Recent questions tagged past papers

If the integral $\begin{align} \int \frac{5 \tan x}{\tan x - 2} dx = x + a \;In |\sin x - 2 \cos x | + k \end{align}$, then $a$ is equal to

asked Dec 11, 2018 by pady_1

1 answer

The negation of the statement "If I become a teacher, then I will open a school" is

asked Dec 11, 2018 by pady_1

1 answer

Statement 1 : The sum of the series $ 1 + ( 1 + 2+4) + (4+6+9) + (9+12+16) + .......+ (361 + 380+400)$ is $8000$. Statement 2 : $\displaystyle\sum_{k=1}^{n} (k^3 - ( k-1)^3 ) = n^3$ for any natural number $n$.

asked Dec 11, 2018 by pady_1

2 answers

A spherical balloon is filled with $4500 \pi$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate if $72 \pi$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the ballon decreases 49 minutes after the leakage began is

asked Dec 11, 2018 by pady_1

1 answer

Let $\hat{a}$ and $\hat{b}$ be two unit vectors. If the vectors $\overrightarrow{c} = \hat{a} + 2 \hat{b}$ and $\overrightarrow{d} = 5 \hat{a} - 4 \hat{b}$ are perpendicular to each other, then the angle between $\hat{a}$ and $\hat{b}$ is

asked Dec 11, 2018 by pady_1

1 answer

The equation $e^{\sin x }- e^{- \sin x} - 4 = 0 $ has

asked Dec 11, 2018 by pady_1

1 answer

Let $I$ be the purchase value of an equipment and $V(t)$ be the value after it has been used for $t$ years. The value $V(t)$ depreciates at a rate given by diferential equation $\frac{dV(t)}{dt} = -k(T-t)$, where $k>0$ is a constant and $T$ is the total life in years of the equipment. Then the scrap value $V(T)$ of the equipment is

asked Dec 11, 2018 by pady_1

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Identify the compound that exhibits tautomerism.

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The entropy change involved in the isothermal reversible expansion of 2 moles of an ideal gas from a volume of $10 \; dm^3$ to a volume of $100\; dm^3$ at $27^ {\circ} C$ is :

asked Dec 11, 2018 by pady_1

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In a face centred cubic lattice, atom A occupies the corner position and atom B occupies the face centre positions. If one atom of B is missing from one of the face centred points, the formula of the compound is :

asked Dec 11, 2018 by pady_1

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Phenol is heated with a solution of mixture of $KBr$ and $KBrO_3$. The major product obtained in the above reaction is

asked Dec 11, 2018 by pady_1

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Which of the following reagents may be used to distinguish between phenol and benzoic acid?

asked Dec 11, 2018 by pady_1

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Silver Mirror test is givn by which one of the following compounds ?

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A gas absorbs a photon of 355 nm and emits at two wavelengths. If one of the emissions is at 680 nm, the other is at :

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Ozonolysis of an organic compound gives formaldehyde as one of the products.. This confirms the presence of :

asked Dec 11, 2018 by pady_1

1 answer

The structure of $IF_7$ is :

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Which of the following statements regarding sulpher is incorrect ?

asked Dec 11, 2018 by pady_1

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The outer electron configuration of Gd (Atomic No:64) is :

asked Dec 11, 2018 by pady_1

0 answers

Which of the following statement is wrong ?

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A 5.2 molal aqueous solution of methyl alcohol, $CH_3OH$, is supplied. What is the mole fraction of methyl alcohol in the solution ?

asked Dec 11, 2018 by pady_1

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In context of the lanthanoids, which of the following statements is not correct ?

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The hybridization of orbitals of N atom in $NO_3^-, NO_2^+$ and $NH_4^+$ are respectively :

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The magnetic moment (spin only) of $[NiCl_4]^{2-}$ is

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The rate of a chemical reaction doubles for every $10^{\circ}C$ rise of temperature. If the temperature is raised by $50^{\circ}C$, the rate of the reaction increases by about :

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Which one of the following order represents the correct sequence of the increasing basic nature of the given oxides ?

asked Dec 11, 2018 by pady_1

1 answer

Ethylene glycol is used as an antifreeze in a cold climate. Mass of ethylene glycol which should be added to 4 kg of water to prevent it from freezing at $-6^{\circ} C$ will be : [$K_f$ for water = 1.86 $K \; kg\; mol^{-1}$, and molar mass of ethylene glycol = 62 $g\; mol^{-1}$ )

asked Dec 11, 2018 by pady_1

0 answers

Which of the following facts about the complex $[Cr (NH_3)_6] Cl_3$ is wrong ?

asked Dec 11, 2018 by pady_1

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Boron cannot form which one of the following anions ?

