Physics Chemistry Mathematics IITJEE Test
April 29, 2017 | Author: Abhay Kumar Nayak | Category: N/A
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Physics Chemistry Mathematics IITJEE Test by Vidyamandir...
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Vidyamandir Classes
I.P. PRACTICE TEST – 1/2010 SECTION : 1 (PHYSICS) 1. 2.
The height of the building is 50ft. The same in millimeter is : (A) 560 mm (B) 285 mm (C) 1786.8 mm
4.
5.
1524 mm
The dimensions of heat capacity is : L2T 2 1 Mark correct option
(A) 3.
(D)
(B)
ML2T 2 1
(C)
M 1L2T 2 1 (D)
(A)
|a b| |a| |b|
(B)
|a b| |a| |b|
(C)
|a b| |a| |b|
(D)
|a b| |a| |b|
None of these
A body starts from rest and moves with a constant acceleration. The ratio of distance covered in the nth second to the distance covered in n second is : 2 1 1 1 2 1 2 1 (A) (B) (C) (D) 2 2 2 2 n n n n n n n n Two particles are projected vertically upwards with the same velocity on two different planes with accelerations due to gravities g1 and g2 respectively. If they fall back to their initial points of projection after lapse of time t1 and t2 respectively. Then t1 g 2 (A) (B) (C) (D) t12 t22 g1 g2 t1t 2 g1 g2 t1 g 1 t2 g2 2 t2 g1
6.
A particle is on a smooth horizontal plane. A force F is applied whose F-t graph is given. Then (A) at t1 acceleration is constant (B) initially body must be in rest (C) at t2 acceleration is constant (D) initially acceleration is non zero
7.
A person wants to drive on the vertical surface of a large cylindrical wooden well commonly known as death well in a circus. The radius of well is R and the coefficient of friction between the tyres of the motorcycle and the wall of the well is s . The minimum speed, the motorcyclist must have in order to prevent slipping should be (A)
VMC/ 2010
Rg s
(B)
s Rg
(C)
1
s g R
(D)
R s g
I.P. PRACTICE TEST- 1
Vidyamandir Classes 8.
A particle of mass m is moving in a horizontal circle of radius r under a centripetal force given by k 2 , where k is a constant, then r
(A)
k the total energy of the particle is (B) 2r
(C)
k the potential energy of the particle is 2r
k the kinetic energy of the particle is r
k the kinetic energy of the particle is r A force of 0.5 N is applied on upper block as shown in figure. Find the work done by lower block on upper for a displacement 3 m of the upper block (Take g = 10 m/s2) (A) 1 joule (B) 1 joule
(D) 9.
(C)
2 joule
(D)
2 joule
10.
Two bodies of masses m and 4 m are moving with equal linear momentum. The ratio of their kinetic energies is : (A) 1:4 (B) 4:1 (C) 1:1 (D) 1:2
11.
Four particles of masses 1 kg, 2 kg, 3 kg and 4 kg are placed at the corners A, B, C and D respectively of a square ABCD of edge 1 m. If point A is taken as origin, edge AB is taken along X – axis and edge AD is taken along Y – axis. Find the co-ordinates of centre of mass in S.I. (A) (1, 1) (B) (5, 7) (C) (0.5, 0.7) (D) None of these
12.
A particle of mass m rotates in a circle of radius a with a uniform angular speed 0 . It is viewed from a frame rotating about the z-axis with a uniform angular speed . The centrifugal force on the particles is : 0 m (A) (B) (C) m a m0 a (D) 2 If the distance between the two particles is increased by 2% , then the force of attraction between them will (A) decrease 6% (B) decrease 4% (C) increase 4% (D) increase 6% 2
2
13.
14.
15.
m02 a
The work done in shifting a particle of a mass m from centre of earth to the surface of earth is : mgR (A) (B) (C) zero (D) None of these mgR 2 The motion of a particle varies with time according to the relation y sin t a cos t . Then (A) (B)
the motion is oscillatory but not S.H.M. the motion is S.H.M. with amplitude a
(C) (D)
the motion is S.H.M. with amplitude None of these
VMC/ 2010
2a
2
I.P. PRACTICE TEST- 1
Vidyamandir Classes 16.
A block of wood float with 1 / 4 of its volume under water. What is the density of the wood ? (Density of water = 1000 kg/m3) (A) 750 kg/m3 (B) 250 kg/m3 (C) 300 kg/m3 (D) 260 kg/m3
17.
