FT4 Physics Past Paper PDF

Question Paper Physics (Maximum Marks: 90) Question No. 1 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. A rod of length l has non-uniform linear mass density given by 2 ρ(x) = a + b( xl ) , where a a...

Question Paper Physics (Maximum Marks: 90) Question No. 1 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. A rod of length l has non-uniform linear mass density given by 2 ρ(x) = a + b( xl ) , where a and b are constants and 0 ≤ x ≤ l The value of x for the centre of mass of the rod is at: 3 a+b A. 2 ( 2a+b )l B. 4 3 ( 2a+b 3a+b )l 4 a+b C. 3 ( 2a+3b )l D. 3 2 ( 2a+b 3a+b )l Question No. 2 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. A particle is having a circular motion in a horizontal plane. It has an angular velocity of 10π rad s−1 at the end of 2 s increases with constant angular acceleration to an angular velocity of 15π rad s−1 at the end of 4 s. The angular acceleration of the particle is A. 5π rad s−2 B. 2. 5π rad s−2 −2 C. 7. 5π rad s D. 2π rad s−2 Question No. 3 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm in such a way that its end closer to the pole is 20 cm away from the mirror. The length of the image is :- A. 2. 5 cm B. 5 cm C. 10cm D. 15 cm Question No. 4 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. If λv, λx and λm represent the wavelengths of visible light, X-rays and microwaves respectively, then A. λm > λx > λv B. λm > λv > λx C. λv > λx > λm D. λv > λm > λx Question No. 5 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. A body is projected horizontally from the top of a tower with an initial velocity 18 m s−1. It hits the ground at angle 45°. What is the vertical component of velocity when strikes the ground? A. 9 m s−1 B. 9√ 2 m s−1 C. 18 m s−1 D. 18√ 2 m s−1 Question No. 6 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Two inductors L 1 and L 2 are connected in parallel and a time varying current i flows as shown in figure. The ratio ot current i 12 at any ime t Is L2 A. L1 L1 B. L2 L 22 C. 2 ( L 1 +L 2 )  L 21 D. 2 ( L 1 +L 2 ) Question No. 7 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. If E = energy, G = gravitational constant, I = impulse and M = mass, then 2 dimensions of GIM2 are same as that of E A. Time B. Mass C. Length D. Force Question No. 8 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. At room temperature, electrical conductivity of semiconductor is A. greater than that of a good conductor. B. zero. C. less than that of a good conductor. D. less than that of a bad conductor. Question No. 9 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. The linear density of a vibrating string is 10−4 kg m −1. A transverse wave is propagating on the string, which is described by the equation y = 0. 02sin(x + 30t) , where x and y are in metre and the time t is in second. The tension in the string is A. 0. 09 N B. 0. 36 N C. 0. 9 N D. 3. 6 N Question No. 10 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. What work must be done to rotate and electric dipole through an angle θ with the electric field, if an electric dipole of moment p is placed in an uniform electric field E with p parallel to E? A. W = pE (1 − cosθ) B. W = pE (1 + cosθ) C. W = 2pE (1 − cosθ) D. None of these Question No. 11 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. A stone of mass 500 g is dropped from the top of a tower of 100 m height and simultaneously another stone of mass 1 kg is thrown horizontally with a speed of 10 m s−1 from the same point. The height of the center of mass of the above two stone system after 3 s is: (g = 10 m s−2 ) A. 45 m. B. 35 m. C. 55 m. D. None of these. Question No. 12 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Two moles of an ideal gas is heated at constant pressure of one atmosphere from 27°C to 127°C. If C v, m = 20 + 10−2 T J K −1 mol −1 , then q and ΔU for the process, respectively are A. 6362. 8 J and 4700 J B. 3037. 2 J and 4700 J C. 7062. 8 J and 5400 J D. 3181. 