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Recent questions and answers in 2014
Questions
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JEEMAIN and NEET
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JEEMAIN PAST PAPERS
>>
2014
If $x = -1$ and $x = 2$ are extreme points of $f(x) = \alpha \log |x| + \beta x^2 + x$, then
jeemain
math
past papers
2014
60
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
jeemain
math
past papers
2014
59
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
jeemain
math
past papers
2014
58
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
jeemain
math
past papers
2014
57
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
jeemain
math
past papers
2014
56
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
jeemain
math
past papers
2014
55
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
jeemain
math
past papers
2014
54
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
jeemain
math
past papers
2014
53
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
jeemain
math
past papers
2014
52
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
jeemain
math
past papers
2014
51
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
jeemain
math
past papers
2014
50
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
jeemain
math
past papers
2014
49
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
jeemain
math
past papers
2014
48
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 $c \in ]0, 1[$
jeemain
math
past papers
2014
47
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
jeemain
math
past papers
2014
46
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
jeemain
math
past papers
2014
43
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
jeemain
math
past papers
2014
44
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
jeemain
math
past papers
2014
45
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
jeemain
math
past papers
2014
42
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 $| x + \frac{1}{2} |$
jeemain
math
past papers
2014
41
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
jeemain
math
past papers
2014
40
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
jeemain
math
past papers
2014
39
answered
Apr 12, 2020
by
priyanka.clay6
1
answer
The statement $\sim (p \leftrightarrow \sim q)$ is
jeemain
math
past papers
2014
38
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
jeemain
math
past papers
2014
37
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
jeemain
math
past papers
2014
36
answered
Apr 11, 2020
by
priyanka.clay6
1
answer
The variance of first 50 even natural numbers is
jeemain
math
past papers
2014
35
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
jeemain
math
past papers
2014
34
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
jeemain
math
past papers
2014
33
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
jeemain
math
past papers
2014
32
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
jeemain
math
past papers
2014
31
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:
jeemain
chemistry
past papers
2014
90
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 :
jeemain
physics
past papers
2014
3
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: $(R = 8.314\; kJ \;mol^{–1} )$
jeemain
chemistry
past papers
2014
89
asked
Dec 11, 2018
by
pady_1
0
answers
Among the following oxoacids, the correct decreasing order of acid strength is:
jeemain
chemistry
past papers
2014
88
asked
Dec 11, 2018
by
pady_1
0
answers
Which one is classified as a condensation polymer?
jeemain
chemistry
past papers
2014
87
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:
jeemain
chemistry
past papers
2014
86
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 :
jeemain
chemistry
past papers
2014
85
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 :
jeemain
chemistry
past papers
2014
84
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:
jeemain
chemistry
past papers
2014
83
asked
Dec 11, 2018
by
pady_1
0
answers
Which one of the following bases is not present in DNA?
jeemain
chemistry
past papers
2014
82
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?
jeemain
chemistry
past papers
2014
81
asked
Dec 11, 2018
by
pady_1
0
answers
Which series of reactions correctly represents chemical reactions related to iron and its compound?
jeemain
chemistry
past papers
2014
80
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:
jeemain
chemistry
past papers
2014
79
asked
Dec 11, 2018
by
pady_1
0
answers
For which of the following molecule significant $\mu \neq 0$? <br>
jeemain
chemistry
past papers
2014
78
asked
Dec 11, 2018
by
pady_1
0
answers
The equation which is balanced and represents the correct product(s) is:
jeemain
chemistry
past papers
2014
77
asked
Dec 11, 2018
by
pady_1
0
answers
The correct statement for the molecule, $CsI_3$ is:
jeemain
chemistry
past papers
2014
76
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:
jeemain
chemistry
past papers
2014
75
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:
jeemain
chemistry
past papers
2014
74
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 :
jeemain
chemistry
past papers
2014
73
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)
jeemain
chemistry
past papers
2014
72
asked
Dec 11, 2018
by
pady_1
0
answers
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