Bernoulli‟s equation is applicable to points (A) in a steadily flowing liquid (B) in a stream line (C) in a straight line perpendicular to a stream line (D) in any non-viscous liquid
18.
One end of a wire 2 m long and diameter 2mm 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 / m2 )
(A) 19.
31.85 105 m (B)
2 mm
(C)
3 mm
(D)
4m
The equation of a wave traveling on a stretched string along the x-axis is y ae(bx ct ) . The direction of propagation of wave is (A) along negative y – axis (C) along negative x – axis
(B) (D)
along positive y – axis along positive x – axis
20.
Along a stretched wire a transverse wave passes with speed 3000 m/s. If the tension in the wire increased four times, then the velocity of the wave is (A) 1500 m/s (B) 300 m/s (C) 6000 m/s (D) 9000 m/s
21.
The velocity of sound is not affected by change in (A) temperature (B) medium (C)
22.
(D)
wavelength
The metal sheet shown in figure, with two holes cut of unequal diameters d1 and d2 (d1 d2 ) If the sheet is heated (A) (B) (C) (D)
23.
pressure
both d1, and d2 will decrease both d1, and d2 will increase. d1 will increase, d2 will decrease d1 will decrease d2 will increase
In a U-tube, a liquid is poured to a height „h‟ in each arm. When left and right arms of the tube is heated to temperature T1 and T2 respectively, the height in each arm changes to h1 and h2 respectively. What is the relation between coefficients of volume expansion of liquid and heights, h1 and h2? h h2 h h2 (A) (B) 1 1 T1h2 T2 h1 T1h2 T2 h1 (C)
VMC/ 2010
h1 h2 T1h2 T2 h1
(D)
h1 h2 T1h1 T2 h2
3
I.P. PRACTICE TEST- 1
Vidyamandir Classes 24.
A gas behaves more closely as an ideal gas at (A) low pressure and low temperature (C) high pressure and low temperature
(B) (D)
low pressure and high temperature high pressure and high temperature
25.
The molar heat capacity of oxygen gas at STP is nearly 2.5R. As the temperature is increased, it gradually increases and approaches 3.5R. The most appropriate reason for this behaviour is that at high temperature (A) oxygen does not behave as an ideal gas (B) oxygen molecules dissociate in atoms (C) the molecules collide more frequently (D) molecular vibrations gradually become effective
26.
A given quantity of an ideal gas is at the pressure P and the absolute temperature T . The isothermal bulk modulus of the gas is : 2 3 (A) (B) (C) (D) 2P P P P 3 2
27.
d One end of a metal rod is kept in steam. In steady state, the temperature gradient dx (A) may be variable (B) must be constant (C) must be variable(D) None of these
28.
If two adjacent walls and the ceiling of a rectangular room are mirror surfaced, then how many images of himself, a man can see (A) 3 (B) 5 (C) 6 (D) 9
29.
A concave mirror with its optic axis vertical and mirror facing upward is placed at the bottom of the water tank. The radius of curvature of mirror is 40 cm and refractive index for water 4 / 3 . The tank is 20 cm deep and if a bird is flying over the tank at a height 60 cm above the surface of water, find the position of image of a bird (A) 3.75 cm (B) 4.23 cm (C) 5.2 cm (D) 3.2 cm
30.
In a double slit experiment, 5th dark fringe is formed opposite to one of the slits. The wavelength of light is (A)
31.
(B)
d2 5D
(C)
d2 15 D
(D)
d2 9D
are same as electric field intensity electric charge
If = surface charge density, = electric permittivity, the dimension of (A) (C)
32.
d2 6D
electric force pressure
(B) (D)
A point charge is projected along the axis of circular ring of charge Q and radius 10 2cm . The distance of the point charge from centre of ring, where acceleration of charged particle is maximum, will be (A) 10 cm (B) 20 cm (C) at infinity (D) None of these
VMC/ 2010
4
I.P. PRACTICE TEST- 1
Vidyamandir Classes 33.
In the given figure, two point charges q1 and q2 are placed distance a and b from centre of a metallic sphere having charge Q. Find electric field due to the metallic sphere at the point P. (A)
1 4 0
2
q1 q2 2 2 a b
(A) (C) 35.
36.
(C)
38.
