Fiitjee Class 11th Phase Test 1 (JEE mains)
May 1, 2017 | Author: Shlok Sah | Category: N/A
Short Description
Fiitjee Class 11th Phase Test 1 (JEE mains)...
Description
FIITJEE - JEE (Mains) PHYSICS, CHEMISTRY & MATHEMATICS Time Allotted: 3 Hours
Maximum Marks: 360
Do not open this Test Booklet until you are asked to do so. Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose.
Important Instructions: 1.
Immediately fill in the particulars on this page of the Test Booklet with Blue / Black Ball Point Pen. Use of pencil is strictly prohibited.
2.
The Answer Sheet is kept inside this Test Booklet. When you are directed to open the Test Booklet, take out the Answer Sheet and fill in the particulars carefully.
3.
The test is of 3 hours duration.
4.
The Test Booklet consists of 90 questions. The maximum marks are 360.
5.
There are three parts in the question paper A, B, C consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct response.
6.
Candidates will be awarded marks as stated above in instruction No.5 for correct response of each question. ¼ (one fourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet.
7.
There is only one correct response for each question. Filling up more than one response in any question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 6 above.
8.
Use Blue / Black Ball Point Pen only for writing particulars / marking responses on Side-1 and Side-2 of the Answer Sheet. Use of pencil is strictly prohibited.
9.
No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any electronic device, etc. except the Admit Card inside the examination hall / room.
10. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the Room / Hall. However, the candidates are allowed to take away this Test Booklet with them. 11. Do not fold or make any stray marks on the Answer Sheet.
Name of the Candidate (in Capital Letters) :_____________________________________ Enrolment Number :_________________________________________________________ Batch :________________________ Date of Examination : ________________________
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2
SECTION – I PHYSICS 1.
A bob is hung from the ceiling of a train compartment. The train moves on an incline track of inclination 300 with horizontal. Acceleration of the train up the plane is g/2. The angle which the string supporting the bob makes with normal to the ceiling in equilibrium condition, is (A) 300 (B) tan-1 (2) 2 (C) tan-1 (D) 450 3
2.
A block of mass 2kg is gently placed over a massive plank moving horizontally over a smooth surface with velocity 6 m/s. The coefficient of friction between the block and plank is 0.2. The distance traveled by the block till it slides on the plank is (g=10 m/s2) (A) 4 m (B) 6 m (C) 9 m (D) 12 m
3.
Power applied to a particle varies with time as P 3t 2 2t 1 watt, where t is in second. Find the change in its kinetic energy between t = 2sec and t = 4sec (A) 32J (B) 46J (C) 61J (D) 100J
4.
A heavy string of mass m hangs between two fixed points A and B at an angle with the horizontal as shown in the figure. The tension at the lowest point in the string is (A) mg/(2 sin ) (C) mg/(2 tan )
5.
6.
Find the minimum value of mass of hanging block so 2 kg block slips over 4 kg block. (A) 30 kg (B) 20 kg (C) 10 kg (D) will not slip for any mass
=1.5
=0
2 kg
4 kg
M
Find the ratio of the acceleration of m1 and m2. All the pulleys are smooth and frictionless. am / am = ? (A) 2 : 1 (B) 1 : 2 (C) 1 : 1 (D) the system is not stable
2
m1
m2
A particle is projected on inclined plane of inclination at angle of elevation to the horizontal. If the particle strikes the plane horizontally then (A) tan 2 tan (B) tan cot (C) tan 2 tan (D) = 2
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B
(B) mg/(2 cos ) (D) mg/(2 cot )
1
7.
A
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8.
9.
3
A block B is resting on movable wedge A. The coefficient of friction between A and B is . The acceleration of the wedge for which B does not experience any friction is/are : (A) g tan (B) g cot (C) g (D) g cos
B A
A block 5 kg is kept on the floor of an elevator at rest. As the elevator starts descending with an acceleration of 12 m/s2, (Taking g = 10 m/s2) the displacement of the block during the first 0.2 sec. (A) 0.04 meter (B) 0.24 meter (C) 0.2 meter (D) 0.02 meter
a=12 m/s2 5 kg
10.
A body of mass 1kg is thrown upwards with a velocity 20m/s. It momentarily comes to rest after attaining a height of 18m. How much energy is lost due to air friction. (g = 10 m/s2) (A) 10J (B) 20J (C) 30J (D) 40J
11.
