Recent questions tagged past papers

The value of $\sqrt{2}\displaystyle\int\frac {sin\;{x}{dx}}{sin(x-\frac{\pi}{4})}$ is

asked Nov 29, 2018 by pady_1

0 answers

The area of the plane region bounded by the curves $x + 2y^2 = 0$ and $x + 3y^2 = 1$ is equal to

asked Nov 29, 2018 by pady_1

0 answers

$Let I ={\displaystyle\int^1_0\frac{sin{x}}{\sqrt{x}}dx}$ and $ J={\displaystyle\int^1_0\frac{cos{x}}{\sqrt{x}}dx}$. Then which one of the following is true?

asked Nov 29, 2018 by pady_1

0 answers

The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is

asked Nov 29, 2018 by pady_1

0 answers

The value of cot $\bigg(cosec^{-1}{\frac{5}{3}}+tan^{-1}{\frac{2}{3}}\bigg)$ is

asked Nov 29, 2018 by pady_1

0 answers

The statement $p \rightarrow(q \rightarrow p)$ is equivalent to

asked Nov 29, 2018 by pady_1

0 answers

How many real solutions does the equation $X^7+14X^5+16X^3+30X-560=0$ have?

asked Nov 29, 2018 by pady_1

0 answers

Suppose the cube $x^3 - px + q$ has three distinct real roots where p > 0 and q > 0. Then which one of the following holds?

asked Nov 29, 2018 by pady_1

0 answers

23. The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

asked Nov 29, 2018 by pady_1

0 answers

Let $f(x) = \left\{ \begin{array} {1 1} (x-1) \sin \bigg(\large\frac{ 1 }{x-1}\bigg),\normalsize & \quad\text{ if x $\neq$ 1 }\\ 0 ,& \quad \text{if x =1}\\ \end{array} \right. $.Then which one of the following is true?

asked Nov 29, 2018 by pady_1

0 answers

In a shop there are five types of ice-creams available. A child buys six ice-creams. Statement -1: The number of different ways the child can buy the six ice-creams is $^{10}C_5$ Statement -2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A’s and 4 B’s in a row.

asked Nov 29, 2018 by pady_1

0 answers

Let p be the statement “x is an irrational number”, q be the statement “y is a transcendental number”, and r be the statement “x is a rational number iff y is a transcendental number”. Statement –1: r is equivalent to either q or p Statement –2: r is equivalent to $\sim (p\leftrightarrow \sim q)$.

asked Nov 29, 2018 by pady_1

0 answers

Statement -1: $\sum^{n}_{r=0}(r+1)^nC_r=(n+2)2^{n-1}$ Statement -2: $\sum^{n}_{r=0}(r+1)^nC_rX^r=(1+X)^n+nX(1+X)^{n-1}$

asked Nov 29, 2018 by pady_1

0 answers

Let A be a $2 \times 2$ matrix with real entries. Let I be the $2 \times 2$ identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that $A^2 = I$. Statement -1: If $A \neq I$ and $A \neq - I$, then det A = - 1. , Statement -2: If $A \neq I$ and $A \neq - I$, then $tr (A) \neq 0$.

asked Nov 29, 2018 by pady_1

0 answers

Statement - 1: For every natural number $n\geq 2$ ,$\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+$........$+\frac{1}{\sqrt{n}}>\sqrt{n}$ Statement -2: For every natural number $n\geq 2$ $\sqrt{{n}({n+1})}$

asked Nov 29, 2018 by pady_1

0 answers

If the straight lines $\frac{x-1}{k}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x-2}{3}=\frac{y-3}{k}=\frac{z-1}{2}$ intersect at a point, then the integer k is equal to

asked Nov 29, 2018 by pady_1

0 answers

The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz-plane at the point $\bigg[0,\frac{17}{2},\frac{-13}{2}\bigg]$. Then

asked Nov 29, 2018 by pady_1

0 answers

The non-zero verctors $\overrightarrow{a}$ , $\overrightarrow{b}$ and $\overrightarrow{c}$ are related by $\overrightarrow{a} =8\overrightarrow{b} and \overrightarrow{c} = -7 \overrightarrow{b}$ .Then the angle between $\overrightarrow{a}$ and $\overrightarrow{c}$ is

asked Nov 29, 2018 by pady_1

0 answers

The vector $\overrightarrow{a}=\alpha \hat{i}+2\hat{j}+\beta \hat{k}$ lies in the plane of the vectors $\overrightarrow{b}=\hat{i}+\hat{j}\; and \overrightarrow{c}=\hat{j}+\hat{k}$ and bisects the angle between $\overrightarrow{b}$ and $\overrightarrow{c}$.Then which one of the following gives possible values of $\alpha$ and $\beta$ ?

asked Nov 29, 2018 by pady_1

0 answers

The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?

asked Nov 29, 2018 by pady_1

0 answers

The solution of the differential equation $\frac{dy}{dx}=\frac{x+y}{x}$ satisfying the condition y (1) = 1 is

asked Nov 29, 2018 by pady_1

0 answers

The perpendicular bisector of the line segment joining P (1, 4) and Q (k, 3) has y-intercept - 4. Then a possible value of k is

asked Nov 29, 2018 by pady_1

0 answers

1. Let R be the real line. Consider the following subsets of the plane $R\times R.$ $S = {(x, y) : y = x + 1 \;and \;0 < x < 2}, T = {(x, y) : x - y\; is\; an\; integer}$. Which one of the following is true?