39. 40.
4 0
Q R2
2
2
10 C0 11 C0
(B)
2C0
(D)
None of these
Three equal resistors, each equals to r are connected as shown in figure. Then the equivalent resistance between points A and B is (A) (B 3r r r 2r (C) (D) 3 3 The resistance between terminal points A and B of the given circuit will be : (A)
37.
1
(B)
q1 q2 Q (C) None of these 2 2 2 (D) 4 0 R b a Find equivalent capacitance between points M and N 1
34.
2
3 1 1 3
(B) (D)
1 3 2 3
Three circular concentric wires of radii a, 2a and 3a are carrying current 3I, 2I and I in same manner. Find the magnetic field at the common centre. 0 I 0 I 130 I (A) (B) (C) (D) None of these 6a a 6a The magnitude of magnetic moment of the current loop in the figure is : (A)
Ia 2
(B (C) (D)
2Ia 2 zero None of these
The flux of B through any closed surface is : (A) (B) 0 0
(C)
0
(D)
0
When the current changes from 2A to 2A in 0.05 s, an emf of 8 V is induced in a coil. The coefficient of self-induction of the coil is : (A) 0.1 H (B) 0.2 H
VMC/ 2010
(C)
5
0.4 H
(D)
0.8 H
I.P. PRACTICE TEST- 1
Vidyamandir Classes 41.
The time constant for the given circuit is : 1 s 4 1 (C) 2s (D) s 2 In the series LCR circuit, calculate the voltmeter and ammeter readings. (A) V = 250 V, I = 4 A (B) V = 150 V, I = 2 A (C) V = 1000 V, I = 5 A (D) V = 100 V, I = 2 A
(A)
42.
43.
4s
(B)
The stopping potentials are V1 and V2. Calculate the (V1 V2 ) , if the 1 and 2 are wavelength of incident lights, respectively. (A)
44.
hc 1 1 (B) e 1 2
hc 1 1 (C) e 1 2
e 1 1 (D) hc 1 2
e 1 1 hc 1 2
The circumference of the second orbit of an atom or ion having single electron, is 4 109 m . The de Broglie wavelength of electron revolving in this orbit should be : (A)
45.
46.
(B)
4 109 m
(C)
8 109 m
(D)
1 109 m
The wavelength of the emitted radiation, if electron in hydrogen atom jumps from the third orbit to second orbit is : 36 5R 5 R (A) (B) (C) (D) 5R 36 R 6 The nucleus 242Pu94 decays to 206Pb82 by emitting (A) (B) 9 and 12 particles 6 and 9 particles (C)
47.
2 109 m
9 and 6 particles
(D)
6 and 12 particles
Calculate the energy released per nucleon of the reactant, in the thermonuclear reaction 3 1H 2 2 He4 1H 1 0 n1 21.6 MeV
(A)
21.6 MeV
(B)
7.2 MeV
(C)
48.
In a zener diode : (A) forward voltage rating is high (B) negative resistance characteristics exists (C) breakdown occurs at a high reverse voltage (D) sharp breakdown occurs at low reverse voltage
49.
In intrinsic semiconductors, current is carried by : (A) electrons (B) (C) ions (D)
50.
3.6 MeV
(D)
1.8 MeV
holes electrons and holes
Which of the following theories is the most satisfactory about the origin of the universe? (A) Big-Bang theory (B) Pulsating theory (C) Steady state theory (D) None of these
VMC/ 2010
6
I.P. PRACTICE TEST- 1
Vidyamandir Classes
I.P. PRACTICE TEST – 1/2010 SECTION : 2 (CHEMISTRY) 1.
2. 3.
4. 5. 6.
In which of the following orbital diagram Aufbau principle is violated ? (A)
(B)
(C)
(D)
The orbital is a space where the probability of finding on electron is (A) (B) (C) 50% 0% 95 98%
(D)
100%
The one which has smallest number of molecules : (A) 0.1 mole of CO2 gas (B)
11.2 L of CO2 gas at NTP
(C)
22.4 103 ml of CO2 gas
22 g of CO2 gas
(D)
A temperature of 40C shall be equal to : (A) 243 K (B) (C) (D) Both a and b 40F 32F The vapour pressure of water at 100C is : (A) 76 cm (B) 760 cm (C) 0.1 atm (D) zero cm The heat of neutralization of four acids, a, b, c and d, against a common base are 13.7, 9.4, 11.2 and 12.4 kcal respectively. The weakest among these acids, is :
(A) 7.
