Question 1. A given function g(x) is defined as . The value of g(2) equals : [A] 1 [B] [C] 22010 [D] 2 Your Answer: Correct Answer: D Explanation: Question 2. If sec A tan B + sec B tan A = 91, then the value of (sec A sec B + tan A tan B)2 is equal to : [A] 8282 [B] 4141 [C] 8280 [D] 4041 Your Answer: Correct Answer: A Explanation:
[A] [B] [C] [D] None of these Your Answer: Correct Answer: C Explanation: Question 4.
If are the roots of the equation , then equation whose roots are , ,
is : [A] [B] [C] [D] Your Answer: Correct Answer: B Explanation: Question 5. The maximum value of , is : [A] 1 + sin 1 [B] cos 1 [C] 1 + cos 1 [D] Your Answer: Correct Answer: A Explanation:
Question 6.
Consider the equation where . It is given that x1, x2 and x1 x2 are the real roots of the equation. If b + c = 2(a + 1), then x1x2 is equal to : [A] 1 [B] 2 [C] [D] Your Answer: Correct Answer: B Explanation: Question 7.
If are three values lying in for which , then
is equal to : [A] 1 [B] 2 [C] 3 [D] 4 Your Answer: Correct Answer: C Explanation:
is : [A] 3 [B] 15 [C] 7 [D] 1 Your Answer: Correct Answer: C Explanation: Question 9.
Let be an even function for all , then the sum of all
possible values of a is : (where [.] and {.} denote greatest integer function and fractional part functions, respectively) [A] 17/6 [B] 53/6 [C] 31/3 [D] 35/3 Your Answer: Correct Answer: D
Explanation:
Question 10.
Let . If x1, x2, x3 are three distinct real numbers such that f (x1) = f (x2) = f (x3) = 0, then
If then g(x) is identically equal to : [A] x [B] [C] [D] Your Answer: Correct Answer: B Explanation: Question 11.
[C] x2 [D] Your Answer: Correct Answer: C Explanation: Question 12. If line L intersects the sides BC, CA and AB of a triangle ABC at P, Q, R respectively, then is equal to : [A] [B] [C] 1/2 [D] 1 Your Answer: Correct Answer: A Explanation: Question 13.
The range of where [.] denotes the greatest integer function and n is a natural number is : [A] [B] [C] [D] Your Answer: Correct Answer: D Explanation: Question 14.
A ray of light travels along the line and strikes a plane mirror lying along the line . The equation of the straight line containing the reflected ray is : [A] [B] [C] [D] Your Answer: Correct Answer: B Explanation:
Question 15. Two points P and Q are taken on the line joining the points A(0, 0) and B(3a, 0) such that AP = PQ = QB. Circles are drawn on AP, PQ and QB as diameters. The locus of the point S, the sum of the squares of the lengths of the tangents from which to the three circles is equal to b2, is : [A] [B] [C] [D] Your Answer: Correct Answer: B Explanation: Question 16.
If and , then :
[A] [B] [C] [D] Your Answer: Correct Answer: B Explanation:
Question 17.
If , then (where , is equal to :
[Hint: You may use ] [A] [B] 1 [C] x0 [D] Your Answer: Correct Answer: C Explanation:
Question 18. Two circles are such that one is inscribed in and the other is circumscribed about a square A1A2A3A4. If the length of each side of the square is a units and P, Q are two points respectively on these circles, then equals : [A] [B] [C] a2 [D] 2a2 Your Answer: Correct Answer: C Explanation: Question 19. If [x] and {x} represent integral and fractional part of x, then the function defined by is : [A] 2[ x ] + {x} [B] 4 x [C] x [D] 4[x] + 1000 {x} Your Answer:
Correct Answer: C Explanation:
Question 20.
If ax = bc, by = ca, cz = ab, then the value of is :
[A] 2 [B] 10 [C] 1 [D] 3 Your Answer: Correct Answer: A Explanation: Question 21.