In system shown in figure mB 4kg and m A 2kg . The pulleys are massless and friction is absent everywhere. The acceleration of block A is g 10m / s2 10 (A) m / s2 3 20 (B) m / s2 3 (C) 2 m / s2 (D) 4 m/s2
12.
B A 300
A bead of mass m is located on parabolic wire with its axis vertical and vertex at the origin as shown in figure and whose equation is x2 = 4ay. The wire frame is fixed and bead can slide on it without friction. The bead is released from the point y = 4a on the wire frame from rest. The tangential acceleration of the bead when it reaches the position given by y = a is g 2 g (C) 2
(A)
3 g 2 g (D) 5
(B)
y
m
O
13.
A body is projected from the top of a tower with an initial velocity of 10 ms–1 horizontally (Assume g = 10 ms–2). The distance of the body from the point of projection after two seconds is (in m): (A) 20 (B) 40 (C) 28.8 (D) 14.4
14.
When a train is at rest, rain drops fall vertically. When it moves along east with a velocity equal to that of rain, the rain will appear to fall, for a passenger in the train: (A) 45° to vertical (B) along north-west (C) from upwards (D) 30° to vertical FIITJEE Ltd., North West Delhi Centre, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000
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15.
4
Block are moving as shown. The ratio v1 / v 2 is sin 1 (A) (B) sin 2 cos 2 (C) (D) cos 1
sin 2 sin 1 cos 1 cos 2
1 A
2 v1
B
v2
16.
A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force constant of 2 3 (A) k (B) k 3 2 (C) 3k (D) 6k
17.
If wedge is moving with acceleration a as shown in the figure then value of net force on m is (A) ma (B) 2 ma (C) mg ma (D) zero
18.
The acceleration-velocity graph of a particle moving in a straight line is as shown in figure. Then slope of velocity-displacement graph (A) increases linearly (B) decreases linearly (C) is constant (D) increases parabolically
a M M M
m
a
V
19.
A man is standing on a weighing machine with a block in his hand. The machine records W. When he takes the blocks upwards with some acceleration the machine records W 1. When he takes the blocks down with some acceleration, the machine records W 2. Then choose correct option. (A) W1 W W2 (B) W1 W W2 (C) W2 W W1 (D) W2 W1 W
20.
A particle is moving on an elliptical path as shown, speed of the particle is constant. Its acceleration is maximum at (A) A (B) B (C) C (D) same everywhere
21.
C
B A
R1 R2 If R1 A B and R2 A B , then will be along R1 R2 (A) A (B) B (C) A B (D) A B
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5 A
22.
g 2
Two monkeys each of mass m move with acceleration a1 a2
relative to the light inextensible string as shown in the figure. The ratio of tensions in the portions AB and BC of the string is (A) 1 : 2 (B) 3 : 1 (C) 4 : 1 (D) 2 : 1
B
a2
C
a1
23.
When a spring is stretched by a distance x, it exerts a force, given by F 5x 16x3 N. The work done, when the spring is stretched from 0.1M to 0.2M is (A) 8.1 102 J (C) 8.1 101J
(B) 12.2 102 J (D) 12.2 101 J
24.
A person walking at the rate of 3km/hour, the rain appears to fall vertically, when he increase his to speed 6 km/hr it appears to meet him at angle of 450 with vertical. The speed of rain is 3 km / hr (A) 3 2 km / hr (B) 2 (C) 6 2 km / hr (D) 2 3 km / hr
25.
In the figure shown there are two pendulums free to move in a vertical circle about one pivoted end. The length of each is and mass of each bob is m. But AB is a light string while PQ is a light rigid rod. The ratio of minimum velocities v1 and v2 given to both as shown to complete the full vertical circle is (A) 1 (C) 2
26.
27.
P
A
B
Q
5 2 3 (D) 2
(B)
A weightless inextensible rope rests on a stationary wedge forming an angle with the horizontal. One end of the rope is fixed to the wall at point A. A small load is attached to the rope at point B. The wedge starts moving to the right with a constant acceleration a. The magnitude of acceleration of the load is given by: (A) a (B) 2a sin 2 (C) a sin (D) g sin The time taken by the projectile to reach from A to B is t. Then the distance AB is equal to ut 3 ut (A) (B) 2 3 (C) 3 ut (D) 2 ut
A
B a
u 60
B O
30
O
A
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v2
v1
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28.
6
Two steel balls A and B are placed inside a right circular cylinder of diameter 54 cm making contacts at point P, Q and R as shown. The radius rA = 12 cm and rB = 18 cm. The masses are m A 60kg and mB = 15 kg. The forces exerted by the floor at the point Q and the wall at R are respectively (taking g = 10 m/s2)(all the surfaces are smooth) (A) 600N, 150N (B) 750N, 100N (C) 600N, 120N (D) 750N, 200N
B
P
R
A
Q 54 cm
29.