(C) c 1 For the following reaction in gaseous phase, CO O2 2 (A)
8.
(RT)1/ 2
(B)
(B)
b
(D) CO2
d
Kp / Kc is :
(RT)1/ 2
(C)
(RT)
(D)
(RT)1
H3O
(C)
H
(D)
O 2
Conjugate base of OH is : (A)
9.
a
H2O
(B)
In the Arrhenius equation, k=A. exp( Ea / RT) , the rate constant : (A) (B) (C) (D)
decreases with increasing activation energy and increases with temperature increases with activation energy and temperature decreases with activation energy and temperature increases with activation energy and decreasing temperature
10.
For determination of molecular mass, Raoult‟s law is applicable only to : (A) dilute solutions of electrolytes (B) concentrated solutions of electrolytes (C) dilute solutions of non-electrolytes (D) concentrated solutions of non-electrolytes
11.
The solubility of a gas in water depends upon : (A) nature of the gas (B) (C) pressure of the gas (D)
VMC/ 2010
7
temperature None of these I.P. PRACTICE TEST- 1
Vidyamandir Classes 12.
Which of the following represents homogeneous catalysis ? (A)
Ni Oil H2 saturatedfat
(C)
H CH3COOH C2 H5OH CH3COOC2H5 H 2O
(D)
None of these
(B)
Fe N2 3H2 2NH3
13.
The brown-ring complex compound of iron is formulated as [Fe(H2O)5(NO)]SO4. The oxidation state of iron is : (A) 1 (B) 2 (C) 3 (D) 0
14.
For the redox reaction, MnO4 C2O42 H Mn 2 CO2 H2O
correct stoichiometric
coefficients of MnO4 , C2O42 and H are (A) 15.
2, 5, 16
(B)
16, 5, 2
(A)
18.
19.
20.
22.
23.
24.
(B)
87Ac
211
(B)
E0
Given
0.52 V
What will be the product, if 92U
(D)
2, 16, 5
(C)
Cr3 / Cr
0.74V, E0
0.13V
Fe2 / Fe
0.44V
(D)
0.26V
(D)
89Ac
emits two and one particle ?
89Ac
235
(C)
89Ac
225
227
In the reaction, Po Pb Bi, if Bi belongs to group 15, to which Po belongs ?
(A) 14 (B) 15 Effective overlapping will be shown by : (A) (B) Θ + Θ +Θ Θ The least stable hydride is : (A) BiH3 (B) SbH3
(C)
13
(D)
16
(C)
Θ + Θ
(D)
None of these
(C)
AsH3
(D)
PH3
The increasing order of size of atoms or ions Ar,K ,S2 ,Cl and Ca 2 , is : (B)
K Ca 2 Ar S2 Cl
(C) (C) Ca 2 K Ar Cl S2 Which of the following is known as “Pearl ash”? (A) K2O3 (B) KOH (C)
S2 Cl Ar K Ca 2
K2CO3
(D)
KMnO4
Cassiterite is an ore of : (A) mercury (B)
lead
(D)
iron
(A) 21.
0.26V
235
(A) 17.
5, 16, 2
What is the value of E 0 cell? Cr | Cr3 (0.1M)| |Fe2 (0.01M)| Fe
16.
(C)
S2 Ca 2 Cl Ar K
tin
(C)
In solid CuSO4 . 5H2O, copper is co-ordinated to: (A) five water molecules (B) (C) one water molecule (D)
one sulphate ion four water molecules
Which of the following is Tollen‟s reagent? (A)
VMC/ 2010
Ag NH3 (B) 2
(C)
Ag 2O
8
Cu OH 4
2
(D)
Cu 2O
I.P. PRACTICE TEST- 1
Vidyamandir Classes 25.
26.
Ammonia gas can be dried using : (A) conc. H2SO4 (B) conc. HCl
(C)
CaO
(D)
P2O5
Silicon carbide is used as a / an : (A) solvent (B) abrassive
(C)
catalyst
(D)
dehydrating agent
27.
The catalyst used in the manufacture of sulphuric acid by contact process is : (A) finely divided iron (B) molybdenum (C) nitrous oxide (D) vanadium pentoxide
28.
