MP SET Physical Science Exam - English

"My friend Raju has more than 1000 books". said Ram. "Oh no, he has less than 1000 book said Shyam.  "Well. Raju certainly has at least one book", said Geeta. If only one of these statements is true. how many books does Raju have ?

Of the following, which is the odd one out ?

An infinite number of identical circular discs each of radius  are tightly packed such that the centres of the discs are at integer values of coordinates x and y. The ratio of the area of the uncovered patches to the total area is —

 It takes 5 days for a steamboat to travel from A to B along a river. It takes 7 days to return from B to A, How many days will it take for a raft to drift from A to B (all speeds stay constant) ?

N is a four digit number. If the leftmost digit is removed, the resulting three digit number is 1/9th Of N. How many such N are possible ?

A granite block of 2m × 5m × 3m size is cut into 
5 cm thick slabs of 2 m × 5 m size. These slabs are laid over a 2 m wide pavement. What is the length of the pavement that can be covered with these slabs?

Which is the least among the following?
0.33^0.33 , 0.44^0.44, 0.55^–1/p , e^–1/e

What is the next number in this “see and tell” sequence?
1   11   21   1211   111221   .........

The frequency range of Ultra High Frequency (UHF) is __ ?

A peacock perched on the top of a 12 m high tree, spots a snake moving towards its hole at the base of the tree from a distance equal to thrice the height of the tree. The peacock flies towards the snake in a straight line and they both move at the same speed. At what distance from the base of the tree will the peacock catch the snake?

One of the four –A, B, C and D – committed a crime. A said, “I did it.” B said, “I didn’t.” C said. “B did it.” D said, “A did it.” Who is lying?

A farmer gives 7 full, 7 half-full and 7 empty bottles of honey to his three sons and asks them to share these among themselves such that each of them gets the same amount of hooey and the same number of bottles. In how many ways can this be done? (bottles cannot be distinguished otherwise, they are sealed and cannot be broken)

If the roots of the equation a(b – c) x² + b(c – a) x + c(a – b) = 0 are equal, then a, b, c are in

What is the next number in the following sequence?
39, 42, 46, 50, ......

A student buys a book from an online shop at 20% discount. His friend buys another copy of the same book in a book fair for Re. 192 paying 20% less than his friend. What is the full price of the book?

Consider the set of numbers {171, 172, ..., 17300}. How many of these numbers end with the digit 3 ?

Average yield of a product in different years is shown in the histogram. If the vertical bars indicates variability during the year, then during which year was the per cent variability over the average of that year the least?

A rectangle of length d and breadth d/2 is revolved once completely around its length and once around its breadth. The ratio of volumes swept in the two cases is

A long ribbon is wound around a spool up to a radius R. Holding the tip of the ribbon, a boy runs away from the spool with a constant speed maintaining the unwound portion of the ribbon horizontal. In 4 minutes, the radius of the wound portion becomes In what further time, it will become R/2?

If n is a positive integer, then n(n + 1) (n + 2) (n + 3) (n + 4) (n + 5) (n + 6) is divisible by

Five congruent rectangles are drawn inside a big rectangle of perimeter 165 as shown. What is the perimeter of one of the five rectangles?

At one instant, the hour hand and the minute hand of a clock are one over the other in between the markings for 5 and 6 on the dial. At this instant, the tip of the minute hand

There are two buckets A and B. Initially A has 2 litres of water and B is empty. At every hour 1 litre of water is transferred from A to B followed by returning 1/2 litre back to A from B half an hour later. The earliest A will get empty is in

A car is moving at 60 km/h. The instantaneous velocity of the upper most points of its wheels is

Density of a rice grain is 1.5 g/cc and bulk density of rice heap is 0.80 g/cc. If a 1 litre container is completely filled with rice. What will be the approximate volume of pore space in the container?

There is an equilateral triangle in the XY plane with its centre at the origin. The distance of its sides from the origin is 3.5 cm. The area of its circumcircle in cm² is

A sphere of iron of radius R/2 fixed to one end of a string was lowered into water in a cylindrical container of base radius R to keep exactly half the sphere dipped. The rise in the level of water in the container will be

A crystal grows by stacking of unit cells of 10 × 20 × 5 nm size as shown in the diagram given below. How many unit cells will make a crystal of 1 cm³ volume? 

What is the value of  to  ?

A solid cylinder of basal area A was held dipped in water in a cylindrical vessel of basal area 2A vertically such that a length h of the cylinder is immersed. The lower tip of the cylinder is at a height h from the base of the vessel. What will be the height of water in the vessel when the cylinder is taken out ?

Find the missing letter
A    B    C    D
F     I     L    O
K    P    U    Z
P   W    D    ?

Consider a right-angled triangle ABC where  AB = AC = 3. A rectangle APOQ is drawn inside it, as shown, such that the height of the rectangle is twice its width. The rec tangle is moved horizontally by a distance 0.2 as shown schematically in the diagram (not to scale).