4 J and 2350 J Question No. 13 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Two masses m 1 and m 2 suspended together by a massless spring of spring constant K. When the masses are in equilibrium, m 1 is removed without disturbing the system. The angular frequency of m 2 is −−K− A. √ m 1 −−K− B. √ m 2 −−−− K − C. √ m 1 +m 2 −−−− K − D. √ m −m 1 2 Question No. 14 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. A child is sitting at the edge of a merry-go-round.The arrow shows the velocity of the child.At the instant shown, he releases the ball on to the ground.Which is the path of the ball according to a stationary observer on the ground ? A.  B. C. D. Question No. 15 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. The moon is 384000 km away from earth. How long does it take the light to make the round trip, if a laser beam is sent to the moon and reflected back to the earth by a mirror placed on the moon by an astronaut? A. 5 min B. 2.5 min C. 2.5 s D. 500 s Question No. 16 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. A cubical block of side L and mass m is placed on a horizontal floor. In the arrangement, as shown, force F is applied at the end of the plane sheet P Q , which is firmly attached with the block. What should be the minimum value of P Q so that the block may be tipped about an edge?  L A. √3 B. L√ 2 L√ 2 C. 3 L√ 3 D. √2 Question No. 17 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. One end of wire 2 m long and diameter 2 mm is fixed in a ceiling. A naughty boy of mass 10 kg jumps to catch the free end and stays there. The change in length of wire is [Take g = 10 m s−2 , Y = 2 × 1011 N m −2 ] −5 A. 31. 85 × 10 m B. 2 mm C. 3 mm D. 4 m Question No. 18 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. An open carriage in a goods train is moving with a uniform velocity of 10 ms−1. If the rain adds water with zero velocity at the rate of 5 kgs−1 , then the additional force applied by the engine to maintain the same velocity of the train is A. 0.5N B. 2.0N C. 50 N D. 25 N Question No. 19 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. In Young's double slit experiment the source is white light. One slit is covered with red filter and the other with blue filter. There shall be A. alternate red and blue fringes. B. alternate dark and pink fringes. C. alternate dark and yellow fringes. D. no interference. Question No. 20 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. A solid which is transparent to visible light and whose conductivity increases with temperature is formed by A. metallicbonding B. ionic bonding C. covalent bonding D. van der waals bonding Question No. 21 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. What is the dimension of specific gravity? 2 A. M L2 T 1 2 1 B. L T 3 1 C. L T D. None of the above Question No. 22 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. On which of the following factors internal resistance of a cell depends: A. Distance between the electrodes B. The nature of electrodes C. Area of the electrodes D. All of these Question No. 23 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. ⃗ A uniform magnetic field B⃗ fills a cylindrical volumes of radius R. A metal rod CD of length l is placed inside the cylinder along a chord of the circular cross- section as shown in the figure. If the magnitude of magnetic field increases in the direction of field at a constant rate dB/dt, find the magnitude of the EMF induced in the rod. −−−−−2− l dB A. 2 dt √ R 2 − l4 −−−−−2− l dB B. 2 dt √ R 2 + l2 −−−−−2− l dB C. 4 dt √ R 2 − l4 −−−−−2− l dB D. 4 dt √ R 2 + l2 Question No. 24 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. As observed from earth, the sun seems to move in an approximate circular orbit. For the motion of another planet like mercury as observed from earth, this would A. be equally true. not be true because the force between earth and mercury is not inverse B. square law. C. not be true because the major gravitational force on mercury is due to sun. not be true because mercury is influenced by forces other than gravitational D. forces. Question No. 25 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. For the wave shown in figure given below, the wavelength and frequency, if its speed is 320 m sec−1 , are :- A. 8 cm, 400 Hz B. 80 cm, 40 Hz C. 8 cm, 4000 Hz D. 40 cm, 8000 Hz Question No. 26 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Ratio of inertial mass to gravitational mass of a body is A. 0. 