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Given that mass of earth is \( M \) and its radius \( R \) body is dropped from a height equal to the radius of the earth above the surface of the earth. When it reaches the ground velocity of body will be \( ^{A} \cdot \frac{G M}{R} \) \( ^{\text {В. }}\left(\frac{G M}{R}\right)^{1 / 2} \) c. \( \frac{2 G M}{R} \) \( ^{\mathrm{D} \cdot}\left(\frac{2 G M}{R}\right)^{1 / 2} \)
3
Physics
When electricity is passed through a solution of \( A l C l_{3} \) and \( 13.5 g \) of \( A l \) is deposited, the number of Faraday required must be: A . 0.5 в. 1.0 c. 1.5 D. 2.0
1
Chemistry
On decreasing temperature, a liquid turns into solid. This is: A. condensation B. melting c. freezing D. sublimation
1
Chemistry
Bacteria which are found in marshy areas and among the flora of cattle rumen are called A. Acidophiles B. Thermophiles c. Methanogens D. Thermoacidophiles
0
Biology
Whenever, current is changed in a coil, an induced e.m.f. is produced in the same coil. This property of the coil is due to A. mutual induction B. eddy currents c. self induction D. hysteresis
3
Physics
Element with atomic number 113 has been reported in August \( 2003 . \) Its electronic configuration is similar to that of: \( \mathbf{A} \cdot S i \) в. \( G a \) \( c . B i \) D. \( A t \)
1
Chemistry
Evaluate \( \cos ^{-1}\left(\cos \left(\frac{\pi}{4}\right)\right) \) A. B. \( -\frac{\pi}{4} \) c. \( \frac{3 \pi}{4} \) D. \( -\frac{3 \pi}{4} \)
2
Maths
The sum of \( n \) terms of the series whose \( \boldsymbol{n}^{t h} \) term is \( \boldsymbol{n}(\boldsymbol{n}+1) \) is equal to A \( \frac{n(n+1)(n+2)}{3} \) B. \( \frac{(n+1)(n+2)(n+3)}{12} \) c. \( n^{2}(n+2) \) D. \( n(n+1)(n+2) \)
2
Maths
For the reaction \( \boldsymbol{O}_{3(g)}+\boldsymbol{O}_{(g)} \rightarrow \mathbf{2} \boldsymbol{O}_{2(g)} \) if the rate law expression is, rate \( = \) \( \boldsymbol{K}\left[\boldsymbol{O}_{3}\right][\boldsymbol{O}] \) the molecularity and order of the reaction are: A . 2 and 2 B. 2 and 1.33 c. 2 and 1 D. 1 and 2
1
Chemistry
The number of spectral line obtained in Bohr spectrum of hydrogen atom when an electron is excited from ground level to 5 th orbit is : A . 10 B. 5 \( c \cdot 8 \) D. 15
1
Chemistry
If the radius of a circle is tripled, the ares becomes. A. 9 times B. 3 times c. 6 times D. 30 times
2
Maths
Find the number of integral solution of \( (1-i)^{x}=2^{x} \)
2
Maths
A small bee produces sound, while it moves. The sound is created due to A. Grinding its teeth as it moves B. Friction due to air c. Flapping of wings D. Sound due to its vocal chord
3
Physics
on by a spring with spring constant \( k \) and a weak frictional force of constant magnitude \( f \). The block is pulled a distance \( x_{0} \) from equilibrium position and then released. It oscillates many times and ultimately comes to rest. Find the number of cycles the mass oscillates before coming to rest: \( ^{\text {A }} \cdot \frac{1}{4}\left[\frac{k x_{0}}{f}-1\right] \) в. \( \frac{1}{2}\left[\frac{k x_{0}}{f}-1\right] \) c. \( \frac{1}{3}\left[\frac{k x_{0}}{f}-1\right] \) D. none of the above
3
Physics
Which part of the eye is a dark muscular diaphragm? A. Iriss B. Cornea c. Pupil D. Retina
3
Physics
Use the elements of \( \operatorname{set} A=\{x, y, z\} \) to form all possible ordered pairs Find the number of elements in the ordered pair.