For each natural number k, let Ck denote the circle with radius k cm and centre at the origin, on the circle Ck a particle moves k cm in the anticlockwise direction. After completing its motion on Ck, the particle movies to Ck +1 in the radial direction. The motion of the particle continues in this manner. The particle starts at (1, 0). If the particle cross the positive direction of Xaxis for the first time on the circle Cn, then n is greater than : [A] 4 [B] 5 [C] 6 [D] 7 Your Answer: Correct Answer: A , B , C Explanation:
Question 22.
are the roots of equation ax2 + 2hx + b = 0. While are those of a1x2 + 2h1x + b1 = 0. If C and D divides AB in the ratio of respectively and also ab1, hh1, a1b are in A.P., then is equal to :
[A] 2 [B] 0 [C] [D] Independent of a, b, h, a1, b1,h1 Your Answer: Correct Answer: B , C , D Explanation: Question 23. In a right angled triangle, the length of the sides are a and b (where 0 < a < b). A circle passes through the midpoint of the smaller side and touches the hypotenuse as its mid point. Which of the following is (are) true? [A] Center of the circle is [B] Center of the circle is
[C] Radius of the circle is [D] Radius of the circle is Your Answer: Correct Answer: A , C Explanation: Question 24.
If x1, x2, x3 are such that : , then the value of
is divisible by : [A] 2 [B] 6 [C] 3 [D] 9 Your Answer: Correct Answer: A , B , C Explanation:
Question 25. Let S be a square with unit area. Consider any quadrilateral which has one vertex on each side of S. If a, b, c, d denote the lengths of the sides of quadrilateral, then where : [A] [B] [C] [D] Your Answer: Correct Answer: B , D Explanation: Question 26. The correct decreasing order of first ionisation enthalpies of five elements of the second period is : [A]
[B] [C] [D] Your Answer: Correct Answer: C Explanation: First ionisation enthalpies : Question 27. The correct sequence which shows decreasing order of the ionic radii of the elements is : [A] [B] [C] [D] Your Answer: Correct Answer: D Explanation: Ionic radius increases with addition of and decreases with removal of . Question 28. The atomic numbers of elements A, B, C and D are and Z + 2, respectively. If 'B' is a noble gas choose the correct answer from the following statements. I. 'A' has higher electron affinity II. 'C' exists in +2 oxidation state III. 'D' is an alkaline earth metal The correct answer is : [A] I and II [B] II and III [C] I and III [D] I, II and III Your Answer: Correct Answer: C Explanation: Question 29. Observe the following statements. I. The physical and chemical properties of element are periodic functions of their electronic configuration. II. Electronegative of fluorine is greater than the electronegative of chlorine.
Explanation: NA Question 30. In the following electrondot structure, calculate the formal charge from left to tight nitrogen atom; : [A] [B] [C] [D] Your Answer: Correct Answer: B Explanation: Question 31. The oxidizing power of chlorine in aqueous solution can be determined by the parameters indication below
of the conversion of to (Using the data)
will be : [A] [B] [C] [D] Your Answer: Correct Answer: B Explanation: Question 32. Lattice energy of a solid increases if : [A] Size of ions is small [B] Charges of ions are small [C] Ions are natural [D] None of these Your Answer: Correct Answer: A Explanation:
For smaller ions, lattice energy is greater. Question 33. have the hybridisations at sulphur atom respectively, as : [A] [B] [C] [D] Your Answer: Correct Answer: C Explanation: have respectively. Question 34. In , oxidation state, state of hybridization of Xe and shape of the molecule are, respectively : [A] , distorted octahedral [B] , square planar [C] , pyramidal [D] , square pyramidal Your Answer: Correct Answer: A Explanation: Question 35.
Correct order of bond angles in and is : [A] [B] [C] [D] Your Answer: Correct Answer: D Explanation:
[A] Different with 1, 0 and 2 lone pairs of electrons on the centre atom, respectively [B] Different with 0, 1 and 2 lone pairs of electrons on the centre atom, respectively [C] The same with 1, 1 and 1 lone pairs of electrons on the centre atoms, respectively [D] The same with 2, 0 and 1 lone pairs of electrons on the centre atom, respectively Your Answer: Correct Answer: A Explanation: Question 37. Consider the following molecules or ions ? I. II. III. IV. V. hybridisation is involved in the formation of : [A] I, II, V only [B] I, II only [C] II only [D] I, II, III, IV only Your Answer: Correct Answer: D Explanation: and are . Question 38. Which species has the maximum number of lone pair of electron on the centre atom ? [A] [B] [C] [D] Your Answer: Correct Answer: D Explanation:
Question 39. The low density of ice compared to water is due to : [A] Induced dipoleinduced dipole interactions [B] Dipoleinduced dipole interactions [C] Different Hbonding networks [D] Dipoledipole interactions Your Answer: Correct Answer: C Explanation: Ice has a cagestructured network whereas. H2O has sheet like network. Due to this, ice has some voids in its structure leading to lesser density. Question 40. Which of the following is an intensive property ? I. Temperature II. Viscosity III. Surface tension IV. Internal energy The correct choice is : [A] I, II [B] I, II, III [C] II, III, IV [D] I, II, III, IV Your Answer: Correct Answer: B Explanation: Temperature, viscosity and surface tension are intensive. Question 41.
