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Recent questions and answers in 2013
Questions
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JEEMAIN and NEET
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JEEMAIN PAST PAPERS
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2013
The term independent of $x$ is expansion of $\begin{pmatrix} \frac{x+1}{x^{2/3}-x^{1/3} + 1 } - \frac{x-1}{x - x^{1/2}} \end{pmatrix}^{10}$ is
jeemain
math
past papers
2013
60
answered
Apr 24
by
priyanka.clay6
1
answer
Distance between two parallel planes $2x + y + 2z = 8$ and $4x + 2y + 4z + 5 = 0$ is
jeemain
math
past papers
2013
59
answered
Apr 24
by
priyanka.clay6
1
answer
If the equation $x^2 + 2x + 3 = 0$ and $ax^2 + bx + c = 0, a, b, c \in R$, have a common root, then a : b : c$ is
jeemain
math
past papers
2013
58
answered
Apr 24
by
priyanka.clay6
1
answer
The $z$ is a complex number of unit modulus an argument $\theta$, then $arg \begin{pmatrix}\frac{1+z}{1+ \overline{z}} \end{pmatrix}$ equals
jeemain
math
past papers
2013
57
answered
Apr 24
by
priyanka.clay6
1
answer
A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is
jeemain
math
past papers
2013
56
answered
Apr 24
by
priyanka.clay6
1
answer
If the vectors $\overline{AB} = 3 \hat{i} + 4 \hat{k}$ and $\overline{AC} = 5 \hat{i} - 2 \hat{j} + 4 \hat{k}$ are the sides of a triangles ABC, then the length of the median through A is
jeemain
math
past papers
2013
55
answered
Apr 24
by
priyanka.clay6
1
answer
Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of $A \times B$ having 3 or more elements is
jeemain
math
past papers
2013
54
answered
Apr 24
by
priyanka.clay6
1
answer
If the lines $\frac{x-2}{1} = \frac{y-3}{1} = \frac{z-4}{-k}$ and $\frac{x-1}{k} = \frac{y-4}{2} = \frac{z-5}{1}$ are coplanar, then $k$ can have
jeemain
math
past papers
2013
53
answered
Apr 24
by
priyanka.clay6
1
answer
If $y = \sec(\tan^{-1}x)$, then $\frac{dy}{dx} $ at $x=1$ is equal to
jeemain
math
past papers
2013
52
answered
Apr 24
by
priyanka.clay6
1
answer
The numbers of values of k, for which the system of equations <br> $( k + 1) x + 8y = 4k $ <br> kx + (k + 3)y = 3k - 1$ <br> has no solution, is
jeemain
math
past papers
2013
51
answered
Apr 24
by
priyanka.clay6
1
answer
If $P = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix}$ is the adjoint of a $3 \times 3$ matrix A and $|A| = 4$, then $\alpha$ is equal to
jeemain
math
past papers
2013
50
answered
Apr 24
by
priyanka.clay6
1
answer
Statement -I : The value of the integral $\begin{align*} \int_{\pi/6}^{\pi/3} \frac{dx}{1+\sqrt{\tan x} } \end{align*}$ is equal to $\frac{\pi}{6}$. <br> Statement-II : $\begin{align*} \int_a^b f(x) dx = \int_a^b f(a+b-x) dx \end{align*}$
jeemain
math
past papers
2013
49
answered
Apr 24
by
priyanka.clay6
1
answer
At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers $x$ is given by $\frac{dP}{dx} = 100 - 12\sqrt{x}$. If the firm employs 25 more workers, then the new level of production of items is
jeemain
math
past papers
2013
48
answered
Apr 24
by
priyanka.clay6
1
answer
Let $T_n$ be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If $T_{n+1} - T_n = 10$, then the value of $n$ is
jeemain
math
past papers
2013
47
answered
Apr 24
by
priyanka.clay6
1
answer
$\displaystyle{\lim_{x \to 0} \frac{(1 - \cos 2x) ( 3 + \cos x)}{ x \tan 4 x}}$ is equal to
jeemain
math
past papers
2013
46
answered
Apr 24
by
priyanka.clay6
1
answer
The real number $k$ for which the equation, $2x^3 + 3x+ k = 0$ has two distinct real roots in $[0, 1]$
jeemain
math
past papers
2013
45
answered
Apr 24
by
priyanka.clay6
1
answer
The expression $\frac{\tan A}{1 - \cot A} + \frac{\cot A}{1 - \tan A} $ can be written as
jeemain
math
past papers
2013
44
answered
Apr 24
by
priyanka.clay6
1
answer
The area (in square units) bounded by the curves $y = \sqrt{x}, 2y - x + 3 = 0$, x-axis, and lying in the first quadrant is
jeemain
math
past papers
2013
43
answered
Apr 24
by
priyanka.clay6
1
answer
Consider : <Br> Statement -I : $(P \wedge \sim q ) \wedge ( \sim p \wedge q )$ is a fallacy. <br> Statement-II : $(p \to q) \leftrightarrow ( \sim q \to \sim p)$ is a tautology.
