Maths-
General
Easy
Question
Which of the following is an equivalence relation ?
- x-y is divisible by 5
- x divides y
The correct answer is: x-y is divisible by 5
xRx since ; 0 is divisible by 5 if xRy , x-y is divisible by 5, y-x is also divisible by 5 if xRy & 
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Maths-
If R = {(x,y): x, yÎN, y is the remainder when x is divided by 7}.Then sum of all numbers in range of R
If R = {(x,y): x, yÎN, y is the remainder when x is divided by 7}.Then sum of all numbers in range of R
Maths-General
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Let 
and 
then R is
Let and then R is
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Let 
and 
then the relation R on A is
Let and then the relation R on A is
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Let Y = { 1,2,3,4,5}, A = {1,2}, B ={3,4,5} and 
denote the null set. If A ´ B denotes the cartesian product of sets A and B, then 
Let Y = { 1,2,3,4,5}, A = {1,2}, B ={3,4,5} and denote the null set. If A ´ B denotes the cartesian product of sets A and B, then
Maths-General
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A container filled with viscous liquid is moving vertically downwards with constant speed 3v0 . At the instant shown, a sphere of radius r is moving vertically downwards (in liquid) has speed v0 . The coefficient of viscosity is h. There is no relative motion between the liquid and the container. Then at the shown instant, the magnitude of viscous force acting on sphere is
A container filled with viscous liquid is moving vertically downwards with constant speed 3v0 . At the instant shown, a sphere of radius r is moving vertically downwards (in liquid) has speed v0 . The coefficient of viscosity is h. There is no relative motion between the liquid and the container. Then at the shown instant, the magnitude of viscous force acting on sphere is
Physics-General
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A cubical block of side 'a' and density 'r' slides over a fixed inclined plane with constant velocity ' v ' . There is a thin film of viscous fluid of thickness ' t ' between the plane and the block . Then the coefficient of viscosity of the thin film will be : (Acceleration due to gravity is g)
A cubical block of side 'a' and density 'r' slides over a fixed inclined plane with constant velocity ' v ' . There is a thin film of viscous fluid of thickness ' t ' between the plane and the block . Then the coefficient of viscosity of the thin film will be : (Acceleration due to gravity is g)
Physics-General
Physics-
In the figure shown, a light container is kept on a horizontal rough surface of coefficient of friction
. A very small hole of area S is made at depth 'h'. Water of volume 'V' is filled in the container. The friction is not sufficient to keep the container at rest. The acceleration of the container initially is
In the figure shown, a light container is kept on a horizontal rough surface of coefficient of friction. A very small hole of area S is made at depth 'h'. Water of volume 'V' is filled in the container. The friction is not sufficient to keep the container at rest. The acceleration of the container initially is
Physics-General
Physics-
A spherical ball of mass 4m, density sand radius r is attached to a pulley-mass system as shown in figure. The ball is released in a liquid of coefficient of viscosity hand density r(< 2 s ). If the length of the liquid column is sufficiently long, the terminal velocity attained by the ball is given by (assume all pulleys to be massless and string as massless and inextensible) :
A spherical ball of mass 4m, density sand radius r is attached to a pulley-mass system as shown in figure. The ball is released in a liquid of coefficient of viscosity hand density r(< 2 s ). If the length of the liquid column is sufficiently long, the terminal velocity attained by the ball is given by (assume all pulleys to be massless and string as massless and inextensible) :
Physics-General
Physics-
A piece of Ice floats in a vessel with water above which a layer of lighter oil is poured. When ice melts :
1. The level of oil water interface falls
2. The level of oil water interface rises
3. The thickness of oil layer decreases
4. The thickness of oil layer remain same
5. The thickness of oil layer increases
6. The level of oil-air interface falls
7. The level of oil-air interface remains same
8. The level of oil-air interface rises Select the correct alternatives :
A piece of Ice floats in a vessel with water above which a layer of lighter oil is poured. When ice melts :
1. The level of oil water interface falls
2. The level of oil water interface rises