2
Maths
\( f\left(\frac{1+\sin \theta-\cos \theta}{1+\sin \theta+\cos \theta}\right)^{2}= \) \( \lambda\left(\frac{1-\cos \theta}{1+\cos \theta}\right), \) then \( \lambda \) equals \( A \) B. 1 \( c \cdot 2 \) D.
2
Maths
White phosphorus \( P_{4} \) has: This question has multiple correct options A. \( \operatorname{six} P-P \) single bonds B. four \( P-P \) single bonds C. four lone pairs of electrons D. \( P-P-P \) angle of 60 degerees
1
Chemistry
Draw a ray diagram to show how a converging lens is able to form the image of the sun.
3
Physics
Phenol \( \frac{1 . C H C l_{3} / N a O H}{2 . H^{+}} \) Salicyl aldehyde The above reaction is known as: A. Gattermann reaction B. Sandmeyer reaction c. Perkin reaction D. Reimer-Tiemann reaction
1
Chemistry
(i) What are the postulates of Werner's theory? (ii) Write the IUPAC names fo \( \boldsymbol{K}_{3}\left[\boldsymbol{F} e(\boldsymbol{C} \boldsymbol{N})_{6}\right],\left[\boldsymbol{C o}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{6}\right] \boldsymbol{C l}_{3} \)
1
Chemistry
Potential energy of a simple harmonic oscillator at its mean position is 0.4 J. If its kinetic energy at a displacement half of its amplitude from mean position is \( 0.6 \mathrm{J}, \) its total energy is A . \( 1.0 J \) в. \( 1.2 J \) c. \( 1.4 J \) D. 1.6 .5
3
Physics
Discuss the behavior of wire under increasing load
3
Physics
The point charges \( -5 n C, 10 n C \) and \( 12 n C \) are located at (0,0,0),(0,0,1) and (0,0,2) respectively. Find the total energy of the system.
3
Physics
If the \( 3^{r d} \) and the \( 9^{t h} \) terms of an \( A P \) are 4 and -8 respectively, then which term of this \( A P \) is zero
2
Maths
The solution of \( \frac{x-5}{2}-\frac{x-3}{5}=\frac{1}{2} \) is \( \mathbf{A} \cdot x=7 \) B. \( x=9 \) c. \( x=8 \) D. \( x=5 \)
2
Maths
Show that square matrix \( A \) and its transpose \( A^{T} \) have the same eigen values.
2
Maths
Let the function \( f(x) \) be defined as \( \boldsymbol{f}(\boldsymbol{x})=\left\{\begin{array}{ll}\tan ^{-1} \boldsymbol{\alpha}-\mathbf{3} \boldsymbol{x}^{2}, & \boldsymbol{0}<\boldsymbol{x}<1 \\ -\boldsymbol{6} \boldsymbol{x}, & \boldsymbol{x} \geq \mathbf{1}\end{array}\right. \) \( f(x) \) can have a maximum at \( x=1 \) if the value of \( \alpha \) is A. B. 2 \( c \) D. None of these
2
Maths
For the identification of the name of species found in an area, one would use: A. Manuals B. Catalogues c. Monographs D. Museum
0
Biology
Fill in the blanks: In the Lassaigne's test, the sulphur present in the organic compound is converted into
1
Chemistry
Find the values of \( x \) and \( y \) which satisfy the given equations \( (x, y \in R) \) \( \frac{x-1}{1+i}+\frac{y-1}{1-i}=i \)
2
Maths
Find the direction cosines of the sides of the triangle whose vertices are (3,5,-4),(-1,1,2) and (-5,-5,-2)
2
Maths
The number of quadratic equation which are unchanged by squaring their roots is
2
Maths
In Blackmann's Law of limiting Factors the rate of photosynthesis continues to increase with the successive increase in the amounts of A. Carbon dioxide, light, temperature B. Temperature, light, carbon dioxide c. Light, temperature, carbon dioxide D. Light, carbon dioxide, temperature
0
Biology
The type of isomerism shown by the \( \operatorname{complex}\left[\boldsymbol{C o C I}_{2}(\boldsymbol{e n})_{2}\right] \) is: A. linkage isomerism B. ionization isomerism c. coordination isomerism D. geometrical isomerism
1
Chemistry
The structure A represents Fischer Projection of a compound. The structures I to IV represents WedgeDash Notations for the same compound. Which Wedge-Dash Notation is the correct representation of structure \( A ? \) \( A \) B. II \( c \) \( D \cdot \mid V \)
1
Chemistry
Using IUPAC norms, write the systematic names of the following. (i) \( \boldsymbol{K}_{\mathbf{4}}\left[\boldsymbol{F} \boldsymbol{e}(\boldsymbol{C} \boldsymbol{N})_{\boldsymbol{6}}\right] \) (ii) \( \left[\boldsymbol{C u}\left(\boldsymbol{N} \boldsymbol{H}_{3}\right)_{4}\right] \boldsymbol{S} \boldsymbol{O}_{4} \)
1
Chemistry
What is the force between the layer of carbon atoms in graphite?
1
Chemistry
A 4.0 -cm-high object is placed at a distance of \( 60 \mathrm{cm} \) from a concave lens of focal length \( 20 \mathrm{cm} . \) Find the size of the image. \( \mathbf{A} \cdot 2.5 \mathrm{cm} \) B. \( 1.0 \mathrm{cm} \) c. \( 3.0 \mathrm{cm} \) D. \( 4.0 \mathrm{cm} \)
3
Physics
When white ppt. of \( A g_{2} C O_{3} \) is dissolved in \( N H_{3} \) solution, then compound \( X \) is formed Find the value of magnetic moment of \( \mathbf{X} \) A. 0 B. 2 \( c \cdot 1 \) D.
1
Chemistry
Iron or steel is used in reinforcement in concrete because: A. Concrete has high coefficient of expansion than iron or steel B. Concrete has low coefficient of expansion than iron or steel c. Both have nearly equal coefficient of expansions D. Iron or steel is a good conductor of heatt
3
Physics
If a train travelling at \( 72 \mathrm{km} / \mathrm{h} \) is to be brought to rest at a distance of \( 200 \mathrm{m} \) then its retardation should be: A \( \cdot 20 m / s^{2} \) B. \( 2 s^{2} \) C \( .10 \mathrm{m} / \mathrm{s}^{2} \) D. \( 1 \mathrm{m} / \mathrm{s}^{2} \)
3
Physics
The difference between the heat of reaction at constant pressure and constant volume for the reaction \( \mathbf{2} C_{6} \boldsymbol{H}_{6}(l)+\mathbf{1 5} \boldsymbol{O}_{2}(\boldsymbol{g}) \rightarrow \mathbf{1 2} \boldsymbol{C} \boldsymbol{O}_{2}(\boldsymbol{g})+ \) \( 6 H_{2} O(l) \) at \( 25^{\circ} C \) in \( k J \) is: A . -7.43 в. 3.72 c. -3.72 D. 7.43
1
Chemistry
Assertion Atom is electrically neutral Reason A neutral particle, neutron is present in the nucleus of the atom A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion c. Assertion is correct but Reason is incorrect D. Both Assertion and Reason are incorrect
1
Chemistry
The magnetic force acting on a charged particle of charge \( -2 \mu C \) in a magnetic field of \( 2 T \) acting in y-direction, when the particle velocity is \( (2 \check{i}+3 j) \) \( \times 10^{6} m s^{-1} \) is : A. \( 8 \mathrm{N} \) in \( \mathrm{z} \) -direction B. 4 N in Z-direction c. 8 N in y-direction D. 4 N in Y-direction
3
Physics
A ball falls on the ground from a height of \( 2.0 m \) and rebounds up to a height of 1.5 \( m . \) Find the coefficient of restitution
3
Physics
The vapour pressure of two pure liquids \( A \) and \( B \) are 50 and 40 torr respectively. If 8 moles of \( A \) is mixed with \( x \) moles of B, then vapour pressure of solution obtained is 48 torr. What is the value of x?
1
Chemistry
Which are true for a standard hydrogen electrode? This question has multiple correct options A. The hydrogen ion concentration is 1 m B. Temperature is \( 25^{\circ} \mathrm{C} \) c. Pressure of hydrogen is 1 bar D. It contains a metallic conductor which does not absorb hydrogen
1
Chemistry
In deriving a formula for the combined resistance of three different resistors in series, Kirchhoffs laws are used. Which physics principle is involved in this derivation? A. The conservation of charge B. The direction of the flow of charge is from negative to positive c. The potential difference across each resistor is the \( \operatorname{same} \) D. The current varies in each resistor, in proportion to the resistor value
3
Physics
The Henry's law constant for helium gas in water at \( 30^{\circ} \mathrm{C} \) is \( 3.70 \times 10^{-4} \mathrm{M} / \mathrm{atm} \) When the partial pressure of helium above a sample of water is 0.650 at \( \mathrm{m} \) the concentration of helium in the water is M. A. \( 5.69 \times 10^{-4} \) В. \( 1.76 \times 10^{3} \) c. 1.30 D. \( 2.41 \times 10^{-4} \) E . \( 3.70 \times 10^{-4} \)
1
Chemistry
Three bulbs \( A, B \) and \( C \) are connected as shown in figure. The bulbs \( B \) and \( C \) are identical. If the bulb \( C \) is fused, then: A. Brightness of both bulbs \( A \) and \( B \) will increase B. Brightness of both bulbs \( A \) and \( B \) will decrease c. Brightness of the bulb \( A \) decrease and that of bulb \( B \) ncreases D. None of the bulbs will glow
3
Physics
If the earth is one-fourth of its present distance from the sun, the duration of the year will be changed to : A. half of the present year B. \( \frac{1}{4} t h \) of the present year c. \( \frac{1}{8} t h \) of the present year D. \( \frac{7}{8} t h \) of the present year E \( \cdot \frac{1}{16} t h \) of the present yea
3
Physics
A sample of acetaldehyde contained some ethyl alcohol as impurity. The reagent useful for the purification of \( \boldsymbol{C H}_{3} \boldsymbol{C H O} \) is : A. \( N a H C O_{3} \) B. \( N a_{2} C O_{3} \) \( \mathbf{c} \cdot \operatorname{NaH} S O_{3} \) D. \( P C l_{5} \)
1
Chemistry
A substance which increases the rate of reaction but itself remain chemically unchanged is called a/an: A. substrate B. enzyme c. reactant D. product
1
Chemistry
Fin an acute angle \( \Theta \), when \( \frac{\cos \Theta-\sin \Theta}{\cos \Theta+\sin \Theta}=\frac{1-\sqrt{3}}{1+\sqrt{3}} \)
2
Maths
For \( z=x+i y \) find the real and imaginary part of \( e^{z} \)
2
Maths
Form the differential equation representing the family of curves \( y= \) \( a e^{2 x}+b e^{-2 x} \) where a and \( b \) are arbitrary constants.
2
Maths
What is the colour code of a corbon resistor having a resistance of \( 470 \Omega \) and a tolerance of 5\%?
3
Physics
The angles is to be bisected to obtain an angle of \( 90^{0} \) is A \( \cdot 60^{0} \) and \( 45^{0} \) B. \( 60^{0} \) and \( 120^{\circ} \) \( \mathrm{c} \cdot 120^{0} \) and \( 180^{\circ} \) D. \( 30^{\circ} \) and \( 60^{\circ} \)
2
Maths
The annual income of Ruby in 2010 was around Rs. \( 21000 . \) If she invested one- third of it at \( 4 \% \) interest compounded quarterly, then what would be her savings at the end of a year? A .7184 B. 7284 \( c .7384 \) D. 7484
2
Maths
A glass sphere of radius \( 15 \mathrm{cm} \) contains a small air bubble at a distance \( 6 \mathrm{km} \) from its centre when viewed along its diameter from the nearest side,
3
Physics
Find volume of Cuboid of \( l=3 m, b= \) \( \mathbf{2} \boldsymbol{m}, \boldsymbol{h}=\mathbf{4} \boldsymbol{m} \)
2
Maths
Covalent compounds are usually liquids or gases due to the weak force of attraction between their molecules. A. True B. False
1
Chemistry
Two men and 7 children complete a certain piece of work in 4 days while 4 men and 4 children complete the same work in only 3 days. The number of days required by 1 man to complete the work is A. 60 days B. 15 days c. 6 days D. 51 days
2
Maths
Calculate the maximum value of the function \( f(x)=1-\cos x \) between 0 and \( 2 \pi \) \( \mathbf{A} \cdot \mathbf{0} \) B. c. 1.5 D. 2 E . 2.5
2
Maths
If pressure \( P, \) Velocity \( V, \) and time \( T \) are taken as fundamental physical quantities, then the dimensional formula for force is: A \( \cdot P V^{2} T^{2} \) B . \( P^{-1} V^{2} T^{-1} \) c. \( P V T^{2} \) D. \( P^{-1} V T^{2} \)
3
Physics
Glycerol contains: A \( \cdot 1^{\circ} \) Carbon B. \( 2^{\circ} \) Carbon \( c \cdot 3^{o} \) Carbon D. Both \( 1^{\circ} \) and \( 2^{\circ} \) carbon
1
Chemistry
A glass is filled with water up to its brim and a thick hand card placed on top of it. Now keeping the card tightly closed and pressed with palm, the glass full of water is inverted and placed upside down. The palm is gently removed from the card. It is observed that the piece of card dose not fall off the glass though the glass is full of water and its whole weight is exerting pressure on the card. Why does it happen?
