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A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is :

asked Jun 5, 2017 by priyanka.c

1 answer

Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity ?

asked Jun 5, 2017 by priyanka.c

1 answer

Time (T), velocity (C) and angular momentum (h) are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be :

asked Jun 5, 2017 by priyanka.c

1 answer

To determine refractive index of glass slab using a travelling microscope, minimum number of readings required are:

asked Jun 2, 2017 by priyanka.c

1 answer

A particle is executing simple harmonic motion with a time period T. At time $t=0$, it is at its position of quilibrium. The kinetic energy - time graph of the particle will look like

asked May 31, 2017 by meena.p

1 answer

The temperature of an open room of volume $30 m^3$ increases from $17^{\circ}C$ to $27^{\circ}C$ due to the sunshine. The atmospheric pressure in the room remains $1×10^5\; Pa$.If $n_i$ and $n_f$ are the number of molecules in the room before and after heating, then $n_f−n_i$ will be :

asked May 31, 2017 by meena.p

1 answer

$C_p$ and $C_v$ are specific heats at constant pressure and constant volume respectively. It is observed that $C_p−C_v=a$ for hydrogen gas $Cp−Cv=b$ for nitrogen gas The correct relation between a and b is :

asked May 31, 2017 by meena.p

1 answer

An external pressure P is applied on a cube at $0^{\circ}C$ so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and α is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by :

asked May 31, 2017 by meena.p

1 answer

A copper ball of mass $100\; gm $is at a temperature T. It is dropped in a copper calorimeter of mass $100\; gm$, filled with $170\; gm$ of water at room temperature.Subsequently, the temperature of the system is found to be $75^{\circ}C$. T is given by : (Given : room temperature$=30^{\circ}C$, specific heat of copper $=0.1\; cal/gm^{\circ}C)$

asked May 31, 2017 by meena.p

1 answer

The contrapositive of the following statement,
“If the side of a square doubles, then its area increases four times”, is :

asked May 30, 2017 by priyanka.c

1 answer

The angle of elevation of the top of a vertical tower from a point $A,$ due east of it is $45^0$. The angle of elevation of the top of the same tower from a point $ B$, due south of $A$ is $30^0$. If the distance between $A$ and $B$ is $54 \sqrt 2$ m , then the height of the tower (in metres), is :

asked May 30, 2017 by priyanka.c

1 answer

If $A>0, B>0$ and $Α + B = \frac{\pi}{6} ,$ then the minimum value of $ \tan A + \tan B$ is :

asked May 30, 2017 by priyanka.c

1 answer

An experiment succeeds twice as often as it fails. The probability of at least 5 successes in the six trials of this experiment is :

asked May 30, 2017 by priyanka.c

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The $mean$ of $5$ observations is $5$ and their $variance$ is $124$. If three of the observations are $1, 2$ and $6$ ; then the mean deviation from the mean of the data is :

asked May 30, 2017 by priyanka.c

1 answer

Let $ABC $ be a triangle whose circumcentre is at $P$. If the position vectors of $A, B, C$ and $P$ are $\overrightarrow{a} , \overrightarrow{b}, \overrightarrow{c}$ and $\frac{\overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c}}{4}$ respectively, then the position vector of the orthocentre of this triangle, is :

asked May 30, 2017 by priyanka.c

1 answer

The number of distinct real values of $λ$ for which the lines $\begin{align} \frac{x-1}{1} = \frac{y-2}{2} = \frac{z+3}{\lambda^2} \end{align}$ and $\begin{align}\frac{x-3}{1} = \frac{y-2}{\lambda^2 } = \frac{z-1}{2} \end{align} $ are coplanar is:

asked May 30, 2017 by priyanka.c

1 answer

ABC is a triangle in a plane with vertices $A(2, 3, 5), B(−1, 3, 2)$ and $C(λ, 5, µ).$ If the median through $A$ is equally inclined to the coordinate axes, then the value of $(λ^3+µ^3+5)$ is :

asked May 30, 2017 by priyanka.c

1 answer

The variation of acceleration due to gravity $g$ with distance d from centre of the earth is best represented by (R=Earth’s radius) :

asked May 30, 2017 by meena.p

1 answer

A slender uniform rod of mass M and length l is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle $\theta$ with the vertical is :

asked May 30, 2017 by meena.p

1 answer

The moment of inertia of a uniform cylinder of length l and radius R about its perpendicular bisector is $I$. What is the ratio $\large\frac{l}{R}$ such that the moment of inertia is minimum ?

