Recent questions tagged past papers

Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X), with replacement, then the probability that A and B have equal number of elements, is :

asked Dec 11, 2018 by pady_1

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Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two unit vectors such that $|\overrightarrow{a} +\overrightarrow{b} |= \sqrt{3}$. If $\overrightarrow{c} = \overrightarrow{a} + 2\overrightarrow{b} + 3(\overrightarrow{a} \times \overrightarrow{b})^2$, then $2|\overrightarrow{c}|$ is equal to:

asked Dec 11, 2018 by pady_1

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If the shortest distance between the lines $\frac{x-1}{\alpha} = \frac{y+1}{-1} = \frac{z}{1},\; (\alpha \neq -1)$ and $x+y+z+1=0=2x-y+z+3$ is $\frac{1}{\sqrt{3}}$, then a value of $\alpha$ is :

asked Dec 11, 2018 by pady_1

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If the points $(1, 1, \lambda)$ and $(-3, 0, 1)$ are equidistant from the plane, $3x+4y+12z+13=0$, then $\lambda$ satisfies the equation :

asked Dec 11, 2018 by pady_1

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An ellipse passes through the foci of the hyperbola, $9x^2 - 4y^2 = 36$ and its major and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is $\frac{1}{2}$ , then which of the following points does not lie on the ellipse ?

asked Dec 11, 2018 by pady_1

1 answer

If the tangent to the conic, $y-6=x^2$ at $(2, 10)$ touches the circle, $x^2+y^2+8x-2y=k$ (for some fixed $k$) at a point $(\alpha, \beta)$; then $(\alpha, \beta)$ is:

asked Dec 11, 2018 by pady_1

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If $y+3x =0$ is the equation of a chord of the circle, $x^2+y^2-30x=0$, then the equation of the circle with this chord as diameter is :

asked Dec 11, 2018 by pady_1

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Let $L$ be the line passing through the point $P(1, 2)$ such that its intercepted segment between the co-ordinate axes is bisected at $P$. If $L_1$ is the line perpendicular to $L$ and passing through the point $(-2, 1)$, then the point of intersection of $L$ and $L_1$ is :

asked Dec 11, 2018 by pady_1

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The points $(0, \frac{8}{3})\; (1,3)$ and $(82, 30)$

asked Dec 11, 2018 by pady_1

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If $y(x)$ is the solution of the differential equation $(x+2) \frac{dy}{dx} = x^2+4x-9,\; x \neq -2$ and $y(0)=0$, then $y(-4)$ is equal to :

asked Dec 11, 2018 by pady_1

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The area (in square units) of the region bounded by the curves $y + 2x^2 =0$ and $y+3x^2 =1$, is equal to :

asked Dec 11, 2018 by pady_1

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For $x>0$, let $f(x) = \begin{align} \int_1^x \frac{\log t}{1+t} dt \end{align}$. Then $f(x) + f(\frac{1}{x})$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

The integral $\begin{align} \int \frac{dx}{(x+1)^{3/4} (x-2)^{5/4}}\end{align}$ is equal to:

asked Dec 11, 2018 by pady_1

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Let the tangents drawn to the circle, $x^2+y^2 = 16$ from the point $P(0,h)$ meet the $x$-axis at point A and B. If the area of $\Delta APB$ is minimum, then $h$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

If Rolle's theorem holds for the function $f(x) = 2x^3 + bx^2+cx,\; x \in [-1, 1]$, at the point $x= \frac{1}{2}$, then $2b+c$ equals :

asked Dec 11, 2018 by pady_1

1 answer

The distance, from the origin of the normal to the curve, $x = 2 \cos t + 2 t \sin t,\; y = 2\sin t - 2t \cos t$ at $ t = \frac{\pi}{4}$, is:

asked Dec 11, 2018 by pady_1

1 answer

$\displaystyle{\lim_{x \to 0} \frac{e^{x^2}-\cos x}{\sin^2x}}$ is equal to :

asked Dec 11, 2018 by pady_1

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The value of $\displaystyle\sum_{r=16}^{30} (r+2)(r-3)$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

If the coefficients of the three successive terms in the binomial expansion of $(1+x)^n$ are in the ratio $1 : 7 : 42$, then the first of these terms in the expansion is :

asked Dec 11, 2018 by pady_1

1 answer

Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is :

asked Dec 11, 2018 by pady_1

1 answer

The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is :

asked Dec 11, 2018 by pady_1

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If $A = \begin{bmatrix} 0 & -1 \\ 1& 0 \end{bmatrix}$, then which one of the following statement is not correct ?

