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JEE Main Mock Test 01
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Total Question : 90
Negative Marks : N/A
Passing Marks : 0/360 Time Alloted : 180 Minute
PHYSICS Q.1
The respective number of significant figures for the numbers 23.023, 0.0003 and 21 x 10-3 are (a) 5, 1, 2 (b) 5, 1, 5 (c) 5, 5, 2 (d) 4, 4, 2
Q.2
The dimensions of magnetic field in M, L, T and C (coulomb) is given as (a) [MLT-1C-1] (c)
Q.3
Q.5
(d) [MT2C-1]
A small particle of mass m is projected at an angle θ with the x-axis with an intial velocity v0 in the x-y plane as shown in the figure. At a time t <
Q.4
(b) [MT2C-2]
[MT-1C-1]
v0 sinθ g
, the angular momentum of the particles is
(a) −mgv 0 t 2 cosθ^ j
^ (b) mgv 0 tcosθk
^ (c) − 12 mgv 0 t 2 cosθk
(d)
1 2
2 ^ mgv 0 t cosθ i
A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out a lengths s = t3 + 5, where s is in metre and t is in second. The radius of the path is 20 m. The acceleration of P when t = 2 s is nearly
(a) 13 ms-2
(b) 12 ms-2
(c) 7.2 ms-2
(d) 14 ms-2
Consider a rubber ball freely falling from a height h= 4.9 m onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time the height as function of time will be
Q.6
(a)
(b)
(c)
(d)
The minimum force required to start pushing a body up a rough (frictional coefficient μ) inclined plane is F1 while the minimum force needed to prevent it from sliding down is F2. If the inclined plane makes an angle θ from the horizontal such that tanθ= 2μ, then the ratio
Q.7
F1 F2
is
(a) 4
(b) 1
(c) 2
(d) 3
The figure shows the position-time (x-t) graph of one-dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is
(a) 0.4 Ns (c) 1.6 Ns
Q.8
Q.9
Two fixed frictionless inclined plane making an angle 300 nd 600 with the vertical are shown in the figure. Two block A and B are placed on the two planes. What is the relaive vertical acceleration of A with respect to B?
(a) 4.9 ms-2 in horizontal direction
(b) 9.8 ms-2 in vertical direction
(c) Zero
(d) 4.9 ms-2 in vertical direction
At time t = 0 s particle starts moving along the x-axis. If its kinetic energy increases uniformly with time t, the net force acting on it most be proportional to (b) Constant (a) √t (c) t
Q.10
(b) 0.8 Ns (d) 0.2 Ns
(d)
1 √t
Statement I when ultraviolet light is incident on a photocell, its stopping potential is V0 and the maximum kinetic energy of the photoelectrons is Kmax. When the ultraviolet light is replaced by X-rays, both V0 and Kmax increase. Statement II Photoelectrons are emitted with speeds ranging from Zero to a maximum value because of the range of frequencies present in the incident light. (a) Statement I is true, Statement II is true; Statement II is the correct (b) Statement I is true, Statement II is true; