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Recent questions and answers in 2014

Questions >> JEEMAIN and NEET >> JEEMAIN PAST PAPERS >> 2014

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

answered Apr 19, 2020 by priyanka.clay6

1 answer

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

answered Apr 19, 2020 by priyanka.clay6

1 answer

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

answered Apr 19, 2020 by priyanka.clay6

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

answered Apr 19, 2020 by priyanka.clay6

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

answered Apr 19, 2020 by priyanka.clay6

1 answer

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

answered Apr 19, 2020 by priyanka.clay6

1 answer

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

answered Apr 18, 2020 by priyanka.clay6

1 answer

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

answered Apr 18, 2020 by priyanka.clay6

1 answer

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

answered Apr 18, 2020 by priyanka.clay6

1 answer

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

answered Apr 18, 2020 by priyanka.clay6

1 answer

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

answered Apr 18, 2020 by priyanka.clay6

1 answer

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

answered Apr 18, 2020 by priyanka.clay6

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

answered Apr 18, 2020 by priyanka.clay6

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 $c \in ]0, 1[$

answered Apr 18, 2020 by priyanka.clay6

1 answer

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

answered Apr 18, 2020 by priyanka.clay6

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

answered Apr 18, 2020 by priyanka.clay6

1 answer

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

answered Apr 18, 2020 by priyanka.clay6

1 answer

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

answered Apr 14, 2020 by priyanka.clay6

1 answer

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

answered Apr 14, 2020 by priyanka.clay6

1 answer

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

answered Apr 12, 2020 by priyanka.clay6

1 answer

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

answered Apr 12, 2020 by priyanka.clay6

1 answer

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

answered Apr 12, 2020 by priyanka.clay6

1 answer

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

answered Apr 12, 2020 by priyanka.clay6

1 answer

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

answered Apr 11, 2020 by priyanka.clay6

1 answer

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

answered Apr 11, 2020 by priyanka.clay6

1 answer

The variance of first 50 even natural numbers is

answered Apr 11, 2020 by priyanka.clay6

1 answer

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

answered Apr 11, 2020 by priyanka.clay6

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

answered Apr 11, 2020 by priyanka.clay6

1 answer

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

answered Apr 9, 2020 by priyanka.clay6

1 answer

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

answered Apr 9, 2020 by priyanka.clay6

1 answer

The most suitable reagent for the conversion of $R-CH_2- OH \to R - CHO$ is:

answered Apr 9, 2019 by madhu17032014

1 answer

A bob of mass m attached to an inextensible string of length $l$ is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed $\omega$ rad/s about the vertical. About the point of suspension :

answered Mar 22, 2019 by ainaraichal

1 answer

For complete combustion of ethanol, $C_2H_5OH (\ell) + 3O_2 (g) \to 2CO_2 (g) + 3H_2O (\ell)$, the amount of heat produced as measured in bomb calorimeter, is $1364.47\; kJ \;mol^{–1}$ at $25^{\circ}C$. Assuming ideality the Enthalpy of combustion, $\Delta_CH$, for the reaction will be: $(R = 8.314\; kJ \;mol^{–1} )$

asked Dec 11, 2018 by pady_1

0 answers

Among the following oxoacids, the correct decreasing order of acid strength is:

asked Dec 11, 2018 by pady_1

0 answers

Which one is classified as a condensation polymer?

asked Dec 11, 2018 by pady_1

0 answers

The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1 : 4. The ratio of number of their molecule is:

asked Dec 11, 2018 by pady_1

0 answers

Given below are the half-cell reactions : <br> $Mn^{2+} + 2e^- \to Mn; \; E^0 = -1.18 \;V$ <br> $2(Mn^{3+} + e^- \to Mn^{2+} ) \; ; E^0 = +1.51 \; V$ <br> The $E^0$ for $2Mn^{2+} \to Mn + 2Mn^{3+} $ will be :

asked Dec 11, 2018 by pady_1

0 answers

The major organic compound formed by the reaction of 1, 1, 1-trichloroethane with silver powder is :

asked Dec 11, 2018 by pady_1

0 answers

The correct set of four quantum numbers for the valence elections of rubidium atom (Z= 37) is:

asked Dec 11, 2018 by pady_1

0 answers

Which one of the following bases is not present in DNA?

asked Dec 11, 2018 by pady_1

0 answers

Considering the basic strength of amines in aqueous solution, which one has the smallest $pK_b$ value?

asked Dec 11, 2018 by pady_1

0 answers

Which series of reactions correctly represents chemical reactions related to iron and its compound?

asked Dec 11, 2018 by pady_1

0 answers

For the non â€“ stoichiometre reaction $2A +B \to C + D$ , the following kinetic data were obtained in three separate experiments, all at $298\; K$. <br> <br> The rate law for the formation of C is:

asked Dec 11, 2018 by pady_1

0 answers

For which of the following molecule significant $\mu \neq 0$? <br>

asked Dec 11, 2018 by pady_1

0 answers

The equation which is balanced and represents the correct product(s) is:

asked Dec 11, 2018 by pady_1

0 answers

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

asked Dec 11, 2018 by pady_1

0 answers

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

asked Dec 11, 2018 by pady_1

0 answers

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

asked Dec 11, 2018 by pady_1

0 answers

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

asked Dec 11, 2018 by pady_1

0 answers

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

0 answers

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