{1030} \times 10^{6}=10$...
Read More →If for some
Question: If for some $\alpha$ and $\beta$ in $R$, the intersection of the following three places $x+4 y-2 z=1$ $x+7 y-5 z=\beta$ $x+5 y+\alpha z=5$ is a line in $\mathrm{R}^{3}$, then $\alpha+\beta$ is equal to:10-1020Correct Option: 1 Solution:...
Read More →Let f be any function continuous on
Question: Let $f$ be any function continuous on $[\mathrm{a}, \mathrm{b}]$ and twice differentiable on (a, b). If for all $x \in(a, b)$, $f^{\prime}(\mathrm{x})0$ and $f^{\prime \prime}(\mathrm{x})0$, then for any $\mathrm{c} \in(\mathrm{a}, \mathrm{b})$, $\frac{f(c)-f(a)}{f(b)-f(c)}$ is greater than :$\frac{b+a}{b-a}$$\frac{b-c}{c-a}$$\frac{c-a}{b-c}$1Correct Option: , 3 Solution:...
Read More →A cylinder containing an ideal gas
Question: A cylinder containing an ideal gas $(0.1$ mol of $1.0 \mathrm{dm}^{3}$ ) is in thermal equilibrium with a large volume of $0.5$ molal aqueous solution of ethylene glycol at its freezing point. If the stoppers $S_{1}$ and $S_{2}$ (as shown in the figure) are suddenly withdrawn, the volume of the gas in litres after equilibrium is achieved will be (Given, $\mathrm{K}_{\mathrm{f}}$ (water) $=2.0 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}{ }^{-1}$, $\mathrm{R}=0.08 \mathrm{dm}^{3}$ atm $\left....
Read More →The true statement amongst the following is:
Question: The true statement amongst the following is: Both $\Delta S$ and $S$ are functions of temperature.$S$ is not a function of temperature but $\Delta S$ is a function of temperature.Both $S$ and $\Delta S$ are not functions of temperature.$S$ is a function of temperature but $\Delta S$ is not a function of temperature.Correct Option: 1 Solution: $\mathrm{ds}=\int \frac{\mathrm{q}_{\mathrm{rev}}}{\mathrm{T}}$...
Read More →If e_1 and e_2 are the eccentricities of the ellipse,
Question: If $e_{1}$ and $e_{2}$ are the eccentricities of the ellipse, $\frac{x^{2}}{18}+\frac{y^{2}}{4}=1$ and the hyperbola, $\frac{x^{2}}{9}-\frac{y^{2}}{4}=1$ respectively and $\left(e_{1}, e_{2}\right)$ is a point on the ellipse, $15 x^{2}+3 y^{2}=k$, then $k$ is equal to :15141716Correct Option: , 4 Solution:...
Read More →The number of sp² hybrid orbitals in a molecule of benzene is :
Question: The number of sp hybrid orbitals in a molecule of benzene is : 2461218Correct Option: , 4 Solution: Each carbon atom is $\mathrm{sp}^{2}$ hybridized Therefore each carbon has $3 \mathrm{sp}^{2}$ hybrid orbitals. Hence total $\mathrm{sp}^{2}$ hybrid orbitals are 18 ....
Read More →A circle touches the
Question: A circle touches the $y$-axis at the point $(0,4)$ and passes through the point $(2,0)$. Which of the following lines is not a tangent to this circle ?$3 x-4 y-24=0$$3 x+4 y-6=0$$4 x+3 y-8=0$$4 x-3 y+17=0$Correct Option: , 3 Solution:...
Read More →Solve this following
Question: The isomer(s) of $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{4} \mathrm{Cl}_{2}\right]$ that has/have a $\mathrm{Cl}-\mathrm{Co}-\mathrm{Cl}$ angle of $90^{\circ}$, is/are :meridional and transcis and transtrans onlycis onlyCorrect Option: , 4 Solution:...
Read More →The product
Question: The product $2^{\frac{1}{4}} \cdot 4^{\frac{1}{16}} \cdot 8^{\frac{1}{48}} \cdot 16^{\frac{1}{128}}$ to $\infty$ is equal to :$2^{\frac{1}{2}}$$2^{\frac{1}{4}}$21Correct Option: 1 Solution:...
Read More →Let the observations
Question: Let the observations $\mathrm{x}_{\mathrm{i}}(1 \leq \mathrm{i} \leq 10)$ satisfy the equations, $\sum_{i=1}^{10}\left(x_{i}-5\right)=10$ and $\sum_{i=1}^{10}\left(x_{i}-5\right)^{2}=40$ If $\mu$ and $\lambda$ are the mean and the variance of the observations, $x_{1}-3, x_{2}-3, \ldots ., x_{10}-3$, then the ordered pair $(\mu, \lambda)$ is equal to :$(6,6)$$(3,6)$$(6,3)$$(3,3)$Correct Option: , 4 Solution:...