1 B. 1 C. 2 D. no fixed number Question No. 27 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. The ends of a uniform metal rod of length 100 cm and area of cross-section 2 cm 2 are maintained at 0 °C and 100 °C. At the mid point of the rod, heat is supplied at a constant rate of 40Js −1. If the temperature gradient on the higher temperature side of the rod in steady state is 50 x° cm −1 , then the value of x is (Thermal conductivity of the metal = 400 J s−1 m −1 K −1 ) A. 2 B. 3 C. 6 D. 9 Question No. 28 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct.  −−→ −→ − − −→ The resultant of the three vectors OA , OB , and OC shown in figure is A. r B. 2r C. r(1 + √ 2) D. r(√ 2 − 1) Question No. 29 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. In an ideal transformer, the voltage and the current in the primary are 200 volt and 2 amp. respectively. If the voltage in the secondary is 2000 volt. Then value of current in the secondary will be A. 0.2 amp B. 2 amp C. 10 amp D. 20 amp Question No. 30 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. A 100 W sodium lamp radiates energy uniformly in all directions. The lamp is located at the centre of a large sphere that absorbs all the sodium light which is incident on it. The wavelength of the sodium light is 589 nm. At what rate are the photons from the lamp associated with the sodium light? 20 A. 3 × 10 photon s−1 are delivered 20 B. 2 × 10 photon s−1 are delivered 20 C. 1 × 10 photon s−1 are delivered 20 D. 4 × 10 photon s−1 are delivered  Chemistry (Maximum Marks: 90) Question No. 1 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. 4HNO 3 + P 4 O 10 ⟶ 4HPO 3 + X In the above reaction the product X is A. NO 2 B. N 2 O 3 C. N 2 O 4 D. N 2 O 5 Question No. 2 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. The volume of a gas measured at 27∘C and 1 atm pressure is 10 litres. To reduce the volume to 5 litres at 1 atm pressure, the temperature required is A. 75 K B. 150 K C. 225 K D. 300 K Question No. 3 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Which is used in the formation of nylon-6,6? A. Sulphurhexa fluoride B. Adipic acid C. Sulphurous acid D. Phthalic acid Question No. 4 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Chromyl chloride oxidises toluene to benzaldehyde this reaction is known as A. Rosennmund reaction B. Wurtz reaction C. Etard reaction D. Fitting reaction Question No. 5 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. The correct statement about orthoboric acid is A. It is a strong monobasic acid B. It is not a proton donor, but a weak Lewis acid C. It is a tribasic acid D. It is harmful for eyes Question No. 6 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. NH 3 and H2 O form NH 4 OH by A. electrovalentbond B. covalent bond C. coordinate bond D. none of these. Question No. 7 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. The alkane is not obtained from A. hydroxylation of ethyne ∘C 150 B. C 2 H 5 OH ⟶ HI/RedP Zn/Hg−HCl C. butanone Reflux D. sodium propionate solution electrolysis Question No. 8 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Le-Chatelier's principle is applicable to A. heterogeneous reaction B. homogeneous reaction C. irreversible reaction D. system in equilibrium Question No. 9 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Tyndall effect can be observed in A. colloidal solution B. solvent C. solute D. precipitate Question No. 10 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. The reactivity of metals with water is in the order of A. Na > Mg > Zn > Fe > Cu B. Cu > Fe > Zn > Mg > Na C. Mg > Zn > Na > Fe > Cu D. Zn > Na > Mg > Fe > Cu Question No. 11 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Which of the following ions is paramagnetic + A. Cu 2+ B. Z n 2− C. O 2 3+ D. Cr Question No. 12 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. The correct name of 'sucrose' is A. α − D - glucopyranosyl −β − D - fructofuranoside B. β − D - glucopyranosyl −β − D - fructofuranoside C. α − D - glucopyranosyl −α − D - fructofurnoside D. β − D - glucopyranosyl- α − L − fructofuranoside Question No. 13 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Which of the following has zero dipole moment A. ClF B. P C l3 C. SiF 4 D. CFCl 3 Question No. 14 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. The expression for Bohr's radius of an atom is n 2h2 A. r = 4π 2 me 4 z 2 n 2h2 B. r = 4π 2 me 2 z n 2h2 C. r = 4π 2 me 2 z 2 n 2h2 D. r = 4π 2 m 2 e 2 z 2 Question No. 15 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. In silicon dioxide Each silicon atom is surrounded by four oxygen atoms and each oxygen A. atom is bonded to two silicon atoms Each silicon atom is surrounded by two oxygen atoms and each oxygen B. atom is bounded to two silicon atoms C. Silicon atom is bonded to two oxygen atoms D. There are double bonds between silicon and oxygen atoms Question No. 16 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Oxidation involves A. Loss of electrons B. Gain of electrons C. Increase in the valency of negative part D. Decrease in the valency of positive part Question No. 17 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. IUPAC name of ⌊Co(NH 3 ) 3 (H2 O) 2 Cl]Cl 2 is A. Diaquachlorodiammine cobalt (III) chloride B. Triamminediaquachloro cobalt (III) chloride C. Chlorodiamminediaqua cobalt (III) chloride D. Diamminediaquachloro cobalt (II) chloride Question No. 18 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. The order of magnitude of ionic radii of ions Na + , Mg 2+ , Al3+ and Si 4+ is + A. Na < Mg 2+ < Al 3+ < Si4+ 2+ B. Mg > Na + > Al 3+ > Si4+ 3+ C. Al > N a + > S i 4+ > M g 2+ + D. Na > Mg 2+ > Al 3+ > Si4+ Question No. 19 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. In which of the following reaction, the value of K p will be equal to K c A. H 2 + I 2 ⇌ 2HI B. P C l5 ⇌ P C l3 + C l2 C. 2NH 3 ⇌ N 2 + 3H 2 D. 2SO 2 + O 2 ⇌ 2SO 3 Question No. 20 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. The standard EMF for the given cell reaction Zn + C u 2+ = Cu + Z n 2+ is 1.10 V at 25∘C. The EMF for the cell reaction, when 0.1M Cu 2+ and 0.1M Zn 2+ solutions are used, at 25∘C is A. 1.10 V B. 0.110 V C. −1.10V D. −0.110 V Question No. 21 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. The composition formula of gypsum is A. (CaSO 4 ) 2 ⋅ H2 O B. 2CaSO 4 C. CaSO 4 ⋅ 2H 2 O D. 2CaSO 4 H 2 O Question No. 22 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. The solubility of CaF 2 is s moles/litre. Then its solubility product is..... A. s 2 B. 4s 3 2 C. 3s D. s 3 Question No. 23 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Size of colloidal particles is A. 0.1 mμ to 0.001 mμ B. 10μ to 20μ C. 0.05 mμ to 0.1 mμ D. 25μ to 30μ Question No. 24 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. What will be the volume of CO 2 at NTP obtained on heating 10 grams of (90 % pure) limestone A. 22.4 litre B. 2.016 litre C. 2.24 litre D. 20.16 litre Question No. 25 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. The energy of a radiation of wavelength 8000Å is E 1 and energy of a radiation ∘ of wavelength 16000Å is E 2. What is the relation between these two A. E 1 = 6E 2 B. E 1 = 2E 2 C. E 1 = 4E 2 D. E 1 = 1/2E 2 Question No. 26 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Among the following compounds (I-III) the correct order of reaction with electrophilic reagent is A. II > III > I B. III < I < II C. I > II > III D. I = II > III Question No. 27 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Molecular shapes of S F4 , C F4 and XeF4 are A. The same with 2, 0 and 1 lone pairs of electrons respectively B. The same, with 1, 1 and 1 lone pairs of electrons respectively C. Different, with 0,1 and 2 lone pairs of electrons respectively D. Different, with 1,0 and 2 lone pairs of electrons respectively Question No. 28 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Among the following the aromatic compound is  A. B. C. D. Question No. 29 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Aniline in a set of reactions yielded a product D. The structure of