asked Dec 11, 2018 by pady_1

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The least value of the product $xyz$ for which the determinant $\begin{vmatrix} x& 1& 1 \\ 1 & y & 1 \\ 1 & 1 & z \end{vmatrix}$ is non negative, is:

asked Dec 11, 2018 by pady_1

1 answer

If $2 + 3i$ is one of the roots of the equation $2x^3 - 9x^2 + kx - 13 = 0, \; k \in R$, then the real root of this equation :

asked Dec 11, 2018 by pady_1

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The largest value of $r$ for which the region represented by the set $\{ \omega \in C | \omega - 4 - i | \leq r \}$ is contained in the region represented by the set $\{z \in C / |z-1| \leq |z+i| \}$, is equal to :

asked Dec 11, 2018 by pady_1

1 answer

In a certain town, 25% of the families own a phone and 15% own a car ; 65% families own neither a phone nor a car and 2,000 families own both a car and a phone. Consider the following three statements : (a) 5% families own both a car and a phone. (b) 35% families own either a car or a phone. (c) 40,000 families live in the town. Then :

asked Dec 11, 2018 by pady_1

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The cation that will not be precipitated by $H_2S$ in the presence of $dil. HCl$ is :

asked Dec 11, 2018 by pady_1

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is used as :

asked Dec 11, 2018 by pady_1

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Complete hydrolysis of starch gives :

asked Dec 11, 2018 by pady_1

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Match the polymers in column-A with their main uses in column-B and choose the correct answer :

asked Dec 11, 2018 by pady_1

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Arrange the following amines in the order of increasing basicity.

asked Dec 11, 2018 by pady_1

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In the presence of a small amount of phosphorous, aliphatic carboxylic acids react with chlorine or bromine to yield a compound in which $\alpha$ - hydrogen has been replaced by halogen. This reaction is known as :

asked Dec 11, 2018 by pady_1

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A compound $A$ with molecular formula $C_{10}H_{13}Cl$ gives a white precipitate on adding silver nitrate solution. $A$ on reacting with alcoholic KOH gives compound $B$ as the main product. $B$ on ozonolysis gives $C$ and $D$. $C$ gives Cannizaro reaction but not aldol condensation. $D$ gives aldol condensation but not Cannizaro reaction. $A$ is :

asked Dec 11, 2018 by pady_1

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A is :

asked Dec 11, 2018 by pady_1

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The optically inactive compound from the following is :

asked Dec 11, 2018 by pady_1

1 answer

$1.4\; g$ of an organic compound was digested according to Kjeldahl's method and the ammonia evolved was absorbed in $60 \;mL$ of $M/10\; H_2 SO_4$ solution. The excess sulphuric acid required $20\; mL$ of $M/10 \;NaOH$ solution for neutralization. The percentage of nitrogen in the compound is :

asked Dec 11, 2018 by pady_1

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Photochemical smog consists of excessive amount of X, in addition to aldehydes, ketones, peroxy acetyl nitrile (PAN), and so forth. X is :

asked Dec 11, 2018 by pady_1

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The correct statement on the isomerism associated with the following complex ions, (a) $[Ni(H_2O)_5NH_3]^{2+},$ (b)$[ Ni(H_2O)_4 (NH_3)_2]^{2+} $ and (c)$[Ni(H_2O)_3 (NH_3)_3]^{2+} $ is :

asked Dec 11, 2018 by pady_1

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Which molecule/ion among the following cannot act as a ligand in complex compounds ?

asked Dec 11, 2018 by pady_1

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An aqueous solution of a salt $X$ turns blood red on treatment with $SCN^-$ and blue on treatment with $K_4 [Fe(CN)_6 ]$. $X$ also gives a positive chromyl chloride test. The salt $X$ is :

asked Dec 11, 2018 by pady_1

1 answer

The geometry of $XeOF_4$ by VSEPR theory is :

asked Dec 11, 2018 by pady_1

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The least number of oxyacids are formed by :

asked Dec 11, 2018 by pady_1

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The correct order of thermal stability of hydroxides is :

asked Dec 11, 2018 by pady_1

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Permanent hardness in water cannot be cured by :

asked Dec 11, 2018 by pady_1

1 answer

In the isolation of metals, calcination process usually results in :

asked Dec 11, 2018 by pady_1

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In the long form of the periodic table, the valence shell electronic configuration of $5s^2 5p^4$ corresponds to the element present in :

asked Dec 11, 2018 by pady_1

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The following statements relate to the adsorption of gases on a solid surface. Identify the incorrect statement among them :

asked Dec 11, 2018 by pady_1

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The reaction $2N_2O_5 (g) \to 4NO_2 (g) +O_2 (g)$ follows first order kinetics. The pressure of a vessel containing only $N_2O_5$ was found to increase from $50\; mm \;Hg$ to $87.5\; mm \;Hg$ in $30\; min$. The pressure exerted by the gases after $60 \;min$. will be (Assume temperature remains constant) :

asked Dec 11, 2018 by pady_1

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A variable, opposite external potential $(E_{ext})$ is applied to the cell $Zn|Zn^{2+} \; (1M) || Cu^{2+} \; (1M) | Cu$, of potential $1.1\;V$. When $E_{ext} < 1.1\;V$ and $E_{ext} > 1.1 \;V$, respectively electrons flow from :

asked Dec 11, 2018 by pady_1

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Gaseous $N_2O_4$ dissociates into gaseous $NO_2$ according to the reaction $ N_2O_4 (g) \leftrightharpoons 2NO_2 (g)$ At $300\; K$ and $1\; atm \;pressure$, the degree of dissociation of $N_2O_4$ is $0.2$. If one mole of $N_2O_4$ gas is contained in a vessel, then the density of the equilibrium mixture is :

asked Dec 11, 2018 by pady_1

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