Recent questions tagged past papers

The correct statement for the molecule, $CsI_3$ is:

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On heating an aliphatic primary amine with chloroform and ethanolic potassium hydroxide, the organic compound formed is:

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Sodium phenoxide when heated with $CO_2$ under pressure at $125^{\circ}C$ yields a product which on acetylation produces $C$. The major product C would be:

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In the reaction, $CH_3COOH \xrightarrow{LiAlH_4} A \xrightarrow{PCl_5} B \xrightarrow{Alc. KOH} C$, the product C is :

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For the reaction, $SO_{2(g)} + \frac{1}{2}O_{2(g)} \leftrightharpoons SO_{3(g)}$, if $K_P = K_C(RT)^x$ where the symbols have usual meaning then the value of $x$ is: (assuming ideality)

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The equivalent conductance of NaCl at concentration C and at infinite dilution are $\lambda_C$ and $\lambda_{\infty}$, respectively. The correct relationship between $\lambda_C$ and $\lambda_{\infty}$ is given as: (where the constant B is positive)

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For the estimation of nitrogen, $1.4\; g$ of organic compound was digested by Kjeldahl method and the evolved ammonia was absorbed in $60 \;mL$ of $\frac{M}{10}$ sulphuric acid. The unreacted acid require$20\; ml$ of $\frac{M}{10}$ sodium hydroxide for complete neutralization. The percentage of nitrogen in the compound is:

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The octahedral complex of a metal ion $M^{3+}$ with four monodentate ligands $L_1, L_2, L_3$ and $L_4$ absorb wavelengths in the region of red, green, yellow and blue, respectively. The increasing order of ligand strength of the four ligands is:

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In $S_N2$ reactions, the correct order of reactivity for the following compounds: $CH_3Cl, \;CH_3CH_2Cl,\; (CH_3)_2CHCl$ and $(CH_3)_3CCl$ is:

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In which of the following reactions $H_2O_2$ acts as a reducing agent? (a) $H_2O_2 +2H^+ + 2e^- \to 2H_2O$ (b) $H_2O_2 - 2e^- \to O_2 + 2H^+$ (c) $H_2O_2 + 2e^- \to 2OH^- $ (d) $H_2O_2 + 2OH^- - 2e^- \to O_2 + 2H_2O$

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Consider separate solutions of $0.500\; M\; C_2H_5OH(aq),\; 0.100\; M \;Mg_3(PO_4)_2(aq),\; 0.250\; M\; KBr(aq)$ and $0.125 \;M \;Na_3PO_4(aq)$ at $25^{\circ}C$. Which statement is true about these solutions, assuming all salts to be strong electrolytes?

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CsCl crystallises in body centred cubic lattice. If ‘a’ is its edge length then which of the following expressions is correct?

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Resistance of $0.2\; M$ solution of an electrolyte is $50 \Omega$. The specific conductance of the solution is $1.4 \;S m^{-1}$ . The resistance of $0.5\; M$ solution of the same electrolyte is $280 \Omega$. The molar conductivity of $0.5\; M$ solution of the electrolyte in $S \;m^2 mol^{-1}$ is:

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The metal that cannot be obtained by electrolysis of an aqueous solution of its salts is:

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If Z is a compressibility factor, van der Waals equation at low pressure can be written as:

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Which one of the following properties is not shown by NO?

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If $x = -1$ and $x = 2$ are extreme points of $f(x) = \alpha \log |x| + \beta x^2 + x$, then

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The slope of the line touching both the parabolas $y^2 = 4x$ and $x^2 = -32y$ is

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The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0$ and $l^2 = m^2 + n^2$ is

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If $(10)^9 + 2(11)^1 (10)^8 + 3(11)^2 (10)^7 + ....+ 10(11)^9 = k(10)^9$, then $k$ is equal to

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Three positive numbers from an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is

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The locus of the foot of perpendicular drawn from the centre of the ellipse $x^2 + 3y^2 = 6$ on any tangent to it is

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If $X = \{4^n - 3n - 1 : n \in N\}$ and $Y = \{9(n - 1) : n \in N\}$, where $N$ is the set of natural numbers, then $X \cup Y$ is equal to

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$\displaystyle{\lim_{x \to 0} \frac{\sin( \pi \cos^2 x)} {x^2}}$ is equal to

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Let PS be the median of the triangle with vertices $P(2, 2), Q(6, -1)$ and $R(7, 3)$. The equation of the line passing through $(1, -1)$ and parallel to PS is

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Let $a, b, c$ and d be non-zero numbers. If the point of intersection of the lines $4ax + 2ay + c = 0$ and $5bx + 2by + d = 0$ lies in the fourth quadrant and is equidistant from the two axes then