product D would be A. C 6 H 5 CH 2 NH 2 B. C 6 H 5 NHCH 2 CH 3 C. C 6 H 5 NHOH D. C 6 H 5 CH 2 OH Question No. 30 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. In the cell Zn∣Z n 2+ ∥C u 2+ ∣Cu , the negative electrode is A. Cu B. Cu 2+ C. Zn D. Zn 2+ Mathematics (Maximum Marks: 120) Question No. 1 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. √ 1+√ 2+x −√ 3 lim x−2 x→2 is equal to 1 A. 8√ 3 1 B. √3 C. 8√ 3 D. √ 3 Question No. 2 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. ∣1 2 3∣ ∣1 6 3∣ If D = ∣ ∣2 −1 0 ∣ , then ∣∣4 −6 ∣ 0∣ ∣is equal to ∣3 4 5∣ ∣3 12 5∣ A. 2D B. 3D C. 6D D. 0 Question No. 3 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. If the four complex numbers z, z̄ , z̄ − 2 Re(z̄ ) and z − 2 Re(z) represent the vertices of a square of side 4 units in the Argand plane, then |z| is equal to : A. 4√ 2 B. 4 C. 2√ 2 D. 2 Question No. 4 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. x 2 −x+1 The function f : R → R defined as f(x) = x 2 +x+1 is A. injective as well as surjective B. injective but not surjective C. surjective but not injective D. neither injective nor surjective Question No. 5 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. 2 2 Let z 1 and z 2 be complex numbers, then |z 1 + z 2 | + |z 1 − z 2 | is equal to: 2 A. |z 1 | + |z 2 | 2 2 B. 2(|z 1 | + |z 2 | 2 ) C. 2(z 12 + z 22 ) D. 4z 1 z 2 Question No. 6 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. The points (3, − 2, − 1), (−1, 1, 2), (2, 3, − 4) and (4, 5, λ) are coplanar when λ = A. 0 −146 B. 17 C. 1 −17 D. 9 Question No. 7 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. A chord is drawn through the focus of the parabola y 2 = 6x such that its distance from the vertex of this parabola is √5 2 , then its slope can be: √5 A. 2 √3 B. 2 2 C. √5 2 D. √3 Question No. 8 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. The first three terms of a geometric sequence are x, y, z and these have the sum 5y equal to 42. If the middle term y is multiplied by 5/4 , the numbers x, 4 , z now form an arithmetic sequence. The largest possible value of x , is- A. 6 B. 12 C. 24 D. 20 Question No. 9 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. If a > 0 , then the equation ax 2 + 1 = 0 has A. real roots B. rational roots C. irrational roots D. non-real roots Question No. 10 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. 3x+2 If f(x) = 5x−3 , then −1 A. f (x) = f(x)  −1 B. f (x) = −f(x) C. f(f(x)) = −x −1 D. f (x) = − −1 19 Question No. 11 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. 1 1 1 The sum of the series 1⋅2 − 2⋅3 + 3⋅4 −.... upto ∞ is equal to A. loge 2-1 B. loge 2 C. 2loge 2 D. loge (4/e) Question No. 12 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. The line passing through (0, 1) and perpendicular to the line x − 2y + 11 = 0 is A. 2x − y +1=0 B. 2x − y +3=0 C. 2x + y − 1 = 0 D. 2x + y − 2 = 0 Question No. 13 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. A stone projected vertically upwards moves under the action of gravity alone and its motion is described by x = 49t − 4.9t 2 , It is at a maximum height when A. t = 10 B. t = 5 C. t = 0 D. none of these Question No. 14 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. sin22°cos8°+cos158°cos98° The value of sin23°cos7°+cos157°cos97° = A. 1  B. 2 C. 1/2 D. 1/4 Question No. 15 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Length of the tangent from (2, 1) to the circle x 2 + y 2 + 4y + 3 = 0 is A. 12 B. 6 C. √ 6 −− D. √ 12 Question No. 16 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. 