The cylindrical tube of a spray pump has a cross-section of 8 cm2, one end of which has 40 fine holes each of area 10-8 m2. If the liquid flows inside the tube with a speed of 0.15 m min-1, the speed with which the liquid is ejected through the holes is
Which one of the following graph represents the variation of maximum kinetic energy (Ek ) of the emitted electrons with frequency v in photoelectric effect correctly?
i.e. graph will be a rectangular hyperbola.
A vessel of height 2d is half filled with a liquid of refractive index √2 and the other half with a liquid of refractive index n (the given liquids are immiscible). Then, the apparent depth of the inner surface of the bottom of the vessel (neglecting the thickness of the bottom of the vessel) will be
The depth of the image of an object submerged in a transperent medium; it is reduced from the real depth of the object by a factor equal to the relative index of refraction of the medium with respect to air.
Refractive index μ =
For 1st liquid
Similarly, for 2nd liquid,
Total apparent depth = x1 + x2
A shell of mass 20 kg at rest explodes into two fragments whose masses are in the ratio 2 : 3. The smaller fragment moves with a velocity of 6 m/s. The kinetic energy of the larger fragment is
Total mass of the shell = 20 kg
Ratio of the masses of the fragments = 2: 3
∴ Masses of the fragments are 8 kg and 12 kg Now, according to the conservation of momentum , m1v1 = m2v2
∴ 8 × 6 = 12 × v
v (velocity of the larger fragment) = 4 m/s
An electric bulb has a rated power of 50 W at 100 V. If it is used on an AC source 200 V, 50 Hz, a choke has to be used in series with it. This choke should have an inductance of
In Young’s double slit experiment with sodium vapour lamp of wavelength 589 nm and the slits 0.589 mm apart, the half angular width of the central maximum is
In Young's double slit experiment half angular width is given by
A parallel plate capacitor with air as the dielectric has capacitance C. A slab of dielectric constant K and having the same thickness as the separation between the plates is introduced so as to fill one-fourth of the capacitor as shown in the figure. The new capacitance will be
Capacitor with air as the dielectric has capacitance
C1 = ɛo/d (3A/4) = 3 ɛoA/4d
Similarly the capacitor with k as dielectric constant has capacitance
Three concurrent coplanar forces 1 N, 2 N and 3 N acting along different directions on a body
We can clearly see that the first two forces 1N,2N if they are in the same direction, then they would equal to the third force 3N. But it is given that the three forces are in different directions. So there is no possibility of equilibrium with these forces in different directions.
The work done by a force acting on a body is as shown in the graph. The total work done in covering an initial distance of 20 m is
Word done W = Area ABCEFDA = Area ABCD + Area CEFD
Horizontal tube of non-uniform cross-section has radii of 0.1 m and 0.05 m respectively at M and N. For a streamline flow of liquid, the rate of liquid flow is
According to principle of continuity, for streamline flow of fluid
through a tube of non-uniform cross-section the rate of flow of fluid
(Q) is same at every point in the tube.
i.e, Av = constant
Therefore, the rate of flow of fluid is same at M and N.
A coil of n number of turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current of strength I is passed through the coil, the magnetic field at its centre is
Number of turns per unit width =
Consider an elemental ring of radius x and with thickness dx Number of turns in the ring
Magnetic field at the centre due to the ring element
∴ Field at the centre
A certain vector in the xy-plane has an x-component of 4 m and a y-component of 10 m. It is then rotated in the xy-plane sothatits x-component is doubled. Then, its new y-component is (approximately)
A police party is moving in a jeep at a constant speed v. They saw a thief at a distance x on a motorcycle which is at rest. The moment the police saw the thief, the thief started at constant acceleration a Which of the following relations is true if the police is able to catch the thief?
Let the police party catch the thief after t
Distance travelled by police party in t = v t
and distance travelled by thief
Since by using the Quadratic equation formula
If two soap bubbles of different radii are connected by a tube, then
The excess pressure inside the soap bubble is inversely proportional to the radius of soap bubble i.e. P ∝1/r, r being the radius of the bubble. It follows that pressure inside a smaller bubble is greater than that inside a bigger bubble. Thus, if these two bubbles are connected by a tube, air will flow from smaller bubble to bigger bubble and the bigger bubble grows at the expense of the smaller one.
The thermo emf of a hypothetical thermocouple varies with the temperature e of hot junction as E = aθ + bθ2 in volts, where the ratio a / b is 700°C. If the cold junction is kept at O°C, then the neutral, temperature is
The thermo emf is given by E = aθ + bθ2
For neutral temperature
⇒ a + 2bθn = 0
But neutral temperature can never be negative (less than zero) i.e., θn< |0oC|
Hence, no neutral temperature is possible for this thermocouple.
A launching vehicle carrying an artificial’ satellite of mass m is set for launch on the surface of the earth of mass M and radius R. If the satellite is intended to move in a circular orbit of radius 7 R, the minimum energy required to be spent by the launching vehicle onthe satellite is (Gravitational constant = G)
The two lenses of an achromatic doublet should have
The two lenses of an achromatic doublet should have, sum of the product of their powers and dispersive power equal to zero.
If the ratio of lengths, radii and Young’s modulus of steel and brass wires shown in the figure are a, b and e respectively, the ratiobetween the increase in lengths of brass and steel wires would be
Free body diagram of the two blocks are
Let Young's modulus of steel is Y1 and of brass is Y2
Dividing Eq. (i) by Eq. (ii), we get
Force on steel wire from free body diagram
T = F1 = 2 g N
Force on brass wire from free body diagram
F2 = T' = T + 2g
= 4 g N
Now, putting the values of F1 , F2 Eq. (iii) we get
A soap bubble of radius r is blown up to form a bubble of radius 2 r under isothermal conditions. If T is the surface tension of soap solution, the energy spent in the blowing
Initially area of soap bubble
Under isothermal condition radius becomes 2 r, Then, area A2 =
Increase in surface area
Energy spent W = T × ΔA
= T . 24
W = 24
A current of 1.6 A is passed through solution of CuSO4. How many Cu++ ions are liberated in one minute? (Electronic charge =1.6 x 10-19 C)
Given:- Current = 1.6 A
t = 1 × 60s = 60 s
Charge flowing in one minute, q = I × t
= 1.6 × 60
Charge required to liberate one copper ion 2C
Number of Cu2+ liberated
A magnetic field exerts no force on
A moving electric charge has a magnetic field associated with it. So, it's magnetic field interacts with the external magnetic field and a force is exerted on the moving charge.
But, a fixed charge does not have any magnetic field associated with it, so id does not experience any force in a magnetic field.
In an L-C-R circuit inductance is changed from L to L/2. To keep the same resonance frequency, C should be changed to
The sound waves after. being converted into electrical waves are not transmitted as such because
The tip of a needle does not give a sharp image on a screen. This is due to
Image is not sharp because of deviation of light from straight line path account of diffraction of light.
An engine moving towards a wall with a velocity 50 m/s emits a note of 1.2 kHz. Speed of sound in air is 350 m/s. The frequency of the note after reflection from the wall as heard by the driver of the engine is
The reflected sound appears to propagate in a direction opposite to that of moving engine. Thus, the source and the observer can be presumed to approach each other with same velocity.
The surface temperature of the sun which has maximum energy emission at 500 nm is 6000 K. The temperature of a star which has maximum energy emission at 400 nm will be
Wein's displacement law:-
Relationship between the temperature of a black body ( an ideal substance that emits and absorbs all frequencies of light) and the wavelength at which it emits the most light.
By using Wein's Displacement law,
⇒ 500 × 6000 = 400 × T2
The truth table given below is for (A and B are the inputs, Y is the output)
Two rectangular blocks A and B of masses 2 kg and 3 kg respectively are connected by a spring of spring constant 10.8 Nm-1 and are placed on a frictionless horizontal surface. The block A was given an ‘initial velocity of 0.15 ms-1 in the direction shown in the figure. The maximum compression of the spring during the motion is
As the block A moves with velocity 0.15ms−1, it compresses the spring which pushes B towards right. A goes on compressing the spring till the velocity acquired by B becomes equal to the velocity of A, ie, 0.15ms−1,
Let this velocity be v. Now, spring is in a state of maximum compression. Let x be the maximum compression at this stage.
According to the law of conservation of linear momentum, we get mAu = (mA+mB)v or v =
According to the law of conservation of energy,
0.1 m3 of water at 80°C is mixed with 0.3 m3 of water at 60°C. The final temperature of the mixture is
Let T°C be final temperature of the mixture.