3
Physics
When a large bubble rises from the bottom of a lake to the surface, its radius doubles. If atmospheric pressure is equal to that of column of water height \( \mathrm{H} \), then the depth of lake is :- \( A \cdot H \) B. 2H c. 7H D. 8H
3
Physics
The formula of the final product formed when acetylene reacts with ammonical silver nitrate is : A. \( A g C \equiv C H \) B. \( A g C \equiv C A g \) \( \mathbf{c} \cdot(A g)_{2} C=C H_{2} \) D. \( C H_{2}=C H_{2} \)
1
Chemistry
State the following statement is True or False If two distinct lines are intersecting each other in a plane then they cannot have more than one point in common. A. True B. False
2
Maths
1 11 \( \left\{\begin{array}{l}= \\ \frac{1}{4}\end{array}\right. \) \( \mid \begin{array}{c}- \\ + \\ ++\end{array}+ \) \( -\quad- \) \( \quad+\frac{j}{+} \) \( \left\{\begin{array}{l}-- \\ ++++++\end{array}\right. \)
1
Chemistry
Integrate: \( 2 x^{2} e^{x^{2}} \)
2
Maths
\( H_{2} S O_{4} \) cannot be used to dry up \( H_{2} S \) because it oxidises \( H_{2} S \) to \( S O_{2} \) and \( S \) If true enter 1 , else enter 0 . A.
1
Chemistry
Which of the following statements is not true about electric field lines? A. Electric field lines start from positive charge and end at negative charge B. Two electric field lines can never cross each other C. Electrostatic field lines do not form any closed loops D. Electric field lines cannot be taken as continuous curve
3
Physics
Find the common area enclosed by the parabolas \( \boldsymbol{y}^{2}=\boldsymbol{x} \) and \( \boldsymbol{x}^{2}=\boldsymbol{y} \)
2
Maths
In the aqueous solution of soap, above CMC (Critical Micelle Concentration): This question has multiple correct options A. the cations associate to form aggregates B. the anions associates to form the clusters of colloidal dimension C. the polar ends forming the clusters are directed towards water D. the non polar (hydrocarbon) ends are directed towards water
1
Chemistry
Presence of nitrogen in which among the following compounds cannot be detected by Lassaigne method? A. Hydrazine B. Aniline c. p-toluidine D. Picric acid
1
Chemistry
Draw \( \triangle A B C, \) where \( m \angle A B C= \) \( 90^{\circ} ; B C=4 c m \) and \( A C=5 c m \) and then construct \( \triangle B X Y \) with \( 4 / 3 \) scale factor. Write points of construction
2
Maths
How long does it take the car to pass it? (in min) A . 4.5 B. 5.5 \( c .3 .5 \) D. 6.5
3
Physics
the isotop of hydrogen Which is radioactive is A. Tritium B. Deuterium c. Nacent hydrogen D. Parahydrogen
1
Chemistry
If \( y=x \sqrt{a^{2}+x^{2}}+ \) \( a^{2} \log (x+\sqrt{a^{2}+x^{2}}) \) then \( \frac{d y}{d x}= \) \( 2 \sqrt{a^{2}+x^{2}} \)
2
Maths
Wave pulse on a string shown in the figure is moving to the right without changing shape. Consider two particles at positions \( x_{1}=1.5 m \) and \( x_{2}= \) 2.5 \( m . \) Their transverse velocities at the moment shown in the figure are along the A. positive y axis and positive y axis respectively B. negative y axis and positive y axis respectively C. positive y axis and negative y axis respectively D. negative y axis and negative y axis respectively
3
Physics
