12 th IIT 13 th May Test paper-1 Solution

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1 1 th IIT 13 th May Test paper-1 Solution Subject-PHYSICS Part : 1 SECTION-A (NEXT TEN QUESTIONS: SINGLE CHOICE ONLY ONE CORRECT ANSWER) Q1 In a capillary tube placed inside the liquid of density ( ) in a container, the rise of liquid is h. When block of density ' ' is placed on the liquid as shown in figure, liquid in the tube is h '. If then h' h h' h h' h (d.) Insufficient data Q Two points A and B are at distances of 'a' and charge density Q ( b a) 0 The work done in moving charge Q from A to B is Q ( b a) 'b' respectively from an infinite conducting plate having Q ( b a) 0 (d.) None of these Q3 A point charge of 0.1 C is placed on the circumference of a non-conducting ring of radius 1 m which is rotating with a constant angular acceleration of 1 rad/sec. at the centre of the ring at t 10 sec, is 10 6 T If ring starts it s motion at t 0 the magnetic field 10 7 T 10 8 T (d.) 10 7 T (b) 101, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 783

2 1 th IIT 13 th May Test paper-1 Solution 3 Q A small sphere and a big sphere are released from rest with a very small gap from height h as shown in the figure. The mass of bigger sphere is very large as compared to mass of smaller sphere. The height from the point of collision of smaller sphere with the bigger sphere to which the smaller sphere will rise if all the collisions are elastic h h 6 h (d.) 9 h (d) Q5 The distance between two parallel plates of a capacitor is a. A conductor of thickness b( b a) is inserted between the plates as shown in the figure. The variation of effective capacitance between the surfaces of conductor and plate as a function of the distance (x) is best represented by (d.) (c) 101, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 783

3 1 th IIT 13 th May Test paper-1 Solution Q6 Three blocks A, B and C having masses m kg, kg and 3 kg are attached by massless strings and ideal pulleys as shown in the figure. When the system is released from rest if the block mass of block ' A ' is ' A ' remains stationary, the. kg.6 kg. kg (d.).8 kg (d) Q7 1 A block of mass kg is attached to one end of a massless rod of length m. The rod is fixed to a horizontal plane at the other end such that the block and rod are free to revolve on a horizontal plane. The coefficient of friction between the block and surface is 0.1. Block is made to rotate with uniform angular speed by applying a 101, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 783

1 th IIT 13 th May Test paper-1 Solution 5 constant external force in tangential direction on the block. The work done by external force till the rod rotates by 0 90 is 0 10 joule (d) joule (d.

4 1 th IIT 13 th May Test paper-1 Solution 5 constant external force in tangential direction on the block. The work done by external force till the rod rotates by 0 90 is 0 10 joule (d) joule (d.) 1 joule Q8 One mole of a monoatomic gas is taken from P to R, via three paths the gas in PQR is W 1, in PR work done is W and in PSR work done is W 3, then PQR, PR and PSR. If work done by (d) W W3 W1 W 1 W W3 W W1 W3 (d.) W 3 W W1 Q9 A block of wood of relative density 0.5 is placed 10 m inside a vessel containing water. The vessel is accelerated upward with an acceleration of 10 m/s. If the block is released at some instant, then the time taken by block to reach the surface of water from that instant is ( g 10 m/s ) 0.5 sec 1 sec sec (d.).5 sec (b) Q10 An insect of negligible mass is sitting on a block of mass M, tied with a spring of force constant k. The block performs simple harmonic motion with amplitude A infront of a plane mirror placed as shown in the figure. The maximum speed of insect relative to its image will be A k m A 3 k m A 3 k m (d.) A m k (c) 101, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 783