According to principle of calorimetry,
Heat lost = Heat gained
∴ 0.1× 103 × swater × (80−T)
= 0.3 × 103 × swater × (T−60)
⇒ T = 65∘C
y = 3 sin π(t/2 -x/4) represents an equation of a progressive wave, where t is in second and x is in metre. The distance travelled by the wave in 5 s is
A body of mass m1 = 4 kg moves at 5i m/s and another body of mass m2 = 2 kg moves at 10 i m/ s. The kinetic energy of centre of mass is
The total kinetic energy of a multiparticle system is equal to the sum of particles in the systems.
The centre of mass is a point that represents the average location for the total mass of system.
A wheel of radius 0.4 m can rotate freely about its axis as shown in the figure. A string is wrapped over its rim and a mass of 4 kg is hung. An angular acceleration of 8 rad- s-2 is produced in it due to the torque. Then, moment of inertia of the wheel is (g = 10 ms-2)
An object start sliding on a frictionless inclined plane and from same height another object start falling freely.
Both start with the same potential energy component ( gh )
When they both reach the ground, both have converted that identical energy component kinetic energy.
Thus, the object sliding down a frictionless incline will reach the same velocity as the one dropped straight down.
The times to reach the speed to reach the speed will not be the same, the dropped one will reach it faster.
A boy on a cycle pedals around a circle of 20 metres radius at a speed of 20 m/s, The combined mass of the body and the cycle makes with the vertical so that it may not fall is (g = 9.8 m/ s2) .
A body that travels an equal distance in equal amounts of time along a circular path has a constant speed but not constant velocity. This is because velocity is a vector and thus it has magnitude as well as direction.
v = ( Rg tanθ )1/2
A coin is dropped in a lift. It takes time t1 to reach the floor when lift is stationary. It takes time t2 when lift is moving up with constant acceleration. Then,
From equation of motion, we have
where u is initial velocity, t is time, g is acceleration due to gravity. At the time of dropping u = 0
When lift moves up
g' = g + a
The engine of a jet aircraft applies a thrown force of 105 N during take off and causes the plane to attain a velocity of 1km/s in 10 s. The mass of the plane is
A stone weighing 1 kg and sliding on ice with a velocity of 2 m/s is stopped by friction in 10 s. The force of friction (assuming it to be constant) will be
The potential energy of a body is given by U = A – Bx2 (where x is the displacement) The magnitude of force acting on the particle is
When a ceiling fan is switched on, it makes 10 revolution in the first 3 s. Assuming a uniform angular acceleration , how many rotation it will make in the next 3 s
A hollow sphere of volume V is floating on water surface with half immersed in it. What should be the minimum volume of water poured inside thesphere so that the sphere now sinks into the water
Which one of the following sets of quantum numbers represents the highest energy level in an atom?
Here, X is
Acetic anhydride is prepared in the laboratory by heating sodium acetate with
For the homogeneous reaction,
4NH3 + 5O2 ⇔ 4NO + 6H2O
the equilibrium constant K; has the units
For the reaction,
NH3 + OCI– → N2H4 + CI–occurring in basic medium, the coefficient of N2H4 in the balanced equation will be
Which one of the following has a coordinate bond?
Which of the following would exert maximum osmotic pressure ? .
Cow milk, an example of natural emulsion, is stabilised by
For a zero order reaction
The extraction of which of the following metals involves bessemerisation?
The correct order of decreasing first ionisation energy is
Consider the following reaction,
What is Y?
Which of the following is most basic in nature?
An example of natural biopolymer is
Which of the following is known as invert soap?
Le-blanc process is employed in the manufacture of
Which one of these is not true for benzene?
The IUPAC name of acryldehdye is
The structures of (CH3)3,CBr and CH3[CH2]3 Br represent
Petrol for aviation purpose must contain
The solubility product of Hg2l2 is equal to
The number of atoms contained in a fcc unit cell of a monoatomic substance is
In the first order reaction, 75% of the reactant gets disappeared in 1.386 h. The rate constant of the reaction is
Moist hydrogen peroxide can not be dried over conc. H2SO4 because
Glauber’s salt is
The most basic element is
Propyne on passing through red hot copper tube forms
Which one of the following is mainly responsible for depletion of ozone layer?
On warming with silver powder, chloroform is converted into
Ammonia is a Lewis base and it forms complexes with many cations. Which one of the following cations does not form a complex with ammonia?
Ammonia is a lewis base. It forms complexes with transition elements like Cd2+ , Cu2+, Ag+ but it does not form complex with Pb2+ as it is not a transition element.
Argol, a brown crust, formed during the fermentation of grape juice contains
The structure of compound B is
The pH value of 0.001 M aqueous solution of NaCI is
Which buffer solution comprising of the following has its pH value greater than 7?