1 The eccentricity of an ellipse with its centre at the origin is 2. If one of the directrices is x = 4, then the equation of the ellipse is A. 3x 2+ 4y 2 = 12 2 2 B. 4x + 3y = 12 2 2 C. 4x + 3y = 1 D. None of these Question No. 17 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. The number of solutions for the equation sin 3 xcosx + sin 2 xcos2 x + sinxcos3 x = 1 in the interval [0, 2π] is/are A. 0 B. 2 C. 3 D. Infinite Question No. 18 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. If AB is a chord of the circle x 2 + y 2 = r 2 subtending a right angle at the centre. Then, the locus of the centroid of ΔP AB as P moves on the circle, is  A. a circle. B. an ellipse. C. a pair of straight line. D. none of these. Question No. 19 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are non-smokers and vegetarian. Their chances of getting a particular chest disorder are 35%, 20% and 10% respectively. A person is chosen from the group at random and is found to be suffering from the chest disorder. The probability that the selected person is a smoker and non-vegetarian is : 14 A. 45 7 B. 45 8 C. 45 28 D. 45 Question No. 20 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. x The function f (x) = is 1+∣ ∣x∣ ∣ A. strictly increasing B. strictly decreasing C. neither increasing nor decreasing D. not differentiable at x = 0 Question No. 21 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. 10 1 The middle term in the expansion of (x + x ) is 1 A. 10 C 4 ⋅ x B. 10 C 6 C. 10 C 5 10 D. C 7 x2 Question No. 22 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. y dy y ϕ(x ) The solution of the differential equation dx = x + y is: ϕ′ ( x ) y A. ϕ ( x ) = kx y B. xϕ (x ) = k y C. ϕ ( x ) = ky y D. yϕ (x ) = k Question No. 23 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. An observer on the top of a tree finds the angle of depression of a car moving towards the tree to be 30°. After 3 minutes this angle becomes 60°. After how much more time, the car will reach the tree A. 4 minutes B. 4. 5 minutes C. 1. 5 minutes D. 2 minutes Question No. 24 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. −−− The value of the sum of i − 2 − 3i + 4 + … upto 100 terms, where i = √ −1 is _____ A. 50(1 − i) B. 25 i C. 25(1 + i) D. 100(1 − i) Question No. 25 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. The principal value of sin −1 (sin 2π 3 ) is  2π A. − 3 2π B. 3 π C. 3 4π D. 3 Question No. 26 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. ⎡2 b 1⎤ det(A) 2 Let A = b b + 1 b , where b > 0. Then the minimum value of b is: ⎣1 b 2⎦ A. 2√ 3 B. −2√ 3 C. √ 3 D. −√ 3 Question No. 27 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. If lim x→0 ϕ(x) = a 3 , a ≠ 0 , then lim x→0 ϕ( xa ) is A. a 2 1 B. a3 1 C. 2 a 3 D. a Question No. 28 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. π 2π 3π 4π 5π 6π 7π The value of cos 7 + cos 7 + cos 7 + cos 7 + cos 7 + cos 7 + cos 7 is A. 1 B. −1 C. 0 D. none of these. Question No. 29 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. On a railway tract, there are 20 stations. The number of tickets required in order that it may be possible to book a passanger from every station to every station after is A. C(20, 2) B. P(20, 2) 2 C. 20 D. none of these Question No. 30 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If now the mean age of the teachers in this school is 39 years, then the age (in years) of the newly appointed teacher is: A. 35 B. 40 C. 25 D. 30 Question No. 31 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. The length of the perpendicular from the point (2, −1, 4) on the straight line x+3 y−2 z 10 = −7 = 1 is A. greater than 3 but less than 4 B. greater than 4 C. less than 2 D. greater than 2 but less than 3 Question No. 32 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. If f is a real-valued differentiable function satisfying |f(x) − f(y)| ≤ (x − y) 2 , x, y ∈ R and f(0) = 0 , thenf(1) equals A. 1  B. 2 C. 0 D. - 1 Question No. 33 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Considering only the principal values of inverse functions, which of the following holds true for the set A = {x ≥ 0 : tan −1 (2x) + tan −1 (3x) = π4 } A. Is an empty set B. Contains more than two elements C. Contains two elements D. Is a singleton Question No. 34 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. 25 people employed for the program A , 50 people for the program B , 10 people for both A & B. So, the number of employees employed for only A is A. 15 B. 20 C. 35 D. 40 Question No. 35 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. π The largest interval lying in (− 2 , π2 ) for which the function, 2 f(x) = 4x −x + cos−1 ( x2 − 1) + log(cosx) is defined, is π A. [− 4 , π2 ] π B. [0, 2 ) C. [0, π] π D. (− 4 , π2 ). Question No. 36 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. 