asked May 30, 2017 by meena.p

1 answer

A hyperbola whose transverse axis is along the major axis of the conic, $\frac{x^2}{3} + \frac{y^2}{4} = 4$ and has vertices at the foci of this conic. If the eccentricity of the hyperbola is $\frac{3}{2}$, then which of the following points does $NOT$ lie on it ?

asked May 30, 2017 by priyanka.c

1 answer

$P$ and $Q$ are two distinct points on the parabola, $y2=4x,$ with parameters $t$ and $t_1$ respectively. If the normal at $P$ passes through $Q$, then the minimum value of $ t_1^2$ is :

asked May 30, 2017 by priyanka.c

1 answer

A time dependent force $F=6t$ acts on a particle of mass $1\;kg$. If the particle starts from rest, the work done by the force during the first 1 sec. will be :

asked May 30, 2017 by meena.p

1 answer

Equation of the tangent to the circle, at the point $(1, −1)$, whose centre is the point of intersection of the straight lines $x−y=1$ and $2x+y=3$ is :

asked May 30, 2017 by priyanka.c

1 answer

A straight line through origin $O$ meets the lines $3y=10−4x$ and $8x+6y+5=0$ at points $A$ and $B$ respectively. Then $O$ divides the segment $AB$ in the ratio :

asked May 29, 2017 by priyanka.c

1 answer

A ray of light is incident along a line which meets another line,$ 7x−y+1=0$, at the point $(0, 1). $ The ray is then reflected from this point along the line, $y+2x=1.$ Then the equation of the line of incidence of the ray of light is :

asked May 29, 2017 by priyanka.c

1 answer

The solution of the differential equation $\begin{align} \frac{dy}{dx} + \frac{y}{2} \sec x = \frac{\tan}{2\;y}, \end{align}$ where $0 \leq x < \frac{\pi}{2},$ and $y(0)= 1,$ is given by

asked May 29, 2017 by priyanka.c

1 answer

For $ x \; \epsilon \;R, x ≠ 0,$ if $y(x)$ is a differentiable function such that $\begin{align} x \int_1^x y\; (t) \;dt = (x+1) \int_1^x t\; y \;(t)\; dt, \end{align}$ then $y(x) $ equals :
(where C is a constant.)

asked May 29, 2017 by priyanka.c

1 answer

The value of the integral $\begin{align} \int_4^{10} \frac{[x^2]dx}{[x^2 -28x + 196] + [x^2] } , \end{align}$ where $[x]$ denotes the greatest integer less than or equal to $x,$ is :

asked May 29, 2017 by priyanka.c

1 answer

The integral $\begin{align} \int \frac{dx}{(1+\sqrt x) \sqrt{x - x^2}} \end{align}$ to :
(where C is a constant of integration.)

asked May 29, 2017 by priyanka.c

1 answer

A body of mass $m=10^{−2}\; kg$ is moving in a medium and experiences a frictional force $F=−kv^2$. Its initial speed is $v_0=10 ms^{−1}$. If, after $10\;s$, its energy is $\large\frac{1}{8}$$ \;mv_0^2$,the value of k will be :

asked May 29, 2017 by meena.p

1 answer

A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time ?

asked May 29, 2017 by meena.p

1 answer

Let $C$ be a curve given by $y (x) = 1 + \sqrt{4x - 3}, x>\frac{3}{4}.$ If P is a point on $ C$, such that the tangent at $P$ has slope $\frac{2}{3},$ then a point through which the normal at $P$ passes is:

asked May 29, 2017 by priyanka.c

1 answer

Let $f(x)=sin^4x+cos^4x.$ Then f is an increasing function in the interval :

asked May 29, 2017 by priyanka.c

1 answer

A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of :

asked May 29, 2017 by meena.p

1 answer

If the tangent at a point on the ellipse $\large\frac{x^2}{27} +\frac{y^2}{3}$$=1$ meets the coordinate axes at A and B, and O is the origin, then the minimum area (in sq. units) of the triangle $OAB$ is :