jeemain
math
past papers
2013
42
answered
Apr 23
by
priyanka.clay6
1
answer
The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, ….. , is
jeemain
math
past papers
2013
41
answered
Apr 23
by
priyanka.clay6
1
answer
The intercepts on x-axis made by tangents to the curve, $\begin{align*} y = \int_0^x |t| dt. x \in R \end{align*}$. which are parallel to the line $y = 2x$, are equal to
jeemain
math
past papers
2013
40
answered
Apr 21
by
priyanka.clay6
1
answer
The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1), (1, 1) and (1, 0) is
jeemain
math
past papers
2013
39
answered
Apr 21
by
priyanka.clay6
1
answer
The equation of the circle passing through the foci of the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$, and having centre at (0, 3) is
jeemain
math
past papers
2013
38
answered
Apr 21
by
priyanka.clay6
1
answer
If $\displaystyle\int f (x) dx = \Psi (x)$, then $\displaystyle\int x^5 f (x^3) dx$ is equal to
jeemain
math
past papers
2013
37
answered
Apr 21
by
priyanka.clay6
1
answer
If $x, y, z$ are in A.P and $\tan^{-1}x. \tan^{-1}y$ and $\tan^{-1}z$ are also in A.P., then
jeemain
math
past papers
2013
36
answered
Apr 21
by
priyanka.clay6
1
answer
All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given ?
jeemain
math
past papers
2013
35
answered
Apr 21
by
priyanka.clay6
1
answer
A ray of light along $x + \sqrt{3}y = \sqrt{3}$ gets reflected upon reaching x-axis , the equation of the reflected rays is
jeemain
math
past papers
2013
34
answered
Apr 21
by
priyanka.clay6
1
answer
Given : A circle, $2x^2 + 2y^2 = 5 $ and a parabola. $y^2 = 4 \sqrt{5} x$. <br> Statement - I : An equation of a common tangent to these curves is $y = x+\sqrt{5}$. <br> Statement - II : If the line, $y = mx + \frac{\sqrt{5}}{m} (m \neq 0)$is their common tangent, then m satisfies $m^4 - 3m^2 +2 = $
jeemain
math
past papers
2013
33
answered
Apr 20
by
priyanka.clay6
1
answer
ABCD is a trapezium such that AB and CD are parallel and $BC \perp CD$. If $\angle{ADB} = \theta, \; BC = p$ and $CD = q$, then AB is equal to
jeemain
math
past papers
2013
32
answered
Apr 20
by
priyanka.clay6
1
answer
The circle passing through (1, -2) and touching the axis of $x$ at $(3, 0)$ also passes through the point
jeemain
math
past papers
2013
31
answered
Apr 20
by
priyanka.clay6
1
answer
Which of the following exists as covalent crystals in the solid state ?
