Recent questions in JEEMAIN and NEET

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

asked Dec 11, 2018 by pady_1

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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:

asked Dec 11, 2018 by pady_1

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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 :

asked Dec 11, 2018 by pady_1

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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)

asked Dec 11, 2018 by pady_1

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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)

asked Dec 11, 2018 by pady_1

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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:

asked Dec 11, 2018 by pady_1

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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:

asked Dec 11, 2018 by pady_1

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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:

asked Dec 11, 2018 by pady_1

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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) $H_2O_2 + 2OH^- - 2e^- \to O_2 + 2H_2O$

asked Dec 11, 2018 by pady_1

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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?

asked Dec 11, 2018 by pady_1

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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?

asked Dec 11, 2018 by pady_1

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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:

asked Dec 11, 2018 by pady_1

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

asked Dec 11, 2018 by pady_1

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

asked Dec 11, 2018 by pady_1

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

asked Dec 11, 2018 by pady_1

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

asked Dec 11, 2018 by pady_1

1 answer

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

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

1 answer

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

asked Dec 11, 2018 by pady_1

1 answer

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

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

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

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

1 answer

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

asked Dec 11, 2018 by pady_1

1 answer

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

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

1 answer

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

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

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

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

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

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

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The variance of first 50 even natural numbers is

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

1 answer

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

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

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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 :

asked Dec 11, 2018 by pady_1

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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 :

asked Dec 11, 2018 by pady_1

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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 $\rho_w$)

asked Dec 11, 2018 by pady_1

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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 :

asked Dec 11, 2018 by pady_1

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A block of mass m is placed on a surface with a vertical cross section given by $y = x^3 /6$. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is :

asked Dec 11, 2018 by pady_1

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