3. The thickness of oil layer decreases
4. The thickness of oil layer remain same
5. The thickness of oil layer increases
6. The level of oil-air interface falls
7. The level of oil-air interface remains same
8. The level of oil-air interface rises Select the correct alternatives :
Physics-General
Physics-
A container open from top, filled with water (density rw ) upto the top, is placed on a weighing machine and the reading is W. A wooden ball of volume V and mass m is put in the water by the given two arrangements. In arrangement–1, the ball is connected by a rigid rod (of negligible volume) and pushed in the water. In arrangement–2, the ball is attached with bottom by a massless string. The reading of weighing machine, (density of wood is less than water) (choose incorrect option) :
A container open from top, filled with water (density rw ) upto the top, is placed on a weighing machine and the reading is W. A wooden ball of volume V and mass m is put in the water by the given two arrangements. In arrangement–1, the ball is connected by a rigid rod (of negligible volume) and pushed in the water. In arrangement–2, the ball is attached with bottom by a massless string. The reading of weighing machine, (density of wood is less than water) (choose incorrect option) :
Physics-General
Physics-
Two forces F1 and F2act on a thin uniform elastic rod placed in space. Force F1 acts at right end of rod and F2acts exactly at centre of rod as shown (both forces act parallel to length of the rod).
i) F1 causes extension of rod while F2 causes compression of rod.
ii) F1 causes extension of rod and F2 also causes extension of rod.
iii) F1 causes extension of rod while F2 does not change total length of rod.
The correct order of True / False in above statements is
Two forces F1 and F2act on a thin uniform elastic rod placed in space. Force F1 acts at right end of rod and F2acts exactly at centre of rod as shown (both forces act parallel to length of the rod).
i) F1 causes extension of rod while F2 causes compression of rod.
ii) F1 causes extension of rod and F2 also causes extension of rod.
iii) F1 causes extension of rod while F2 does not change total length of rod.
The correct order of True / False in above statements is
Physics-General
Physics-
In the given figure, two elastic rods A & B are rigidly joined to end supports. A small block of mass ‘ m ‘ is moving with velocity v between the rods. All collisions are assumed to be elastic & the surface is given to be smooth. The time period of oscillations of small mass ‘ m ‘ will be: (A = area of cross section, Y = young’s modulus, L = length of each rod)
In the given figure, two elastic rods A & B are rigidly joined to end supports. A small block of mass ‘ m ‘ is moving with velocity v between the rods. All collisions are assumed to be elastic & the surface is given to be smooth. The time period of oscillations of small mass ‘ m ‘ will be: (A = area of cross section, Y = young’s modulus, L = length of each rod)
Physics-General
Physics-
A uniform solid cone of mass m, base radius ‘R’ and height 2R, has a smooth groove along its slant height as shown in figure. The cone is rotating with angular speed ‘w’, about the axis of symmetry. If a particle of mass ‘m’ is released from apex of cone, to slide along the groove, then angular speed of cone when particle reaches to the base of cone is
A uniform solid cone of mass m, base radius ‘R’ and height 2R, has a smooth groove along its slant height as shown in figure. The cone is rotating with angular speed ‘w’, about the axis of symmetry. If a particle of mass ‘m’ is released from apex of cone, to slide along the groove, then angular speed of cone when particle reaches to the base of cone is
Physics-General
Physics-
Two particle of mass m each are fixed to a massless rod of length 2l . The rod is hinged at one end about a smooth hinge and it performs oscillations of small angle in vertical plane. The length of the equivalent simple pendulum is
Two particle of mass m each are fixed to a massless rod of length 2l . The rod is hinged at one end about a smooth hinge and it performs oscillations of small angle in vertical plane. The length of the equivalent simple pendulum is
Physics-General
Physics-
A uniform disc of mass m is attached to a spring of spring constant k as shown in figure and there is sufficient friction to prevent slipping of disc. Time period of small oscillations of disc is:
A uniform disc of mass m is attached to a spring of spring constant k as shown in figure and there is sufficient friction to prevent slipping of disc. Time period of small oscillations of disc is:
Physics-General