3 dy 2 d2y Given a differential equation x( dx ) − 1 = 2( dx 2 ) + sinx , whose order and degree are p & q respectively, then A. p + q =3 B. p − q = 1 C. pq + qp = 8 q p D. p − q = 1 Question No. 37 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. 4 − x 3 + 2x 2 + 3x, x>0 Let f : R → R be defined as f(x) = { 3. Then 3xex , x≤0 f is increasing function in the interval 1 A. (− , 2) 2 B. (0, 2) 3 C. (−1, ) 2 D. (−3, − 1) Question No. 38 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. 1 −1−x −− The value of the integral ∫ √ 1+x dx is 0 A. −1 B. 1 ​π C. 2 −1 π D. 2 +1 Question No. 39 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct.  1/3 1/3 1/3 (n+1) (n+2) (2n) lim ( n 4/3 + n 4/3 +..... + n 4/3 ) is equal to n→∞ A. 3 4 (2) 4/3 − 3 4 4 3/4 B. 3 (2) C. 4 3 (2) 4/3 D. 3 4 (2) 4/3 − 4 3 Question No. 40 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. x2 y2 Let LL ′ be the latus rectum through the focus of the hyperbola a2 − = 1 and b2 A be the farther vertex. If ΔALL ′ is equilateral, then the eccentricity of the hyperbola is (axes are coordinate axes) A. √ 3 B. √ 3 + 1 √ 3+1 C. √2 √ 3+1 D. √3 English and LR (Maximum Marks: 90) Question No. 1 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Dr. R.P. Singh said to his assistant, 'I go to see this patient at his residence after every 3.30 hours. I have already gone to the patient 1.20 hours ago and next time I shall go at 1.40 p.m.' At what time this information was given to the compounder by the doctor? A. 10.10 B. 11.30 C. 11.20 D. 8.50 Question No. 2 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. In each of the following options, four terms/words have been given, out of which three are alike in some manner and one is different. Choose the odd one out.  A. Nephrology B. Entomology C. Astrology D. Mycology Question No. 3 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Ashok said, "This girl is the wife of grandson of my Mother" Who is Ashok to the girl? A. Husband B. Father C. Grandfather D. Father-in-law Question No. 4 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Anil introduces Rohit as the son of the only brother of his father’s wife. How is Rohit related to Anil? A. Son B. Brother C. Uncle D. Cousin Question No. 5 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Three different positions of a dice are shown below. How many dots lie opposite 2 dots? A. 1 B. 3 C. 5  D. 6 Question No. 6 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. In each of the following questions, select the answer figure that will fit in the blank space in the question figure, maintaining the pattern in the proper sequence. A. B. C. D. Question No. 7 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. In the following question, there is a letter series in which one term is missing. Find out the missing term from the given options. GTZ, FSY, ERX, DQW, ? A. VCP B. VPC C. CPV D. CVP Question No. 8 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. 1 1 The simplified value of ( √ + ) is: 2+ 3−√ 5 √ √ 2−√ 3−√ 5 A. 1 3 B. √2 √2 C. 2 D. 0 Question No. 9 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. In the following question, select the number which can be placed at the sign of question mark (?) from the given alternatives. A. 242 B. 250 C. 201 D. 243 Question No. 10 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. A man walks 15 m towards South from a fixed point. From there he goes 12 m towards North and then 4 m towards West. How far and in what direction is he from the fixed point? A. 3 m, South B. 7 m, South - West C. 5 m, South - West D. 5 m, South - East Question No. 11 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. In a certain code, Green is written as ITGGP, so how will Pink be written as in the same code? A. RKPM B. TUMJ C. KLON D. RKQS Question No. 12 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. In a certain code, if H = 8, HE = 13. Then ‘HEN’ Will be equal to ______. A. 22 B. 24 C. 25 D. 27 Question No. 13 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. If