Read More →Solve this following
Question: The reaction of $\mathrm{H}_{3} \mathrm{~N}_{3} \mathrm{~B}_{3} \mathrm{Cl}_{3}$ (A) with $\mathrm{LiBH}_{4}$ in tetrahydrofuran gives inorganic benzene $(B)$. Further, the reaction of (A) with (C) leads to $\mathrm{H}_{3} \mathrm{~N}_{3} \mathrm{~B}_{3}(\mathrm{Me})_{3}$. Compounds (B) and (C) respectively, are:Boron nitride and $\mathrm{MeBr}$Borazine and $\mathrm{MeMgBr}$Borazine and MeBrDiborane and MeMgBrCorrect Option: , 2 Solution:...
Read More →Negation of the statement:
Question: Negation of the statement: $\sqrt{5}$ is an integer or 5 is irrational is :$\sqrt{5}$ is irrational or 5 is an integer.$\sqrt{5}$ is not an integer and 5 is not irrational.$\sqrt{5}$ is an integer and 5 is irrational.$\sqrt{5}$ is not an integer or 5 is not irrational.Correct Option: , 2 Solution:...
Read More →The number of real roots of the equation,
Question: The number of real roots of the equation, $e^{4 x}+e^{3 x}-4 e^{2 x}+e^{x}+1=0$ is :4231Correct Option: , 4 Solution:...
Read More →A, B and C are three biomolecules. The results of the tests performed on them are given below:
Question: A, B and C are three biomolecules. The results of the tests performed on them are given below: $\mathrm{A}=$ Glucose, $\mathrm{B}=$ Fructose, $\mathrm{C}=$ Albumin$\mathrm{A}=$ Lactose, $\mathrm{B}=$ Fructose, $\mathrm{C}=$ Alanine$\mathrm{A}=$ Lactose, $\mathrm{B}=$ Glucose, $\mathrm{C}=$ Alanine$\mathrm{A}=$ Lactose, $\mathrm{B}=$ Glucose, $\mathrm{C}=$ AlbuminCorrect Option: , 4 Solution: Alanine does not show Biuret test because Biuret test is used for deduction of peptide linkage ...
Read More →If the matrices
Question: If the matrices $\mathrm{A}=\left[\begin{array}{ccc}1 1 2 \\ 1 3 4 \\ 1 -1 3\end{array}\right], \mathrm{B}=\operatorname{adj} \mathrm{A}$ and $C=3 A$, then $\frac{|\operatorname{adj} B|}{|C|}$ is equal to :722816Correct Option: , 3 Solution:...
Read More →Prove the following
Question: If $f^{\prime}(x)=\tan ^{-1}(\sec x+\tan x),-\frac{\pi}{2}x\frac{\pi}{2}$, and $f(0)=0$, then $f(1)$ is equal to :$\frac{\pi-1}{4}$$\frac{\pi+2}{4}$$\frac{\pi+1}{4}$$\frac{1}{4}$Correct Option: , 3 Solution:...
Read More →The value of
Question: The value of $\int_{0}^{2 \pi} \frac{x \sin ^{8} x}{\sin ^{8} x+\cos ^{8} x} d x$ is equal to :$2 \pi$$4 \pi$$2 \pi^{2}$$\pi^{2}$Correct Option: , 4 Solution:...
Read More →Consider the following reactions,
Question: Consider the following reactions, Correct Option: , 2 Solution:...
Read More →In a box, there are 20 cards,
Question: In a box, there are 20 cards, out of which 10 are lebelled as A and the remaining 10 are labelled as B. Cards are drawn at random, one after the other and with replacement, till a second A-card is obtained. The probability that the second A-card appears before the third B-card is:$\frac{11}{16}$$\frac{13}{16}$$\frac{9}{16}$$\frac{15}{16}$Correct Option: 1 Solution:...
Read More →Solve this following
Question: $5 \mathrm{~g}$ of zinc is treated separately with an excess of (a) dilute hydrochloric acid and (b) aqueous sodium hydroxide. The ratio of the volumes of $\mathrm{H}_{2}$ evolved in these two reactions is :$1: 4$$1: 2$$2: 1$$1: 1$Correct Option: , 4 Solution:...
Read More →Let z be complex number such that
Question: Let $z$ be complex number such that $\left|\frac{z-i}{z+2 i}\right|=1$ and $|z|=\frac{5}{2}$. Then the value of $|z+3 i|$ is :$\sqrt{10}$$2 \sqrt{3}$$\frac{7}{2}$$\frac{15}{4}$Correct Option: , 3 Solution:...
Read More →The solubility product of
Question: The solubility product of $\mathrm{Cr}(\mathrm{OH})_{3}$ at $298 \mathrm{~K}$ is $6.0 \times 10^{-31}$. The concentration of hydroxide ions in a saturated solution of $\mathrm{Cr}(\mathrm{OH})_{3}$ will be :$\left(18 \times 10^{-31}\right)^{1 / 4}$$\left(2.22 \times 10^{-31}\right)^{1 / 4}$$\left(4.86 \times 10^{-29}\right)^{1 / 4}$$\left(18 \times 10^{-31}\right)^{1 / 2}$Correct Option: 1 Solution:...
Read More →If the number of five digit numbers with distinct digits
Question: If the number of five digit numbers with distinct digits and 2 at the $10^{\text {th }}$ place is $336 \mathrm{k}$, then $\mathrm{k}$ is equal to :8647Correct Option: 1 Solution:...
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