For the reaction , the concentration of at equilibrium can be increased
by : I. Lowering the temperature II. Low pressure III. Taking excess of IV. Taking excess of The correct choice is : [A] I, III, IV [B] I, II, III [C] II, III, IV
Also by taking excess N2 or H2, NH3 increases. Question 42. A balloon containing 1 mole air at 1 atm initially is filled further with air till pressure increases to 4 atm. The initial diameter of the balloon is 1 m and the pressure at each stage is proportion to diameter of the balloon. How many no. of moles of air added to change the pressure from 1 atm to 4 atm. (Assume temperature to be constant during the process) [A] 256 [B] 257 [C] 255 [D] 80 Your Answer: Correct Answer: C Explanation: Question 43.
Statement : 1 At low temperature and pressure Z > 1 for H2 and He whereas Z < 1 for CO2, CH4 and N2.
Statement : 2 The effect of attractive forces dominates for CO2, CH4 and N2 whereas the molecular size effect dominates for H2 and He to explain deviations at low temperature and pressure. [A] Statement1 is True, Statement2 is True and Statement2 is a correct explanation for Statement1 [B] Statement1 is True, Statement2 is True and Statement2 is NOT a correct explanation for Statement1 [C] Statement1 is True, Statement2 is False [D] Statement1 is False, Statement2 is True Your Answer: Correct Answer: A Explanation:
Check Z vs P graph for van der waals equation. Question 44. A mixture of CO and CO2 having a volume of 20 mL mixed with X mL of oxygen and electrically sparked. The volume after explosion is 16 + X mL under the same conditions. What would be the residual volume if 30 mL of the original mixture is treated with aqueous NaOH ? [A] 12 mL [B] 9 mL [C] 6 mL [D] 3 mL Your Answer: Correct Answer: A Explanation: Question 45.
COCl2 gas decomposed as : If one mole of He gas is added in the vessel at equilibrium at constant P then : I. [COCl2] increases II. Moles of CO will increase III. The reaction goes in forward direction IV. Kc = 1 The correct choice is: [A] I, II [B] I, II, III [C] II, III [D] II, III, IV Your Answer: Correct Answer: C Explanation:
Your Answer: Correct Answer: A , B , D Explanation: Water freezer when it loses heat, exothermic. Neutralisation is always exothermic defined as heat at constant volume. Question 47. Consider the following two reactions : I. II. Which of the following is true ? [A] Reaction I is balanced and correct
[B] Reaction II is balanced but incorrect because H2O2 is reducing K2Cr2O7 as well as disproportionating itself [C] The nfactor of K2Cr2O7 is reaction I is 6 [D] The nfactor of H2O2 in reaction I is 2 Your Answer: Correct Answer: A , B , C , D Explanation: Reaction II is balanced but H2O2 cannot act as reducing agent as well as disproportionate at the same time. nfactor of nfactor of Question 48. Which of the following is(are) correct for a H like species ? [A] The energy gap between the consecutive energy orbits decreases as the value of "n" increases [B] The longest wavelength in any spectral series corresponds to aline in that series [C] Each spectral series is bounded by minimum and maximum wavelengths [D] Kinetic energy of the electron decreases, whereas the potential energy increases as the value of "n" increases Your Answer: Correct Answer: A , B , C , D Explanation: As we increase the value of n, energy levels become closer to each other. Question 49. The first element of each group s and pblocks shows anomalous behavior as compared to the rest of elements in the same group. This is due to : [A] Very small size as compared to atoms of other elements in the same group [B] Its comparatively high ionization energy [C] Its highest electronegativity in the group [D] Nonavailability of dorbitals for the formation of bond Your Answer: Correct Answer: A , B , D Explanation: NA Question 50. Which of the following is(are) correct ?
[A] The order of repulsion between different pair of electron is lp lp > lp bp > bp bp
[B] In general, as the number of lone pair of electrons on central atom increases, value of bond angle from normal bond angle also increases [C] The number of lone pair on O in H2O is 2 while on N in NH3 is 1.