asked Dec 11, 2018 by pady_1

0 answers

A vessel at 1000 K contains $CO_2$ with a pressure of 0.5 atm. Some of the $CO_2$ is converted into $CO$ on the addition of graphite. If the total pressure at equilibrium is 0.8 atm, the value of $K$ is

asked Dec 11, 2018 by pady_1

0 answers

a' and 'b' are van der Waals' constants for gases. Chlorine is more easily liquefied than ethane because

asked Dec 11, 2018 by pady_1

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The degree of dissociation $(\alpha$) of a weak electrolyte $A_xB_y$ is related to vant Hoff factor (i) by the expression :

asked Dec 11, 2018 by pady_1

0 answers

The strongest acid amongst the following compounds is :

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The reduction potential of hydrogen half cell will be negative if :

asked Dec 11, 2018 by pady_1

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Sodium ethoxide has reacted with ethanoyl chloride. The compound that is produced in the above reaction is :

asked Dec 11, 2018 by pady_1

1 answer

Trichloroacetaldehyde was subjected to Cannizzaro's reaction by using NaOH. The mixture of the products contains sodium trichloroacetate and another compound. The other compound is :

asked Dec 11, 2018 by pady_1

0 answers

The presence or absence of hydroxyl group on which carbon atom of sugar differentiates RNA and DNA ?

asked Dec 11, 2018 by pady_1

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Among the following the maximum covalent character is shown by the compound :

asked Dec 11, 2018 by pady_1

0 answers

For $x \in (0, \frac{5 \pi}{2})$, define $f(x) = \int_0^x \;\sqrt{t} \;\sin t \;dt$. Then $f$ has

asked Dec 11, 2018 by pady_1

0 answers

The area of the region enclosed by the curves $ y = x,\; \; x = e, \; \; y = \frac{1}{x}$ are the positive x-axis is

asked Dec 11, 2018 by pady_1

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The value of p and q for which the function $ f(x) = \begin{cases} \frac{\sin (p+1) x + \sin x}{x} &, x < 0 \\ \; \; \;\; \;q &, x = 0 \\ \frac{\sqrt{x+x^2} - \sqrt{x}}{x^{3/2}} & , x > 0 \end{cases} $ is continuous for all $x$ in $R$, is

asked Dec 11, 2018 by pady_1

0 answers

If $\omega (\neq 1)$ is a cube root of unity, and $(1 + \omega)^7 = A + B \omega$. Then $(A, B)$ equals

asked Dec 11, 2018 by pady_1

0 answers

Let A and B be two symmetric matrices of order 3. Statement-1 : A (BA) and (AB) A are symmetric matrices. Statement -2 : AB is symmetric matrix if matrix multiplication of A and B is commutative.

asked Dec 11, 2018 by pady_1

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Statement-1 : The point A (1, 0, 7) is the mirror image of the point B (1, 6, 3) in the line $\frac{x}{1} = \frac{y-1}{2} = \frac{z-2}{3}$ Statement-2 : The line $\frac{x}{1} = \frac{y-1}{2} = \frac{z-2}{3}$ bisects the line segment joining A (1, 0, 7) and B (1, 6, 3)

asked Dec 11, 2018 by pady_1

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If the mean deviation about the medium of the numbers a, 2a, . . . ., 50a is 50, then |a| equals

asked Dec 11, 2018 by pady_1

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The shortest distance between line $ y-x=1$ and curve $x=y^2$ is

asked Dec 11, 2018 by pady_1

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Consider the following statements P : Suman is brilliant Q : Suman is rich R : Suman is honest The negative of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as

asked Dec 11, 2018 by pady_1

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The number of values of k for which the linear equations 4x + ky + 2z = 0; kx + 4y + z=0; 2x + 2y + z = 0 possess a non-zero solution is

asked Dec 11, 2018 by pady_1

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If C and D are two events such that $C \subset D$ and $P(D) \neq 0$, then the correct statement among the following is

asked Dec 11, 2018 by pady_1

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The two circles $x^2+y^2=ax$ and $x^2+y^2 =c^2 (c>0)$ touch each other if

asked Dec 11, 2018 by pady_1

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The vector $\overrightarrow{a}$ and $\overrightarrow{b}$ are not perpendicular and $\overrightarrow{c}$ and $\overrightarrow{d}$ are two vectors satisfying : $\overrightarrow{b} \times \overrightarrow{c} = \overrightarrow{b} \times \overrightarrow{d}$ and $\overrightarrow{a}.\overrightarrow{d} =0$. Then the vector $\overrightarrow{d}$ is equal to

asked Dec 11, 2018 by pady_1

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