5 1 th IIT 13 th May Test paper-1 Solution 6 SECTION-B (MULTIPLE CHOICE ONE OR MORE THAN ONE CORRECT ANSWER) Q1 When an electron of hydrogen like atom jumps from a higher energy level to a lower energy level. Then, angular momentum of the electron remains constant. kinetic energy increases. wavelength of de-broglie wave, associated with motion of the electron, decreases. (d.) all of the above (b, c) Q If the filament current in Coolidge tube is increased by increasing the voltage in the filament circuit then min remain same Max. K.E. of electron not affected. Intensity increases (d.) Intensity decreases (a, b, c) Q3 A parallel plate capacitor of plate area 0. m and spacing 10 m is charged to 3 10 volt and then disconnected from the battery, and pulled apart to double the plate spacing Work required to pull the plate is J Final voltage on the capacitor is 3 10 Volts. Final charge on the capacitor becomes two times of initial (d.) Final charge becomes half of initial value. (a, b) Q Two particles A and B are projected simultaneously in the direction shown in the figure with velocities v 0 m/s and v 10 m/s respectively. They collide in air after 1/ sec. Then A B The angle is 60 The distance x is 5 3 m 101, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 783

6 1 th IIT 13 th May Test paper-1 Solution 7 The angle is 30 (d.) The distance x is 15 3 m (b, c) Q5 A uniform square plate of mass m and edge a initially at rest starts rotating about one of the edge under the action of a constant torque. Then at the end of the 5 th sec after start Angular momentum is equal to 5 75 Kinetic energy is equal to ma (a, d) Angular momentum is equal to.5 (d.) 75 Kinetic energy is equal to ma SECTION-D Integer Answer Type This section Contains 5 questions. The answer to each of the questions is a single digit integer, ranging from 00 to 99. The appropriate bubbles below the respective question numbers in the OMR have to be darkened. Q1 A light rod of length L, is hanging from the vertical smooth wall of a vehicle moving with acceleration 3 g (8) having a small mass attached at it s one end is free to rotate about an axis passing through the other end. The minimum velocity given to the mass at it s equilibrium position so that it can complete vertical circular motion is KgL. Find the value of K. Q Find energy stored in the capacitor in it s steady state. 101, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 783

7 1 th IIT 13 th May Test paper-1 Solution 8 (0) Potential across capacitor is zero, hence energy stored is zero. Q3 The potential difference between two points A and B which are separated by a distance of 1 m along the () 1 field in a uniform electric field of 10 NC is 5 K Volt. Find the value of K. Q The power factor of a circuit in which a box having unknown electrical devices connected in series with a resistor of resistance 3 is 3/5. Find the reactance of the box in. () Q5 In the given circuit the reading of ideal voltmeter is E /. Find the internal resistance of the battery in. (1) 101, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 783

1 th IIT 13 th May Test paper-1 Solution 9 Subject-CHEMISTRY Part : SECTION-A (NEXT TEN QUESTIONS: SINGLE CHOICE ONLY ONE CORRECT ANSWER) Q1 18 7.5 10 18 7.5 10 19.5 10 7 (d.

8 1 th IIT 13 th May Test paper-1 Solution 9 Subject-CHEMISTRY Part : SECTION-A (NEXT TEN QUESTIONS: SINGLE CHOICE ONLY ONE CORRECT ANSWER) Q (d.) (b) Q 3 / 1 / / 3 (d.) 7 / 8 Q3 shift in forward direction shift in backward direction 101, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 783

9 1 th IIT 13 th May Test paper-1 Solution 10 remain unchanged (d.) be unpredictable Q (d) (d.) (c) Q5 (d.) Q6 (c) I > II > IV > III II > I > IV > III II > I > III > IV (d.) I > IV > III > II Q7 (b) Which of the following compounds can form silicones on hydrolysis? 101, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 783