jeemain
chemistry
past papers
2013
26
answered
Jul 22, 2019
by
bathinapavankumar789
1
answer
Two short bar magnets of length 1 cm each have magnetic moments $1.20\; Am^2$ and $1.00\; Am^2 $ respectively. They are placed on a horizontal table parallel to each other with their N poles pointing towards the South. They have a common magnetic equator and are separated by a distance of 20.0 cm. The value of the resultant horizontal magnetic induction at the mid - point O of the line joining their centres is close to (Horizontal component of earth’s magnetic induction is $3.6 \times 10^{–5} Wb/m^2$)
jeemain
physics
past papers
2013
90
asked
Dec 11, 2018
by
pady_1
0
answers
The magnetic field in a travelling electromagnetic wave has a peak value of 20 nT. The peak value of electric field strength is :
jeemain
physics
past papers
2013
89
asked
Dec 11, 2018
by
pady_1
0
answers
Diameter of plano-convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material of lens is $2 \times 10^8$ m/s, the focal length of the lens is :
jeemain
physics
past papers
2013
88
asked
Dec 11, 2018
by
pady_1
0
answers
The amplitude of a damped oscillator decreases to 0.9 times its original magnitude is 5s. In another 10s it will decrease to $\alpha$ times its original magnitude, where $\alpha$ equals
jeemain
physics
past papers
2013
87
asked
Dec 11, 2018
by
pady_1
0
answers
This question has Statement I and Statement II. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement – I : A point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as $f (\frac{1}{2} mv^2 )$ then $f = (\frac{m}{M+m})$. Statement – II : Maximum energy loss occurs when the particles get stuck together as a result of the collision.
jeemain
physics
past papers
2013
86
asked
Dec 11, 2018
by
pady_1
0
answers
The I – V characteristic of an LED is
jeemain
physics
past papers
2013
85
asked
Dec 11, 2018
by
pady_1
0
answers
If a piece of metal is heated to temperature $\theta$ and then allowed to cool in a room which is at temperature $\theta_0$ the graph between the temperature T of the metal and time t will be closest to :
jeemain
physics
past papers
2013
84
asked
Dec 11, 2018
by
pady_1
0
answers
A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 2.0 A flows through the smaller loop, then the flux linked with bigger loop is
jeemain
physics
past papers
2013
83
asked
Dec 11, 2018
by
pady_1
0
answers
A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is: <br>
jeemain
physics
past papers
2013
82
asked
Dec 11, 2018
by
pady_1
0
answers
An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and cylinder have equal cross sectional area A. When the piston is in equilibrium, the volume of the gas is $V_0$ and its pressure is $P_0$. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency:
jeemain
physics
past papers
2013
81
asked
Dec 11, 2018
by
pady_1
0
answers
A hoop of radius r and mass m rotating with an angular velocity $\omega_0$ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?
jeemain
physics
past papers
2013
80
asked
Dec 11, 2018
by
pady_1
0
answers
Two capacitors $C_1$ and $C_2$ are charged to 120 V and 200 V respectively. It is found that by connecting them together the potential on each one can be made zero. Then :
jeemain
physics
past papers
2013
79
asked
Dec 11, 2018
by
pady_1
0
answers
A projectile is given an initial velocity of $(\hat{i} + 2 \hat{j}) m/s$, where $\hat{i}$ is along the ground and ˆj is along the vertical. If $g = 10 m/s^2$, the equation of its trajectory is:
jeemain
physics
past papers
2013
78
asked
Dec 11, 2018
by
pady_1
0
answers
What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?
jeemain
physics
past papers
2013
77
asked
Dec 11, 2018
by
pady_1
0
answers
This question has statement I and statement II. Of the four choices given after the statements, choose the one that best describes the two statements. <br> Statement- I: Higher the range, greater is the resistance of ammeter. <br> Statement- II: To increase the range of ammeter, additional shunt needs to be used across it.
jeemain
physics
past papers
2013
76
asked
Dec 11, 2018
by
pady_1
0
answers
A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1 %. What is the fundamental frequency of steel if density and elasticity of steel are $7.7 \times 10^3 \;kg/m^3$ and $2.2 \times 10^{11}N/m^2$ respectively?
jeemain
physics
past papers
2013
75
asked
Dec 11, 2018
by
pady_1
0
answers
<br> The above p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat extracted from the source in a single cycle is
jeemain
physics
past papers
2013
74
asked
Dec 11, 2018
by
pady_1
0
answers
Let $[\varepsilon_0]$ denote the dimensional formula of the permittivity of vaccum. If M = mass, L = length, T = time and A = electric current, then :
jeemain
physics
past papers
2013
73
asked
Dec 11, 2018
by
pady_1
0
answers
The graph between angle of deviation (δ) and angle of incidence (i) for a triangular prism is represented by:
jeemain
physics
past papers
2013
72
asked
Dec 11, 2018
by
pady_1
0
answers
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