What is the value of the ratio 

80 gsm paper is cut into sheets of 200 mm × 300 mm size and assembled in packets of 500 sheets. What will be the weight of a packet? (gsm = g/m²)

Three indentical flat equilateral-triangular plates of side 5 cm each are placed together such that they form a trapezium. The length of the longer of the two parallel sides of this trapezium is

An archer climbs to the top of a 10 m high building and aims at a bird atop a tree 17 m away. The line of sight from the archer to the bird makes an angle of 45° to the horizontal. What is the height of the tree?

Which one of the following has the highest value of specific heat ?

If Here a, b, c and d are digits. Then a + b =

An infinite number of identical circular discs each of radius  are tightly packed such that the centers of the discs are at integer values of coordinates x and y . The ratio of the area of the uncovered patches to the total area is .

It takes 5 days for a steamboat to travel from A to B along a river. It takes 7 days to return from B to A. How many days will it take for a raft to drift from A to B (all speeds stay constant ) ?

“ My friend Raju has more than 1000 books “, said Ram . “ Oh no , he has less than 1000 books”, said Shyam .’’ Well , Raju certainly has at least one books “, said Geeta . If only one of these statements is true , how many books does Raju have ?

Of the following , Which is the odd one out ?

A student appearing for an exam is declared 1oto have failed the exam if his /her  score.This implies

Find the next figure ‘D'

N is a four digit number . If the leftmost digit is removed , the resulting three digit number is 1/9 ^th of N. How many such N are possible ?

AB and CD are two chords of a circle subtending 60^o and 120^o respectively at the same point on the circumference of the circle . Then AB:CD

Which of the following inferences can be drawn from the above graph?

What is the minimum number of moves required to transform figure 1 to figure 2 ? A move is defiend as removing a coin and placing it such that it touches two other coins in its new position

The relatiopnship among the numbers in each corner squre is the same as that in the other corner squres . Find the missing

Which of the following best approximates sin (0.5^o )?

What comes next in the sequence ?

Which of the following statements is logically incorrect

How many times strating at 1:00 pm would the minute and hour hands of clock make an angle of 40^o  with each other in the next 6 hour ?

Brothers Santa and Chris walk to school from their house .The former takes 40 minutes While the latter , 30 minutes. One day Santa Started 5 minutes earlier than Chris. In how many minutes would Chirs overtake Santa ?  

The set of numbers (5,6,7,m,6,7,8,n) has an arthimetic mean of 6 and mode (most frequency occuring number ) of 7. Then = mX n =

The diagram shows a block of  marble having the shape of a triangular prism. What is the maximum number slabs of 10X10X5 cm³ Size that can be cut parallel to the face on which the block is resting ?

A soild contains a spherical cavity is filled with a liqued and includes a spherical bubble of gas . The radii of cavity and gas bubble are 2 mm and 1 mm , respetively . What  proportion of the cavity is filled with liquid ?

Fill in the blank : F2 , _______, D8, C16, B32 , A64.

The radaius of convergence of the Taylor series expansion of the function around x=0, is

The Value of the contour integral around the unit circle traversed in the anti-clockwise direction , is

The Gauss hypergeometric function F(a,b,c ;z) , defined by the Taylor series expension around z = 0 as  F(a,b,c ;z= satisfies the recusion relation

Let X and Y be two independent random variables, each of Which follow a normal distribution with the same standard deviation σ , but with means +μ and –μ , respectively Then the sum X + Y follows a

Using dimensional analysis , planks defined a characteristic  temperature T_p from powers of the gravitational constant G, Planck’s constant h, Boltzmann constant K_B and the speed of light c in vacuum.The expression for T_P is proportional to

Let (x,t) and (x’,t’) be the coordinate systems used by the observers O and O’ , respectively . Observer O’ moves with a celocity v = βc along their common positive x-axis. If x₊ = x+ct  and x_-=x-ct are the linear combinations of the coordinates , the Lorentz transformation relating O and O’ taks the form

A ball of mass m, initially at rest , is dropped from a height of 5 meters . if the coefficient of restitution is 0.9 , the speed of the ball just before it hits the floor the second time is approximately (take g = 9.8 m/s²)

Four equal charges of +Q each are kept at the vertices of a square of side R. A particle of mass m and charge +Q is placed in the plane of the square. at a short distance a(<<R) from the center . If the motion of the particle is confined to the plane , it will undergo small osillations with an angular frequency

Hemilationian of a system with generalized coordinate and momenutum (q,p) is H=p²q² A solution of the Hamiltonian equation of motion is (in the following A and B are constants

Two Parallel plate capacitors ,seprated by distance x and 1.1x respectively , have a diectric material of dielectric constant 3.0 inserted between  the plates , and are connected to a baterry of voltage V .The difference in charge on the second capacitor compared to the first is

The half space regions x>0 and x<0 are filled with dielectric media of dielectric constants  and  respectively . There is a uniform electric field in each part .In the right half , the electric field makes an angle  to the interface . The corresponding angle in the left half satisfies

The x- and Z- components of a static magnetic field in a region are B_x=B₀(x²-y²) and B_z=0, respectively .Which of the following solutions for its y-component is consistent  with the Maxwell equations ?