Bessemerisation is involved in the extraction of : (A) Ag (B) Cu (C)
Fe
(D)
Al
29.
The slag obtained during extraction of copper from copper pyrites is composed mainly of : (A) FeSiO3 (B) CuSiO3 (C) SiO2 (D) Cu2S
30.
The reagent NH4Cl and aqueous NH3 will precipitate : (A)
Ca 2
(B)
Al3
(C)
Mg 2
(D)
Zn 2
31.
The IUPAC name of the compound : (A) 1,4-dichloro-2,6-dioxo-4-carbamoly-1-oic acid (B) 1,4-dichloro-2, 4, 6-dioxocyclohexane-1-carboxylic acid (C) 1,4-dichloro-4-formyl-2, 6-dioxocyclohexane-1-carboxylic acid (D) 2,4-dioxo-1,4-dichlorohexane-1-carboxylic acid
32.
Which of the following is the correct order of stability of different conformations of butane ? (A) Gauche staggered partially eclipsed fully eclipsed (B) Staggered gauche partially eclipsed fully eclipsed (C) Staggered fully eclipsed partially eclipsed gauche (D) None of these
33.
A substance is found to contain 7% nitrogen. The minimum molecular weight of it is : (A) 700 (B) 100 (C) 200 (D) 70
34.
In C6H6 molecule, the carbon atoms are : (A) sp-hybridised (C) sp3-hybridised
(B) (D)
sp2-hybridised both sp and sp2 hybridised alternately
35.
The compound, which on reductive ozonolysis gives one mole of O = CH(CH2)3 . CH = O is : (A) 1-methyl but-1 – ene (B) 1, 2-dimethyl propene (C) 3-methyl but-1-ene (D) cyclopentene
36.
In the reaction, the product (Y) is : (A) (C)
37.
o-cresol (B) 2, 4-dihydroxytoluene (D)
p-cresol benzoic acid
Which alcohol will have the highest value of pKa ? (A) Ethanol (B) 2-propanol (C)
VMC/ 2010
9
tert-butyl alcohol (D)
Methanol
I.P. PRACTICE TEST- 1
Vidyamandir Classes 38.
39.
40.
41. 42.
43. 44.
45. 46.
47.
48.
In which of the following reactions, reactions, phenol is not obtained ?
(A)
(B)
(C)
(D)
Cannizzaro reaction is not given by : (A) triethyl acetaldehyde (C) benzaldehyde
(B) (D)
CH COOH
50.
A and B respectively are :
(A) (CH3)2C = N NH2, CH3CONH2 (B) (CH3)2C = N NH2, CH3CONH . NH2 (C) (CH3)2C = N N = C(CH3)2, CH3CONH2 (D) None of these Pyruvic acid is : (A) keto acid keto acid (B) keto acid (D) keto acid (C) Carbyl amine test is used in the detection of : (A) aliphatic 2 amine (C) aliphatic 1 amine
(B) (D)
aromatic 1 amine both aliphatic and aromatic 1 amines
Natural polymer is : (A) Polyester
(C)
Starch
(B) (D)
methanoic acid methyl methanoate
(B)
Glyptal
Formalin is : (A) 40% aq solution of methanal (C) 100% methanal
Arsenic drugs are mainly used in the treatment of : (A) jaundice (B) typhoid (C)
(D)
syphilis
(D)
Nylon-6
cholera
The product of which of the following reactions on heating gives crotonaldehyde ? (A)
dil. NaOH Acetone + acetaldehyde
(B)
dil. NaOH Acetaldeyde
(C)
dil. NaOH Formaldehyde + acetaldehyde
(D)
None of these
Pd / BaSO
4 (A) CH3COCl [H ] 2
The isomers of CH3COCl and (A) will respectively :
(A) CH2ClClCHO, oxirane chlorethyl alcohol, epoxyethane (C) The unit of conductivity is : (A)
49.
CH COCI
3 3 NH . NH 2 A B 2 2
acetaldehyde formaldehyde
ohm cm1
(B)
ohm cm2
(B) (D)
chloral, vinyl alcohol None of these
(C)
ohm1cm1
(D)
ohm1cm2
Which of the following represents hexadentate ligand ? (A) 2, 2-bipyridyl (B) DMG (C) Ethylenediammine (D)
None of these
Ordinary white phosphorus consists of phosphorus molecules of formula (A) P10 (B) P2 (C) P4 (D)
P5
VMC/ 2010
10
I.P. PRACTICE TEST- 1
Vidyamandir Classes
I.P. PRACTICE TEST – 1/2010 SECTION : 3 (MATHEMATICS) 1.