asked May 29, 2017 by meena.p

1 answer

Consider the following two statements : <br> P : If 7 is an odd number, then 7 is divisible by 2. <br> Q : If 7 is a prime number, then 7 is an odd number. <br> If $V_1$ is the truth value of the contrapositive of $P$ and $V_2$ is the truth value of contrapositive of Q, then the ordered pair $(V_1, V_2)$ equals :

asked May 29, 2017 by meena.p

1 answer

If $m$ and $M$ are the minimum and the maximum values of $4 +\large\frac{1}{2} $$\sin ^2 2x - 2 \cos ^4 x , x \in R$ then $M−m$ is equal to :

asked May 29, 2017 by meena.p

1 answer

The number of $x \in [0, 2 \pi]$ for which $| \sqrt{2 \sin ^4 x +18 \cos ^2 x} - \sqrt {2 \cos ^4 x +18 \sin ^2 x}|=1$ is :

asked May 29, 2017 by meena.p

1 answer

If $A$ and $B$ are any two events such that $P(A)= \large\frac{2}{5}$ and $P(A \cap B)=\large\frac{3}{20}$,then the conditional probability, $P(A |(A' \cup B')),$ where $A'$ denotes the complement of A, is equal to :

asked May 29, 2017 by meena.p

1 answer

Let $a, b \;\epsilon \; R, (a ≠ 0). $ If the function f defined as $f(x) = \begin{cases} \frac{2x^2}{a}, & 0 \leq x < 1 \\ a , & 1 \leq x < \sqrt 2 \\ \frac{2b^2 - 4b}{x^3}, & \sqrt 2 \leq x < \infty \end{cases}$ is continuous in the interval $[0, ∞)$, then an ordered pair $(a, b)$ is

asked May 29, 2017 by priyanka.c

1 answer

If the mean deviation of the numbers $1, 1+ d, ..., 1+100d$ from their mean is $255$, then a value of $d$ is :

asked May 29, 2017 by meena.p

1 answer

In a triangle $ABC$, right angled at the vertex $A$, if the position vectors of A, B and C are respectively $3 \hat i + \hat j - \hat k , \hat i+3 \hat j +p \hat k $ and $5 \hat i+q \hat j -4 \hat k$ then the point $(p, q)$ lies on a line :

asked May 29, 2017 by meena.p

1 answer

The distance of the point $(1, −2, 4)$ from the plane passing through the point $(1, 2, 2)$ and perpendicular to the planes $x−y+2z=3$ and $2x−2y+z+12=0,$ is :

asked May 29, 2017 by meena.p

1 answer

$\begin{align}\lim_{x\to o}\frac{(1 - \cos2x)^2}{2x \; \tan x -x \tan 2x } \end{align} $ is :

asked May 29, 2017 by priyanka.c

1 answer

The shortest distance between the lines $\large\frac{x}{2}=\frac{y}{2}=\frac{z}{1}$ and $\large\frac{x+2}{-1} = \frac{y-4}{8} =\frac{z-5}{4}$ lies in the interval

asked May 29, 2017 by meena.p

1 answer

The sum $\displaystyle\sum_{r =1}^{10} (r^2 + 1) \times (r!)$ is equal to :

asked May 29, 2017 by priyanka.c

1 answer

Let a and b respectively be the semitransverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation $9e^2−18e+5=0$. If $S(5, 0)$ is a focus and $5x=9$ is the corresponding directrix of this hyperbola, then $a^2−b^2$ is equal to

asked May 29, 2017 by meena.p

1 answer

Let $a_1, a_2, a_3, ......, a_n, .....$ be in A.P. If $a_3+a_7+a_11+a_15=72,$ then the sum of its $first\; 17\; terms$ is equal to :

asked May 29, 2017 by priyanka.c

1 answer

If the coefficients of $x^{−2}$ and $x^{−4}$ in the expansion of $\begin{align} \begin{bmatrix}x^{\frac{1}{3}}+ \frac{1}{2x^{\frac{1}{3}}} \end{bmatrix}^{18}, (x>0) \end{align}$ are $m$ and $n$ respectively, then $\frac{m}{n}$ is equal to :

asked May 29, 2017 by priyanka.c

1 answer

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