A weight W is attached to two weightless strings AB and AC as shown in figure. The tension in each string will be W (A) 4
(C)
30.
3W 2
W (B) 2
C
B 120
T
A 120°
(D) W W
A projectile is projected at an angle (>450) with an initial velocity u (t=0). the time t at which its horizontal component velocity will equal to the vertical component velocity u u (A) t = (cos sin ) (B) t = (cos sin ) g g u u (C) t = (sin cos ) (D) t = (sin 2 cos 2 ) g g
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7
SECTION – II CHEMISTRY 1.
Which of the following species has the greatest bond angle? (A) NH4 (B) NO2 (C) CH3
(D) PH4
2.
A vessel contains equal mass of methane and helium gases at 120oC and 800 mm Hg pressure. What is the partial pressure of methane in the vessel? (A) 600 mm Hg (B) 400 mm Hg (C) 160 mm Hg (D) 200 mm Hg
3.
Which of the following compound of magnesium evolves NH3 gas when reacts with water? (A) Mg(N3)2 (B) Mg3N2 (C) Mg(NO3)2 (D) Mg(NO2)2
4.
H2O2 decomposes as: 2H2O2 2H2O O2 Which of the following structure of H2O2 explains its easiest decomposition? H
H
O
(A)
(B)
O
O
O
H
H H
(C)
O
O
(D)
2H O22
H
5.
NH4 2 Cr2O7 Cr2O3 4H2O N2 What is the equivalent weight of (NH4)2Cr2O7 (Molar mass = M g) in the above reaction? M M (A) (B) 4 3 M M (C) (D) 6 8
6.
What is the third ionization energy(I.E3) of lithium atom in electron volt unit? 9 (A) 13.6 (B) (9 13.6) 4 1 4 (C) 13.6 (D) 13.6 9 9
7.
Which of the following two elements have maximum number of identical properties? (A) Si and Al (B) Mg and K (C) Be and Al (D) Na and Mg
8.
Which of the following molecule contains identical covalent bonds? (A) SF6 (B) PF5 (C) SF4 (D) IF7
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8
9.
Which of the following does not represent the root mean square velocity of an ideal gas? 3RT 3P (A) (B) M d 2E 2d (C) (D) M M
10.
In aqueous solution BeSO4 exists as (A) [Be(H2O)2]2+ and SO24
(B) [Be(H2O)4]2+ and SO24
(C) [Be(H2O)6]2+ and SO24
(D) [Be(H2O)3]2+ and SO24
11.
Which of the following solution of the given substance produces I2 when reacts with acidified H2O2? (A) NaIO3 (B) KI3 (C) I2O5 (D) NaIO4
12.
0.7 g of Na2CO3.xH2O is dissolved in 100 mL of water, 20 mL of which required 19.8 mL of 0.1 N HCl. Therefore, x is: (A) 1 (B) 2 (C) 3 (D) 4
13.
How many maximum number of electrons of an atom will have n + = 5? n = principal quantum number = azimuthal quantum number (A) 6 (B) 8 (C) 10 (D) 18
14.
Which of the following species has maximum spin value? (A) O2 (B) O2 (C) O2
(D) O22
15.
Which of the following substance has the highest value of second ionization energy? (A) Na (B) Mg (C) Al (D) Ca
16.
The radius of each atom of helium is r. What would be the excluded volume for an atom of helium which touches other helium atoms in a vessel at high pressure and low temperature. 4 8 (A) r 3 (B) r 3 3 3 16 3 32 3 (C) (D) r r 3 3
17.
Which of the following gas reacts with NaOH? (A) NH3 (B) CO (C) H2 (D) C2H4
18.
Which of the following substance forms a white colour product when reacts with H2O2? (A) K2Cr2O7 (B) FeSO4 (C) PbS (D) Na2SO3
19.
Which of the following molecule has zero dipole moment? FIITJEE Ltd., North West Delhi Centre, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000
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(A) SOF4 (C) XeF4
9
(B) SF4 (D) XeOF4
20.
Electrons with which of the following azimuthal quantum number, are present in maximum number in an atom of zinc? (A) = 0 (B) = 1 (C) = 2 (D) = 3
21.
Reaction of P4O10 with MgO forms only magnesium phosphate. How many moles of MgO can completely react with one mole of P4O10? (A) 4 (B) 5 (C) 6 (D) 8
22.