[D] In cumulated diene, ; there are 2 sp2, 1 sp and 1 sp3 hybrid carbon atoms Your Answer: Correct Answer: A , C , D Explanation: NA Question 51. An elastic ball strikes a moving elevator with a velocity v. if the elevator has a speed v, the maximum height attained by the ball after the collision measured from the point of collision is: [A] [B] [C] [D] Your Answer: Correct Answer: D Explanation: Vsep = eVapp V1 v = 2v V1 = 3v Hence height w.r.t point of collision Question 52. The acceleration of a particle varies with time as speed of the particle at t = 4sec, if the particle was moving along + ve xaxis with a speed of 4 m/s at t = 0 sec [A] 28
Question 53. Block A of mass m and block B of mass M are connected by a massless spring over a pulley on a rough plane with coefficient of friction as . A force F is applied on block A to the left. Find the minimum value of M to move the block A towards right: [A] [B] [C] [D] Your Answer: Correct Answer: A Explanation: Question 54. In the figure shown two blocks of equal mass m = 10 kg attached to the two ends of a light spring of spring constant K = 100 N/m. Both the blocks are placed over a rough horizontal fixed surface.
At certain instant of time A and B have velocities V1 = 10 m/s towards left and V2 = 20 m/s towards right respectively as shown. If the coefficient of friction between A and ground is between 'B' and ground is then the acceleration of center of mass of the system at that instant is:
[A] 2 m/s2 towards left [B] 2 m/s2 towards left [C] 2 m/s2 towards left [D] 1 m/s2 towards right Your Answer: Correct Answer: B Explanation: Net force = acm = 1m/s2 Question 55. A small block enters the top A of the circular path with a horizontal velocity and gathers speed as it moves down the path. Here g is the acceleration due to gravity and r is the radius of circular segment. The block leaves the surface at point C. Neglect friction and treat the block as a particle. The angle in the figure is : [A] cos 1 (4/9) [B] cos 1 (3/4) [C] cos 1 (1/2) [D] cos 1 (5/6) Your Answer: Correct Answer: D Explanation: Question 56. A particle is moving in a circular path of constant radius r such that its centripetal acceleration is varying with time t, and is proportional to rt2. The power delivered to the particle by the force acting on it will be proportional to : [A] rt2 [B] rt [C] r2t [D] r/t
Question 57. From the uniform circular disc of radius 4 R, three small disc of radius R are cut off. The position vector centre of mass of the new structure will be: (Centre of lower circular cavity lies on xaxis and centre of upper and lower circular cavities lies on yaxis. The centre of each cavity is at distance 3R from centre of disc of radius 4R) [A] [B] [C] [D] Your Answer: Correct Answer: C Explanation: Question 58. A uniform chain of mass m and length l hangs from a hook. Determine the amount of work required to raise the middle link to the hook. [A] [B] [C] [D] Your Answer: Correct Answer: B Explanation:
Work done Question 59. Block A and B each of mass 1 kg are moving with 4 m/sec and 2m/sec respectively as shown. The coefficient of friction for all surface is 0.10. Find the distance by which centre of mass will travel before coming to rest (in m) : [A] 1 [B] 2 [C] 4 [D] 3 Your Answer: Correct Answer: D Explanation: acm till 2nd sec = 0 Hence distance
After 2nd sec to 4th sec distance by A = 2m Hence COM = 1m Hence = 3m Question 60. Sphere A is thrown up with velocity 20 m/sec from the ground. Sphere B of same mass in just dropped from a height of 80 m simultaneously at time t = 0 so that both collide in air and suck together. Find the time (in second) after which combined mass will fall to the ground (Calculated from t = 0) (g = 10 m/s2). [A] 1 [B] 4 [C] 6 [D] 2 Your Answer: Correct Answer: B
[A] 1m [B] 2m [C] 7m [D] 4m Your Answer: Correct Answer: A Explanation: As Hence 1m Question 62. A block A having a mass MA = 5 kg is released from rest at the position P shown and slides freely down the smooth fixed inclined ramp. When it reaches the bottom of the ramp it slides horizontally onto the surface of a cart of mass mc = 5 kg for which the coefficient of friction between the cart and the box is be the initial height of A, determine the position 'x' of the box on the card after it comes to rest relative to cart. (The cart moves on smooth horizontal surface) write x in cm. (Take g = 10 m/s2) [A] x = 150 cm [B] x = 250 cm [C] x = 100 cm [D] x = 300 cm Your Answer: Correct Answer: C Explanation: Question 63.