asked Nov 29, 2018 by pady_1

0 answers

The conjugate of a complex number is $\frac{1}{i-1}$.The conjugate of a complex number is

asked Nov 29, 2018 by pady_1

0 answers

Let $f : N\rightarrow Y$ be a function defined as $f (x) = 4x + 3$, where $Y = {y\; \epsilon \;N : y = 4x + 3 for \;some\; x \;\epsilon\; N}$. Show that f is invertible and its inverse is

asked Nov 29, 2018 by pady_1

0 answers

The point diametrically opposite to the point P (1, 0) on the circle $x^2 + y^2 + 2x + 4y - 3 = 0$ is

asked Nov 29, 2018 by pady_1

0 answers

A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at

asked Nov 29, 2018 by pady_1

0 answers

A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is $\frac{1}{2}$. Then the length of the semi-major axis is

asked Nov 29, 2018 by pady_1

0 answers

A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then $P (A\cup B)$ is

asked Nov 29, 2018 by pady_1

0 answers

It is given that the events A and B are such that $P(A)=\frac{1}{4}P\bigg(\frac{A}{B}\bigg)=\frac{1}{2}$$P\bigg(\frac{B}{A}\bigg)=\frac{2}{3}$.Then P(B) is

asked Nov 29, 2018 by pady_1

0 answers

AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point A from a certain point C on the ground is $60^\circ$. He moves away from the pole along the line BC to a point D such that CD = 7 m. From D the angle of elevation of the point A is $45^\circ$. Then the height of the pole is

asked Nov 29, 2018 by pady_1

0 answers

In conversion of limestone to lime, $CaCO_3 (s) \to CaO(s) + CO_2(g)$ the values of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are $+179.1\;kJ\; mol^{-1}$ and $160.2\;J/K$ respectively at 298 K and 1 bar. Assuming that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not change with temperature, temperature above which conversion of limestone to lime will be spontaneous is :

asked Nov 29, 2018 by pady_1

0 answers

A mixture of ethyl alcohol and propyl alcohol has a vapour pressure of 290 mm at 300 K. The vapour pressure of propyl alcohol is 200 mm. If the mole fraction of ethyl alcohol is 0.6, its vapour pressure (in mm) at the same temperature will be:

asked Nov 29, 2018 by pady_1

0 answers

The first and second dissociation constants of an acid $H_2A$ are $1.0 \times 10^{-5}$ and $5.0 \times 10^{-10}$ respectively. The overall dissociation constant of the acid will be :

asked Nov 29, 2018 by pady_1

0 answers

The density (in $g\; mL^{-1}$) of a 3.60 M sulphuric acid solution that is $29\% \; H_2SO_4$ (molar mass =$98\;g\;mol^{-1}$) by mass will be :

asked Nov 29, 2018 by pady_1

0 answers

The charge/size ratio of a cation determines its polarizing power. Which one of the following sequences represents the increasing order of the polarizing power of the cationic species, $K^+, Ca^{2+}, Mg^{2+}, Be^{2+}$ ?

asked Nov 29, 2018 by pady_1

0 answers

Identify the incorrect statement among the following :

asked Nov 29, 2018 by pady_1

0 answers

The stability of dihalides of Si, Ge, Sn and Pb increases steadily in the sequence :

asked Nov 29, 2018 by pady_1

0 answers

Which of the following species exhibits the diamagnetic behaviour ?

asked Nov 29, 2018 by pady_1

0 answers

asked Nov 29, 2018 by pady_1

0 answers

The compound formed as a result of oxidation of ethyl benzene by $KMnO_4$ is

asked Nov 29, 2018 by pady_1

0 answers

Which one of the following is the strongest base in aqueous solution ?

asked Nov 29, 2018 by pady_1

0 answers

The equivalent conductances of two strong electrolytes at infinite dilution in $H_2O$ (where ions move freely through a solution) at $25^{\circ}C$ are given below : $\bigwedge^{\circ}_{CH_3COONa }= 91.0\;S \;cm^2/equiv $ $ \bigwedge^{\circ}_{HCl} = 426.2 \; S\;cm^2/equiv$ What additional information/quantity one needs to calculate $\bigwedge^{\circ}$ of an aqueous solution of acetic acid ?

asked Nov 29, 2018 by pady_1

0 answers

Which of the following nuclear reactions will generate an isotope ?

asked Nov 29, 2018 by pady_1

0 answers

Identify the correct statement regarding a spontaneous process :

asked Nov 29, 2018 by pady_1

0 answers

Regular use of which of the following fertilisers increases the acidity of soil ?

asked Nov 29, 2018 by pady_1

0 answers

In the reaction, $ 2Al (s) + 6 HCl (aq) \to 2Al^{3+} (aq) + 6 Cl^- (aq) + 3H_2(g)$

asked Nov 29, 2018 by pady_1

0 answers

Which of the following hydrogen bonds is the strongest ?

asked Nov 29, 2018 by pady_1

0 answers

Which of the following sets of quantum numbers represents the highest energy of an atom ?

asked Nov 29, 2018 by pady_1

0 answers

In the following sequence of reactions, $CH_3CH_2OH \xrightarrow{P + I_2} A \xrightarrow[\text{ether }]{\text{Mg}} B \xrightarrow{HCHO} C \xrightarrow{H_2O} D$ the compound 'D' is :

asked Nov 29, 2018 by pady_1

0 answers

Ask Questions, Get Answers