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The area of the region described by $A = \{(x, y) : x^2 + y^2 \leq 1$ and $y^2 \leq 1 - x\}$ is

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Let C be the circle with centre at $(1, 1)$ and $radius = 1$. If T is the circle centred at $(0, y)$, passing through origin and touching the circle C externally, then the radius of T is equal to

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Let the population of rabbits surviving at a time t be governed by the differential equation $\frac{dp(t)}{dt} = \frac{1}{2} p(t) - 200$ . If $p(0) = 100$, then $p(t)$ equals

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If f and g are differentiable functions in $[0, 1]$ satisfying $f(0) = 2 = g(1), g(0) = 0 $ and $f(1) = 6$, then for some $c \in ]0, 1[$

asked Dec 11, 2018 by pady_1

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et A and B be two events such that $P (\overline{A \cup B}) = \frac{1}{6} , \; P ( A \cap B) = \frac{1}{4} $ and $P(\overline{A}) = \frac{1}{4}$ , where $\overline{A}$ stands for the complement of the event A. Then the events A and B are

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Let $\alpha$ and $\beta$ be the roots of equation $px^2 + qx + r = 0,\; p \neq 0$. If $p, q, r$ are in A.P. and $\frac{1}{\alpha} + \frac{1}{\beta} = 4$, then the value of $|\alpha - \beta|$ is

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Let $f_K(x) = \frac{1}{k} (\sin^k x + \cos^k x)$ where $x \in R$ and $k \geq 1$. Then $f_4(x) - f_6(x)$ equals

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If $\alpha, \beta \neq 0$, and $f(n) = \alpha^n + \beta^n$ and $ \begin{vmatrix} 3 & 1+f(1) & 1+f(2) \\ 1+f(1) & 1+f(2) & 1+f(3) \\ 1+f(2) & 1+f(3) &1+f(4) \end{vmatrix} = K(1 - \alpha)^2 (1 - \beta)^2 (\alpha - \beta)^2$, then $K$ is equal to

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If $g$ is the inverse of a function $f$ and $f'(x) = \frac{1}{1+x^5}$ , then $g'(x)$ is equal to

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If z is a complex number such that $|z| \geq 2$, then the minimum value of $| x + \frac{1}{2} |$

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The integral $\begin{align} \int \begin{pmatrix}1 + x - \frac{1}{x} \end{pmatrix} e^{x + \frac{1}{x}} dx \end{align}$ is equal to

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If A is an $3 \times 3$ non-singular matrix such that $AA' = A'A$ and $B = A^{-1}A'$, then $BB'$ equals

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The statement $\sim (p \leftrightarrow \sim q)$ is

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The integral $\begin{align} \int_0^{\pi} \sqrt{1 + 4 \sin^2 \frac{x}{2} - 4 \sin \frac{x}{2} \; dx} \end{align}$ equals

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A bird is sitting on the top of a vertical pole $20\; m$ high and its elevation from a point O on the ground is $45^{\circ}$. It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to $30^{\circ}$. Then the speed (in m/s) of the bird is

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The variance of first 50 even natural numbers is

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If $[ \overrightarrow{a} \times \overrightarrow{b} \; \overrightarrow{ b} \times \overrightarrow{c } \; \overrightarrow{c} \times \overrightarrow{a} ] = \lambda [ \overrightarrow{a} \; \overrightarrow{b} \; \overrightarrow{c} ]^2$ , then $\lambda$ is equal to

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If $a \in R$ and the equation $-3(x - [x])^2 + 2 (x - [x]) + a^2 = 0$ (where $[x]$ denotes the greatest integer $\leq x$) has no integral solution, then all possible values of a lie in the interval

asked Dec 11, 2018 by pady_1

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If the coefficients of $x^3$ and $x^4$ in the expansion of $(1 + ax + bx^2 ) (1 - 2x)^{18}$ in powers of $x$ are both zero, then $(a, b)$ is equal to

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The image of the line $\frac{x-1}{3} = \frac{y-3}{1} = \frac{z-4}{-5}$ in the plane $2x-y+z+3 = 0$ is the line

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Assume that an electric field $\overrightarrow{E} = 30 x^2 \hat{i}$ exists in space. Then the potential difference $V_A - V_O$, where $V_O$ is the potential at the origin and $V_A$ the potential at $x=2$ is :

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Two beams, A and B, of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam A has maximum intensity (and beam B has zero intensity), a rotation of Polaroid through $30^{\circ}$ makes the two beams appear equally bright. If the initial intensities of the two beams are $I_A$ and $I_B$ respectively, then $I_A/I_B$ equals :

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On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If r < < R, and the surface tension of water is T, value of r just before bubbles detach is : (density of water is $\rho_w$)

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When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude $F = ax + bx^2$ where a and b are constants. The work done in stretching the unstretched rubber band by L is :

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