The state of a particle of mass m in a one – dimensional rigid box in the interval  0 to L is given by the normalized wavefunction If its energy is mesured the posible outcomes and the average vlaue of energy are respectively.
 

If  and are the components of the angular momentum operator in three dimensions , the commutor [] may be simplified to

Suppose that the coulomb potential of the hydrogen atom is changed by adding an inverse-square term such that the total potential is , Where g is a constant . The energy eigenvalues E_nlm in the modified Potential

The eigenstates corresponding to eigen – values E₁ and E₂ of time – independent Hamiltonian are |1> and |2> respectively . if at t=0 , the system is in a state |ψ(t=0) > =sin Ï´|1>+cosÏ´|2> the value of<ψ(t)|ψ(t) > at time t will be

The specific heat per molecule of gas of diatomic molecules at high temperatures is

When an ideal monatomic gas is expended adiabatically from an initial  volume V₀ to 3 V_o its temperature changes from T₀ to T. Then the ratio T/T₀ is

A box of  Volume V containing N molecules of an ideal gas , is divided by a wall with a hole into two compartments . If the volume of the smaller compartment is V/3 , the varience of the number of particles in it , is

A gas of non-relativistic classical particles in one dimension is subjected to a potential V(x) = a|x| (Where α is a constant ). The partition function  is

The dependence of current 1 on the Voltage V of a certain device is given by   I=I₀( Where I₀ and V₀ are constants. In an experiment the current I is measured as the voltage V applied across the device  is increased .The parameters V₀ and  can be graphically determined  as

In the schematic figure given below , assume that the propagation delay of each logic gate is t _gate The propagation delay of the circuit will be maximum when the logic inputs A and B make the transition

Given the input voltage V_i , Which of the following waveforms correctly represents the output voltage V₀ in the circuit shown below?

The intensity distribution of a red LED on an absorbing layer of material is a Gaussian centred  at the wavelength λ₀ = 660 nm and width 20 nm. if the absorption coefficient varies with wavelength as α₀-K(λ-λ₀), Where α₀ and K are positive constants, the light emerging from the absorber will be

What is the Fourier transform  of Where is the Dirac delta-function?

The Integral equation  is equivalent to the differential equation

A part of the group multiplication table for a six element group G= {e,a,b,c,d,f} is shown below (In the following e is the identity element of G )The entries  x, y and z should be

In finding the roots of the polynomial f (x) = 3x³ - 4 x - 5 using the iterative Newton-Raphson method , the initial guess is taken to be x=2 In the next iteration its value is nearest to

For a particle of energy and momentum P (in a frame F) , the rapidity y is defined as y= In () . In a Frame F’ moving with velocity v= (0,0,βc) with respect to F, the rapidity y’ will be

A canonical transformation (q,p) -> (Q,P) is made through the generating function F(q,p)=q²p  on the Hamiltonian Where α and β are constants . The equations of motion for (Q,P) are

The Lagrangian of a system moving in three dimensions is The independent constant(s) of motion is/are

Consider a sphere S1 of radius R Which carries a uniform charge of density p. A smaller sphere S₂ of radius a<R/2 is cut out and removed from it . The centers of the two spheres are separated by the vector  as shown in the  figure .The electric field at a point P inside S₂ is

The Values of the electric and magnetic fields in a particular reference frame (in Gaussian units ) are   and  , respectively . An inertial observer  moving with respect  to this frame  measures the magnitude of the magnetic field to be |E’| . The magnitude of the magnetic field |B’| measured by him  is

A loop of radius a, carrying a current I, is placed in uniform magnetic field B. If the normal to the loop is denoted by ,the force F and the torque T on the loop are

An inverted cone is filled with water at a constant rate. The volume of water inside the cone as a function of time is represented by the curve :
​
 

A spacecraft flies at a constant height R above a planet of radius R. At the instant the spacecraft is over the north pole, the lowest latitude visible from the spacecraft is :

An experiment consists of tossing a coin 20 times. Such an experiment is performed 50 times. The number of heads and the number of tails in each experiment are noted. What is the correlation coefficient between the two ?

Which of these groups of numbers has the smallest mean ?
Group A : 1, 2, 3, 4, 5, 6, 7, 8, 9
Group B : 1, 2, 3, 4, 6, 6, 7, 8, 9
Group C : 1, 2, 2, 4, 5, 6, 7, 8, 9
​Group D : 1, 3, 3, 4, 5, 6, 7, 9, 9

Identical balls are tightly arranged in the shape of an equilateral triangle with each side containing n balls. How many balls are there in the arrangement ?