In the conversion of \( \boldsymbol{O}_{2} \longrightarrow \boldsymbol{O}_{2}^{-} \) the incoming electron goes to the orbital: A \( \cdot \pi^{*} 2 p x \) B . \( \pi_{2 p x} \) \( \mathbf{c} \cdot \sigma_{2 p z}^{*} \) \( D \cdot \sigma_{2 p^{2}} \)
1
Chemistry
Find the binomial distribution for which the mean is 4 and variance 3
2
Maths
Give the structural formulae for the following: Diethyl ether
1
Chemistry
DNA strands A. Have quaternary structure like protein B. Are bonded by disulphide bonds C. Have same polarity D. Are antiparallel
0
Biology
\( x \) \( c \) \( = \)
1
Chemistry
The opening of right auricle into the right ventricle is guarded by A . Mitral valve B. Pulmonary semilunar valve c. Bicuspid valve D. Tricuspid valve
0
Biology
There are 30 tickets in a box numbered from 1 to \( 30 . \) A ticket is drawn out at random. Let \( A \) be the event that the number on the ticket is a multiple of 6 Write the sample set \( S \) and outcomes of event \( A \) in set form.
2
Maths
How Many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word \( D A U G H T E R ? \)
2
Maths
Micelles are: A. adsorbed catalyst B. ideal solution \( \mathbf{C} \cdot \operatorname{gel} \) D. associated colloids
1
Chemistry
In a coil of area \( 10 \mathrm{cm}^{2} \) and 10 turns with magnetic field directed perpendicular to the plane and is changing at the rate of \( 10^{8} \) Gauss/second. The resistance of the coil is \( 20 \Omega \). The current in the coil will be A. \( 0.5 \mathrm{A} \) B. 5A \( c . \) 50 A D . \( 5 \times 10^{8} A \)
3
Physics
\( A, B, C \) are the three angles of a triangle \( . \) if \( \boldsymbol{A}-\boldsymbol{B}=\mathbf{1 5}^{\circ}, \boldsymbol{B}-\boldsymbol{C}=\mathbf{3 0}^{\circ} \) find \( \angle \boldsymbol{A}, \angle \boldsymbol{B}, \angle \boldsymbol{C} \)
2
Maths
Redox indicators are substances that undergo a colour change at specific A \( . p H \) B. electrode potential c. both \( A \) and \( B \) D. none of them
1
Chemistry
A metal 'X' is prepared by the electrolysis of fused chloride. It reacts with hydrogen to form a colourless solid, from which hydrogen gas is released on treatment with water. The metal'X' is : \( A \cdot A \) в. са \( c \cdot c u \) D. zn
1
Chemistry
Aqueous solutions of \( \boldsymbol{H} \boldsymbol{N} \boldsymbol{O}_{3}, \boldsymbol{K} \boldsymbol{O} \boldsymbol{H}, \boldsymbol{C} \boldsymbol{H}_{3} \boldsymbol{C O O H}, \) and \( \boldsymbol{C H}_{3} \boldsymbol{C O O N a} \) of identical concentrations are provided. The pair(s) of solutions which form a buffer upon mixing is/ are: This question has multiple correct options A. \( H N O_{3} \) and \( C H_{3} \) COOH в. \( K O H \) and \( C H_{3} C O O N a \) c. \( H N O_{3} \) and \( C H_{3} C O O N a \) D. \( C H_{3} C O O H \) and \( C H_{3} C O O N a \)
1
Chemistry
Grills of doors and windows are always painted before they are used? Give reason
1
Chemistry
A circle of radius \( 3 \mathrm{cm} \) can be drawn through two points \( A, B \) such that \( A B=6 \mathrm{cm} \) State True or False \( A \). False B. True c. Cannot be determined D. None of the above
2
Maths
Which of the following is a complex salt? A. Fischer salt B. Mohrs salt c. Glaubers salt D. Microcosmic salt
1
Chemistry