Which of the following atom attains a half-filled electronic configuration by gaining one electron? (A) Boron (B) Carbon (C) Nitrogen (D) Oxygen
23.
Which of the following ion has the largest ionic radius? (A) N3– (B) O2– 4– (C) C (D) F–
24.
Which of the following molecule is formed by overlapping of pure half-filled p-orbitals according to valence bond theory? (A) H2 (B) H2O (C) CH4 (D) F2
25.
The pressure of an ideal gas increases by one atm when the gas was transferred from a 9 L vessel to a 6 L vessel at constant temperature. What is the pressure of the gas in the smaller vessel? (A) 4 atm (B) 2 atm (C) 3 atm (D) 6 atm
26.
Which of the following is not a product of the reaction between sodium and oxygen? (A) Na2O (B) Na2O2 (C) NaO2 (D) NaO
27.
Which of the following type of hydrogen is formed in the hydrogen torch which is used for welding of metals? (A) Atomic hydrogen (B) Nascent hydrogen (C) Ortho hydrogen (D) Para hydrogen
28.
How many gram of NaOH can be completely neutralized by 200 mL of 0.4 M HCl solution? (A) 2.8 (B) 0.08 (C) 3.2 (D) 0.04
29.
Which of the following ratio of the characteristics of an orbit and electron is equal to principal quantum number of the orbit? Area of orbit Circumference of orbit (A) (B) Frequency of electron motion Wavelength of electron motion Radius of orbit Area of orbit (C) (D) Wave number of electron motion Circumference of orbit FIITJEE Ltd., North West Delhi Centre, 31-32-33, Central Market, West Avenue Road, Punjabi Bagh (West), New Delhi - 110026, Ph: 011-45634000
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30.
10
The energy change of which of the following process is called the ionization energy of sodium? (s = Solid state and g = gaseous state) (A) Na g Na s (B) Na s Na s (C) Na g Na g
(D) Na s Na g
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11
SECTION – III MATHEMATICS 1.
3 , then 2 (A) 2 cos (C) 2 cos
If 2
2 2 2 cos 4 is equal to
(B) 2 sin (D) 2 sin 3 cos ec20 sec 20 is equal to (B) 4 (D) none of these
2.
The numerical value of (A) 2 (C) 6
3.
The maximum value of 12 sin 9 sin2 is equal to (A) 3 (B) 4 (C) 21 (D) none of these 1 1 , cos and 0 , , then lies in the interval 2 3 2 (A) (60°, 90°) (B) (90°, 120°) (C) (120°, 300°) (D) (150°, 180°)
4.
If sin
5.
Given that sin3 x. sin 3x c m cos mx, c n 0, is an identity. The value of n is
n
m 0
(A) 2 (C) 6 6.
7.
The number of positive integral values of ‘m’ for which the x-coordinate of the point of intersection of the lines 3x + 4y = 9 and y = mx + 1 is an integer, is (A) 0 (B) 1 (C) 2 (D) infinitely many If the point , lies on the line 2x 3y 6 , the smallest value of 2 2 is 36 13 (C) 6
(A)
8.
9.
(B) 4 (D) cannot be calculated
6 13 13 (D) 13
(B)
The distance of the point 4,1 from the line y 3x measured along a line with gradient 1 is 11 2 11 2 (A) (B) 2 4 (C) 1 (D) none of these A point P 4,1 undergoes the following three transformations successively: (i) reflection about the line y x, (ii) translation through 2 units along the positive direction of x-axis, and (iii) rotation through an angle about the origin in the anticlockwise sense. 4 The final position of P is 1 7 (A) (B) 2,7 2 , 2 2
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1 7 (C) , 2 2
10.
11.
(D)
The number of common tangents to the circles x 2 y 2 6x 14y 48 0 and (B) 2 (D) 4
The equation of the circle passing through the points (2, 0) and (0, 4) and having the minimum possible radius is (A) x 2 y 2 x y 3 (B) x 2 y 2 2x 4y 0 (C) x 2 y 2 7x y 8 0
13.
2,7 2
A line passing through the point 21,30 and normal to the curve y 2 x has its slope equal to (A) 2 (B) 3 (C) 2 (D) 5
x 2 y 2 6x 0 is (A) 1 (C) 0
12.
(D) none of these
The incentre of the triangle formed by the lines y x and y 1 is
(C) 2
2,0
(D) 0,2 2
(A) 0,2 2
(B) 2 2,0
14.