(A) 2.
3.
X Y
YX
(B)
X Y
(C)
6
(D)
None of these
6
1/ 2 1/ 2 The degree of the polynomial x x3 1 x x3 1 is equal to : (A) 9 (B) 8 (C) 10 (D) None of these
1 i 3 If i 1 , then 4 5 2 2
(A) 4.
X 8n 7n 1 : n N and Y 49 n 1 : n N then :
1 i 3
334
1 i 3 3 2 2
1 i 3
(B)
335
equal to :
(C)
i 3
(D)
i 3
(C)
16 i
(D)
16 i
The value of 2 cos 56 15 sin 5615 is : (A) 4i (B) 8i 8
5.
If the equation
x 2 2 m x m2 4m 4 0 has coincident roots, then :
(A)
m = 0, m = 1
(B)
m = 0, m = 2
(C)
m
2 , m 6 (D) 3
m
2 , m 1 3
6.
The number of real solution if x2 3 | x | 2 0 is :
7.
(A) 1 (B) 2 (C) 3 (D) 4 If the A.M. and G.M. between two numbers are in the ratio m : n, then the numbers are in the ratio : (A)
m n 2 m2 : m n 2 m2
(B)
m m2 n 2 : m m 2 n 2
(C)
m m2 n 2 : m m2 n 2
(D)
None of these
8.
If a, b, c are in G.P. where b c, c a, a b are in H.P. then the value of a b c is :
9.
3 ac (A) 0 (B) (C) (D) None of these 2ac The sum of all five digit numbers that can be formed using the digits 1, 2, 3, 4, 5, when repetition of digits is not allowed is : (A) 366000 (B) 660000 (C) 360000 (D) 3999960
10.
11.
The number of ways in which a team of eleven players can be selected from 22 players including 2 of them and excluding 4 of them is : 16 16 16 20 (A) C11 (B) C5 (C) C9 (D) C9 1 1 1 1 The value of if n is odd is : ... 1!(n 1)! 3!(n 3)! 5!(n 5)! n! (A)
VMC/ 2010
2n 1
(B)
2n 1 (n 1)!
(C)
11
2n 1 n!
(D)
None of these
I.P. PRACTICE TEST- 1
Vidyamandir Classes 12.
13.
The expression n3 3n2 5n 3, n N is divisible by (A) 3 (B) 4 (C) 5
(A)
a3 b3 c3 3abc
(B)
3abc a3 b3 c3
(C)
3abc a3 b3 c3
(B)
None of these
If 1, , 2 are the cube roots of unity, then 2 n
n (A) 15.
(B)
bn
(B)
an
(B)
n
2n
1
n
2n
1
2
1
3
e5 x e x is expanded in a series of ascending power of x and n is an odd natural number, then e3 x the coefficient of xn is :
2n n!
(B)
2n 1 (2n)!
1 0 0 If A 0 1 0 then A2 2 A equals : 0 0 1 (A) A (B) 2A
(C)
22 n (2n)!
(D)
None of these
(C)
3A
(D)
4A
(D)
2 e
A square matrix can always be expressed as a : (A) sum of diagonal matrix and a symmetric matrix (B) Difference of a symmetric and a skew symmetric matrix (C) sum of a symmetric and a skew symmetric matrix (D) None of these
19.
The value of lim
x 0
(A)
1
(1 x)1 / x e is equal to : x e (B) 2
(C)
The set of all point where the function f ( x) (A)
21.
(D)
a bx (a bx) (a bx) (a bx)n ... ... 1! 2! 3! n! (C) e a . bn (D) None of these 2
18.
20.
has the value:
If
(A)
17.
zero
The coefficient of x n in the series 1 (A)
16.
6
bc ab a The value of the determinant c a b c b is equal to : ab ca c
1
14.
(D)
,
(B)
x x x x Let f x cot 1 2 (A) (B) 1
VMC/ 2010
e 2
x , is differentiable is : 1 |x|
0, 0
(C)
, then f 1 equals to : 1 (C)
12
, 0 0,
log 2
(D)
(D)
0,
log 2
I.P. PRACTICE TEST- 1
Vidyamandir Classes
22.