The speed of an train increase at a constant rate from zero to v and then remains constant for an interval and finally decreases to zero at a constant rate The total distance travelled by the train is l. The time taken to complete the journey is t. Then : [A] [B] [C] t is minimum when [D] t is minimum when Your Answer: Correct Answer: B Explanation: Question 64.
A particle is projected at an angle with speed m/s, from the point A, as shown in the figure. At the same time the wedge is made to move with speed m/s towards right as shown in the figure. Then the time after which particle will strike will wedge is : [A] 2 s [B] [C] [D] None of these Your Answer: Correct Answer: A
Question 65. A sphere of radius R is an contact with a wedge. The point of contact is from the ground as shown in the figure. Wedge is moving with velocity of towards left then the velocity of the sphere at this instant will be : [A] [B] [C] [D] Your Answer: Correct Answer: B Explanation: Question 66. Two beads A and B move along a semicircular wire frame as shown in figure. The beads are connected by an inelastic string which always remains tight. At an instant the speed of A is u, and where O is the centre of the semicircular arc. The speed of bead B at that instant is :
[A] [B] [C] [D] Your Answer: Correct Answer: A Explanation: Question 67. A smooth chain AB of mass m rests against a surface in the form of a quarter of circle of radius R. If it is released from rest, the velocity of the chain after it comes over the horizontal part of the surface is : [A] [B] [C] [D] Your Answer: Correct Answer: C Explanation:
[A] [B] [C] [D] Your Answer: Correct Answer: B Explanation: Question 69. n elastic balls are placed at rest on a smooth horizontal plane which is circular at the ends with radius r as shown in the figure. The masses of the balls are m, respectively. What is the minimum velocity which should be imparted to the first ball of mass m such that nth ball completes the vertical circle : [A] [B] [C] [D] Your Answer: Correct Answer: A Explanation:
Velocity of nth ball = (To just complete the circle)
A chain of length l and mass m lies in a pile on the floor. If its end A is raised vertically at a constant speed v0, the magnitude of the force P applied to end A terms of the length y of chain which is off the floor at any given instant. [A] [B] [C] [D] None of these Your Answer: Correct Answer: A Explanation: Force applied Question 71. When a chain is lowered onto the ground such that it will be heaped: [A] The fallen part does not experience reaction force due to the falling part [B] The falling part does not experience reaction force due to the fallen part [C] The fallen part experiences reaction force due to the falling part [D] The reaction force offered by ground must be lesser than the weight of the chain Your Answer: Correct Answer: B , C Explanation: NA Question 72. A block of mass m is pulled by an external agent by an inextensible string with velocity v and acceleration a at point P as shown in the figure then at this instant :
[B] Power delivered by the external agent is [C] Total power delivered by the string is zero [D] Work done by the string on the block is nonzero Your Answer: Correct Answer: A , B , C , D Explanation: Velocity of block will be = V/5 and acceleration of block will be = a/5 Question 73. A bob of a simple pendulum of mass m rests on the inclined plane of a wedge. If the wedge moves with a velocity v and acceleration a, disregarding friction at each surface: [A] Tension in the string is [B] Acceleration of the bob is [C] Tension in the string is greater than [D] Normal reaction on the wedge due to the bob is Your Answer: Correct Answer: C , D Explanation: Question 74. A horizontal force F pushes a wedge of mass M on a smooth horizontal surface. A block of mass m is stationary relative to the wedge, then: [A] Friction force is equal to mg between M and m [B] Minimum coefficient of friction between M and m is
[C] Minimum force required to prevent relative sliding between M and m is [D] The reaction between M and m is Your Answer: Correct Answer: A , B , C Explanation: Acceleration of both the blocks should be same for no slipping. Reaction between M & m vector sum of f and N Question 75. Choose the correct statement(s) of the following: [A] Force acting on a particle for equal time intervals can produce the same change in momentum but different change in kinetic energy [B] Force acting on a particle for equal displacement can produce the same change in kinetic energy but different change in momentum [C] Force acting on a particle for equal time intervals can produce different change in momentum but the same change in kinetic energy [D] Force acting on a particle for equal displacement can produce different change in kinetic energy but the same change in momentum Your Answer: Correct Answer: A , B Explanation: NA