The common chord of the circles x 2 y 2 4x 4y 0 and x 2 y 2 16 subtends at the origin an angle equal to (A) (B) 6 4 (C) (D) 3 2
15.
The chord of contact of the pair of tangents to the circle x 2 y 2 1 drawn from any point on the line 2x y 4 passes through the point 1 1 (A) , 2 4 1 (C) 1, 2
16.
1 1 (B) , 4 2 1 (D) , 1 2
If a circle passes through the point a,b and cuts the circle x 2 y 2 p2 orthogonally, then the equation of the locus of its center is (A) 2ax 2by a2 b2 p2 0 (B) 2ax 2by a2 b2 p2 0
(C) x y 3ax 4by a b p 2
17.
2
If the circle
2
2
2
0
x 2 y 2 4x 22y c 0
2
2
bisects the circumference of the circle
x y 2x 8y d 0 , then c d equals (A) 60 (B) 50 (C) 40 (D) none of these 2
2
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(D) x y 2ax 3by a b2 p2 0 2
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18.
If one vertex of an equilateral triangle of side 2 is the origin and another vertex lies on the line x 3y , then the third vertex can be
(D)
(A) 0,2 (C) 2, 2 19.
20.
(B) 3, 1
3,1
The sum of the squares of the length of the chord intercepted by the line x y n, n N on the circle x 2 y 2 4 is (A) 11 (C) 33
(B) 22 (D) none of these
The statement ~ p ~ q is (A) a tautology (C) equivalent to p q
(B) a fallacy (D) ~ p q
x 1 x 2 x 4 0 3
21.
The number of integral solutions of
x2 (B) 2 (D) 4
(A) 0 (C) 3 22.
dy is equal to dx 1 cos t (B) sin t cos t (D) 1 sin t
If x a t sin t , y a 1 cos t , then sin t 1 cos t cos t (C) 1 sin t
(A)
23.
log
The set of real values of x for which 2
25.
2
x 1
x 5 is
(A) , 1 4,
(B) 4,
dy 1 t2 2t , y , then 2 2 dx 1 t 1 t y (A) x x (C) y
(B)
(C) , 1 24.
is
(D) 1,4
If x
y x x (D) y
If log4 5 a and log5 6 b, then log3 2 (A)
1 2a 1
(C) 2ab 1
1 2b 1 1 (D) 2ab 1
(B)
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26.
dx
x x (A)
7
1
14
1 x7 ln c 7 x7 1
x7 (C) ln 7 c x 1
27.
If
1 dx k, then k is equal to sin x cos2 x 2
(D) none of these
/3
2
/ 4
(A)
1 x7 (B) ln 7 c 7 x 1
3
(C) 2
(B)
3
(D) 5 1 x2 x 1 x3
x 4 sin
28.
lim
x
(A) 0 (C) 1 29.
If A = tan 6° tan 42° and B = cot 66° cot 78°, then (A) A = 2B (C) A = B
30.
(B) 1 (D) doesn’t exist
1 B 3 (D) 3A = 2B
(B) A
The maximum value of sin cos x is equal to (A) sin1 (B) 1 1 (C) sin 2
3 (D) sin 2
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15
FIITJEE INTERNAL TEST PHASE – I BATCHES:
ANSWERS IIT MAINS
QP CODE: SR. NO 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.
PHYSICS
C.CODE
CHEMISTRY
C. CODE
MATHS
C.CODE
C C B C D B C A C B A C C A C B B C C C A C A A B B A D D C
P110403 P110401 P110504 P110403 P110403 P110320 P110310 P110405 P110326 P110502 P110404 P110415 P110326 P110320 P110416 P110404 P110404 P110325 P110404 P110318 P110201 P110403 P110507 P110320 P110508 P110409 P110314 P110405 P110403 P110310
B C B C C B C A D B B B D B A C B C C B C B C D C D A C B C
C110305 C111207 C110903 C111006 C111101 C110103 C110702 C110306 C111206 C110902 C111006 C110202 C110107 C110112 C110703 C111204 C110808 C111006 C110304 C110107 C110202 C110108 C110706 C110306 C111202 C110803 C111003 C111102 C110103 C110704
D B B B C A A B C D D B A D A A B A B C C B B C D A A B C A
M111303 M111402 M111411 M111403 M111407 M110701 M110714 M110718 M110728 M110712 M110822 M110802 M110704 M110820 M110809 M110821 M110815 M110702 M110823 -
M110109 M120509 M110203 M120508 M110202 M120701 M120803 M110606 M111402 M111308
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