1 x2 1 x2 If y tan 1 1 x 2 1 x 2 1
(A) 23.
25.
x
(C)
1 x4
x
(D)
1 x4
1 x4
Let f x e x x 1 x 2 dx . Then f decreases in the interval :
, 2
(B)
2 , 1
(C)
1,2
(D)
2,
The resistance R of a circuit having a battery with an e.m.f. E is given by the formula R E / I where I is the current in the circuit. If possible errors in E and I are 20% and 10% respectively, the percentage error in R is : (A) (B) (C) (D) None of these 5% 10% 15% dx is equal to : 2 4 x ( x 1)3 / 4
1 1 x 4
(A) 26.
1
(B)
1 x4
(A) 24.
dy , then equals : dx
If
1/ 4
1/ 4
c (B)
(x4 + 1)1/4 + c
(C)
1 1 x 4
1/ 4
1 (D) 1 4 x
c
c
4e x 6e x dx Ax B log (9e2 x 4) c then : 9e x 4e x
(A) (C)
3 35 ,B , c0 2 36 3 35 A ,B , cR 2 36
A
35 3 ,B , cR 36 2
(B)
A
(D)
None of these b
27.
For any functions f (x) and g (x), integrable over the interval (a, b)
f ( x) g ( x) dx
is :
a
b
(A)
a
(C)
28.
29.
f 2 x dx
b
b
g 2 x dx
(B)
b
a
a
f 2 x dx
a
a
b
2 2 f x dx g x dx
(D)
b
2 g x dx a
None of these
1m 2m 3m .... nm lim equal to : n nm 1 1 1 1 (A) (B) (C) (D) m m 1 m2 dy ( x 2 xy y 2 ) / x 2 is : The solution of the differential equation dx y x (A) (B) tan1 log x c tan1 log y c x y y x tan1 log y c (C) (D) tan1 log x c x y
VMC/ 2010
13
1 m3
I.P. PRACTICE TEST- 1
Vidyamandir Classes 30.
31. 32.
33.
The solution of the differential equation (1 y 2 ) dx ( x e tan tan1 x c
yetan
(C)
y tan1 x . etan
1 x
c
1 y
)dy 0 is :
tan1 y c
(B)
xetan
(C)
y xetan
1 x
c
If P(1,2), Q (4,6), R(5, 7) and S(a, b) are the vertices of a parallelogram PQRS, then : (A) a = 2, b = 4 (B) a = 3, b = 4 (C) a = 2, b = 3 (D) a = 3, b = 5 x y x y x y If 1 be any line through the intersection of 1 and 1 then : c d a b b a 1 1 1 1 1 1 1 1 1 1 1 1 (A) None of these (B) (C) (D) c d a b d a b c b d c a If 2 x 4 y 9 and 6 x 12 y 7 0 are common tangents to a circle, then radius of the circle is : 3 5
(A) 34.
1 x
(A)
1 y
17
(B)
2 3
(C)
6 5
(D)
17 3 5
The angle between the tangents from , to the circle x 2 y 2 a 2 is : a a s (B) None of these tan 1 2 tan 1 2 tan 1 1 (D) (C) s s a 1 1 If the normal at (ct, c/t) on the curve xy = c2 meets the curve again in t then : 1 1 1 1 (A) (B) (C) (D) t 3 t 2 t 2 2 t t t t t A rectangular hyperbola whose centre is C is cut by any circle of radius r, in four points P, Q, R
(A) 35.
36.
and S. Then CP2 CQ2 CR 2 CS 2 is equal to : (A) r2 (B) 2r2 (C) 37.
3 1
/3
0
6
(C)
(D)
None of these
(B)
/4
(C)
/6
(D)
None of these
2 abc
(B)
(C)
3 a b c
(D)
None of these
If b and c are any two perpendicular unit vectors and a is any vector, then
a . b b a . c c (A) 41.
2 1
(B)
The value of a b . b c c a is : (A)
40.
4r2
The smallest angle of triangle whose side are 6 12, 48, 24 is : (A)
39.
(D)
In a triangle ABC, a = 2, b 1 3 , C 60 then the side c is equal to : (A)
38.