O = 16, FOR = 42, then what is FRONT equal to? A. 61 B. 65 C. 73 D. 78 Question No. 14 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Choose the odd one out. A. 36 − 72 B. 17 − 34 C. 28 − 49 D. 24 − 48 Question No. 15 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Directions—Which of the following will come in place of the question-mark? ZX, XV , ?, T R, RP A. V U B. V S C. V T D. V W Question No. 16 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Select the related letter/word/ number from the given alternatives. Distance : Odometer :: ? : Barometer A. Humidity B. Pressure C. Thickness D. Wind Question No. 17 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. What is the number of straight lines in the following figure (Check the lines which are starting to ending)? A. 11 B. 14 C. 16 D. 17 Question No. 18 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Select the missing alphabets/number from the given responses. 31 (CAGE) 75 89 (?) 45 A. HIDE B. HILL C. CALL D. SAFE Question No. 19 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Each problem has a figure in the box. Find the one identical figure from the amongst the four figures (a, b, c or d) in the boxes. A. B. C.  D. Question No. 20 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. In the question given below, which one of the following five answer figures on the right should come after the problem figures on the left, if the sequence were to be continued ? A. 1 B. 2 C. 3 D. 4 Question No. 21 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Choose the alternative which best expresses the meaning of the idiom/phrase given in bold. We should not look down upon the wretched of the earth. A. sympathise with B. to consider someone or something inferior C. be indifferent to D. regard with contempt Question No. 22 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Choose the alternative, which best expresses the meaning of the idiom/phrase. A close shave  A. A narrow escape from danger B. Stubble C. Very short hair D. Hairless skin Question No. 23 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Directions: In the question given below, a sentence with a blank is given. Choose the alternative that completes the sentence grammatically and contextually. Stories depicting our culture and traditions have been _____ from generation to generation. A. handed in B. handed back C. handed down D. handed up Question No. 24 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Directions: In the question given below, a sentence with a blank is given.Choose the alternative that completes the sentence grammatically and contextually. The _____ of cotton is very heavy. A. bail B. bale C. band D. bald Question No. 25 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. In the following question, from the given alternative words, select the word which cannot be formed using the letters of the given word. Biological A. Logic B. Globe C. Bail D. Bill Question No. 26 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Find out the error in the following sentence: Neither she nor we takes the decision. A. neither B. nor C. takes D. the Question No. 27 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Out of four alternatives, choose the one which best expresses the meaning of the given word. PROPHYLACTIC A. Preventive B. Superficial C. Depend D. Obvious Question No. 28 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Select the correct word or phrase to complete a grammatical and idiomatic sentence. If only you had spoken clearly, you-  A. would not be misunderstood. B. would not have been misunderstanding. C. would not have been misunderstood. D. would not have misunderstood. Question No. 29 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Choose the word or phrase that is most nearly opposite in meaning to the given word Jettison (to leave) A. Abandon B. Strengthen C. Accept D. Modify Question No. 30 Only One Option Correct Type Each question has multiple options out of which ONLY ONE is correct. Find out the SYNONYM of the word: GESTICULATION A. Dynamics B. Notion C. Respite D. Jumble