10 1 th IIT 13 th May Test paper-1 Solution 11 Q8 (CH 3) SiCl (SiH ) 3 N 3 SiCl (d.) All of these (d.) Q9 (c) Which of the following compounds on decomposition, releases two gases containing the same elements? FeSO FeCO 3 Fe (NO ) (d.) Fe (ClO ) 3 3 Q10 Gold number gives amount of gold in colloid. weight in mg of colloid required to break gold sol. weight in mg of colloid to protect gold sol. (d.) amount of NaCl required to coagulate gold sol. (c) SECTION-B (MULTIPLE CHOICE ONE OR MORE THAN ONE CORRECT ANSWER) Q1 Which of the following compounds does not disproportionate on treating with conc. NaOH? (d.) (c, d) 101, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 783

11 1 th IIT 13 th May Test paper-1 Solution 1 Q (a, c) Ni at cathode H at cathode O at anode (d.) S at anode O 8 Q3 Which of the following is/are correct: [CrCl (CN) (NH3) ] and [CrCl3 (NH3 ) 3], both have d sp 3 hybridization. Magnetic moment of [PdCl is zero. ] [Cu (NH and [Ni(CN) ], 3 ) ], [Pt(NH3) ] all have dsp hybridization of central metal. (d.) It is difficult to substitute chelating ligands compared to similar monodentate ligands. (a, b, c, d) Q (d.) (a, d) 101, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 783

12 1 th IIT 13 th May Test paper-1 Solution 13 Q5 (d.) (a, d) SECTION-D Integer Answer Type This section Contains 5 questions. The answer to each of the questions is a single digit integer, ranging from 00 to 99. The appropriate bubbles below the respective question numbers in the OMR have to be darkened. Q1 () Q (3) 101, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 783

13 1 th IIT 13 th May Test paper-1 Solution 1 Q3 (3) Q (3) Q5 (8) 101, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 783

14 1 th IIT 13 th May Test paper-1 Solution 15 Subject-Mathematics Part : 3 SECTION-A (NEXT TEN QUESTIONS: SINGLE CHOICE ONLY ONE CORRECT ANSWER) Q1 1 (c) 1 (d.) None of these Q (d) (d.) 5 Q3 (d.) Q (d.) None of these 101, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 783

15 1 th IIT 13 th May Test paper-1 Solution 16 Q5 (d.) None of these Q6 (d) (d.) Q7 Q8 7 1 C C 8 C (d.) 3 cuts the given circle orthogonally touches the given circle internally touches the given circle externally (d.) none of these Q9 An ellipse is sliding along the co-ordinate axes. If at an instant, the foci of the ellipse are (1, 1) and (3, 3), then area of the director circle of the ellipse (in sq. units) is 6 (d.) 8 (d) (0, 0) lies on the director circle 101, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 783

1 th IIT 13 th May Test paper-1 Solution 17 Q10 10 105 70 (d.

Quadrilateral may be cyclic Diagonals of the quadrilateral may be equation All possible pairs of

16 1 th IIT 13 th May Test paper-1 Solution 17 Q (d.) 11 SECTION-B (MULTIPLE CHOICE ONE OR MORE THAN ONE CORRECT ANSWER) Q1 (d.) (a, b, d) Q G.M. of a and b is 3 one possible value of a b is 11 A.M. of a and b is 6 (d.) greatest value of a b is 8 (a, b, d) Q3 A quadrilateral is inscribed in parabola, then Quadrilateral may be cyclic Diagonals of the quadrilateral may be equation All possible pairs of adjacent sides may be perpendicular (d.) None of these (a, b) Q (b, d) (d.) , Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 783

The answer to each of the questions is a single digit integer, ranging from 00 to 99.

17 1 th IIT 13 th May Test paper-1 Solution 18 Q5 (d.) (a, d) SECTION-D Integer Answer Type This section Contains 5 questions. The answer to each of the questions is a single digit integer, ranging from 00 to 99. The appropriate bubbles below the respective question numbers in the OMR have to be darkened. Q1 () Q () Q3 () Q 101, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 783

18 1 th IIT 13 th May Test paper-1 Solution 19 (1) Q5 () 101, Blue Diamond Complex, Fatehgunj, Vadodara-0.Tel. No / / 783

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