3r2
b
a . b c |b c |
2
(B)
b c a
equal to :
(C)
c
(D)
None of these
The centre of the circle given by r i 2 j 2k 15 and |r j 2k | 4 is equal to : (A)
VMC/ 2010
(0, 1, 2, 3)
(B)
(1, 3, 4)
(C)
14
(1, 3,4)
(D)
None of these
I.P. PRACTICE TEST- 1
Vidyamandir Classes 42.
The plane through the point (1, 2, 1 ) and perpendicular to the line of intersection of the planes
r . i 4 j 2k 2 and r . 3i j k 1 is equal to :
(A) (C)
r . 2i 7 j 13k 1 r . 2i 7 j 13k 0
(B) (D)
r . 2i 7 j 13k 0
r . 2i 7 j 13k 1 0
43.
Let f (x) be a polynomial. Then if f ( x1 ) f ( x2 ) 0 , f (x) = 0 has : (A) atleast one or an odd number of roots in (x1, x2) (B) any number of roots in (x1, x2) (C) no roots or an even number of roots in (x1, x2) (D) None of these
44.
The maximum number of real roots of the equation x 2n 1 0 (A) 2 (B) 3 (C) n
45.
(D)
2n
The maximum and minimum values of z 5x 2 y , subject to the constraints 2 x 3 y 6 ; x 2 y 2 ; 6 x 4 y 24 ; 3x 2 y 3 ; x, y 0 are respectively : 18 2 63 (B) (C) 19, 63 (D) 19, 13 , 19, 7 7 13 By graphical methods, the solution of linear programming problem (L.P.P.) Maximize subject to : z 3x1 5x2 , 3x1 2 x2 18 , x1 4 , x2 6 , x1 0 , x2 0 is : (A) x1 = 2, x2 = 0, z = 6 (B) x1 = 2, x2 = 6, z = 36 (C) x1 = 4, x2 = 3, z = 27 (D) x1 = 4, x2 = 6, z = 42
(A) 46.
47.
What is the standard deviation of the following series (A) 81 (B) 7.6 (C) 9 (D) 2.26
48.
A sample of 35 observations has the mean 80 and S.D as 4. A second sample of 65 observations from the same population has mean 70 and S.D. 3. Then the S.D. of the combined sample is : (A) 5.85 (B) 5.58 (C) 34.2 (D) None of these A single letter is selected at random from the word “PROBABILITY”. The probability that it is a vowel is : 3 4 2 (A) (B) (C) (D) 0 11 11 11 Four persons are selected at random from a group of 3 men, 2 women and 4 children. What is the chance that exactly two of them are children ? (A) 9 / 21 (B) 10 / 23 (C) 11 / 24 (D) 10 / 21
49.
50.
VMC/ 2010
15
I.P. PRACTICE TEST- 1
Vidyamandir Classes ANSWERS FOR I.P. PRACTICE TEST – 1 PHYSICS 1 D 11 C 21 C 31 B 41 B
2 B 12 B 22 B 32 A 42 D
3 C 13 A 23 A 33 A 43 A
4 A 14 B 24 B 34 A 44 A
5 B 15 C 25 B 35 C 45 A
6 C 16 B 26 B 36 C 46 C
7 A 17 D 27 B 37 A 47 C
8 A 18 A 28 C 38 B 48 D
9 B 19 C 29 A 39 C 49 D
10 B 20 C 30 D 40 A 50 A
CHEMISTRY 1 A 11 D 21 A 31 C 41 A
2 A 12 C 22 B 32 B 42 D
3 A 13 A 23 D 33 C 43 C
4 D 14 A 24 A 34 B 44 A
5 A 15 A 25 C 35 D 45 C
6 B 16 D 26 B 36 D 46 B
7 B 17 D 27 D 37 C 47 A
8 D 18 C 28 B 38 B 48 C
9 A 19 B 29 A 39 B 49 D
10 C 20 C 30 B 40 B 50 C
MATHEMATICS 1 2 A A 11 12 C A 21 22 A D 31 32 C B 41 42 B B
3 C 13 B 23 C 33 B 43 A
4 C 14 D 24 B 34 B 44 A
5 C 15 D 25 D 35 A 45 B
6 D 16 D 26 C 36 D 46 B
7 C 17 C 27 C 37 C 47 C
8 C 18 C 28 A 38 C 48 A
9 D 19 C 29 B 39 A 49 B
10 C 20 A 30 B 40 B 50 D
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I.P. PRACTICE TEST- 1
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