Which of the following has sp2-hybridisation?
Hydrogen molecule differs from chlorine molecule in the following respect.
The ratio of the difference in energy between the first and the second Bohr orbit to that between the second and the third Bohr orbit is
Graphite is a
Which one of the following transition metal ions is diamagnetic?
Which of the following metal carbonates decomposes on heating?
Gel electrophoresis is used for
Polysome is formed by
Which type of white blood cells are concerned with the release of histamine and the natural anticoagulant heparin?
Which one of the following in birds, indicates, their reptilian ancestry?
Select incorrect pair
Bilateral symmetry, metameric segmentation, coelom and open circulatory system are the features of
Ancestor of man who first stood erect was
Core zone, buffer zone and manipulation zone. are found in
Which insecticide is more hazardous to human health?
Universal donor is
One of these is not concerned with wildlife conservation
Largest tiger population is found in
Genetic material found in human Immunodeficiency Virus (HIV) is
Gigantism and acromegaly are due to
If a child is of 0 blood group and his father is of B blood group, the genotype of father is
Spermatogenesis is under the regulatory influence of
Which of the following can be controlled by using biopesticides?
Which hormone is secreted in a woman if pregnancy has occurred?
Product of biotechnology is
Phase common in aerobic and anaerobic respiration is
Oxyntic cells secrete
Menstruation is due to sudden
Correctly matched set of phylum, class and example is
Urea synthesis occurs in
Which is common to kidney and skeleton in mammals?
Which is regarded as urinary bladder of embryo?
Deficiency of vitamin -B12 causes
Blood is a kind of
Which of these is used• to control human population?
Addiction to alcohol causes
In alcoholic person, some part of alcohol is changed into acetaldehyde, which stimulates the formation of fat. This fat is deposited over the wall of arteries and also accumulates in liver cells. Due to which liver gets failed and there is very little regulation of carbohydrate, protein and fat metabolism. This disorder is known as fatty liver syndrome. Later on, the liver gets turned into solid, hard, fibrous organ causing liver cirrhosis.
The most primitive vertebrates are
Change in the number of body parts is called
Which has an additional X-chromosome?
Origin of life occurred in
Branch of zoology dealing with the study of fishes is called
Theory of continuity of germplasm was propounded by
Which extraembryonic membrane in humans prevents desiccation of the embryo inside the uterus?
The most active phagocytic white blood cells are
During the propagation of a nerve impulse, the action potential results from the movement of
Darwin’s finches are an excellent example of
In which one of the following, male and female gametophytes do not have free-living independent existence?
A transgenic food crop, which may help in solving the problem of nightblindness in developing countries is
Vascular tissues in flowering plants develop from
Nitrogen-fixation in root nodules of Alnus is brought about by
A mature pollen grain of Pinus has
Polyploidy can be induced by the application of
Quantasome are present in
In mitochondria, enzyme cytochrome oxidase is present in
Which of the following bio-engineered bacteria is utilized for cleaning of marine oil slicks?
Green potatoes are toxic due to
Cells obtained from cancerous tumours are known as
The plant of Triticum aestivum is
Which of the following is a total root parasite?
Which of the following tissues consist of living cells?
Which is a useful product of epidermal origin?
Fern spores are usually
When pollen tube enters through micropyle, the process is called
Outer wall of pollen grain is made up of
Nucleotides are formed by
DNA replication occurs in
Which of the following plant cells is not surrounded by a cell wall?
Which of the following cell organelles stores hydrolytic enzymes?
A monocarpic plant is one, which
AIDS virus contains
Calyptra develops from
Protonema is the stage in the life cycle of
A fern differs from a moss in having
Female cone of Pinus is a
Development of an embryo without fertilization is called as
Which of the following floral parts forms pericarp after fertilization?
Prothallus of the fern produces
Which of the following cell organelles is associated with photorespiration?
The thickness of unit membrane is
Chromosomes are arranged along the equator during
Width of the DNA molecule is
In gymnosperms, the Ovule is naked because
The rupture and fractionation do not usually occur in the water column in vessel/tracheids during the ascent of sap because of
The fleshy receptacle of syconus of fig encloses number of
Which one of the following is linked to the discovery of bordeaux mixture as a popular fungicide?
Unisexuality of flowers prevents
Directions (Q 1-5) Out of the four alternatives choose the one which expresses the correct meaning of the given word and blacken the appropriate rectangle [〉] in the Answer Sheet.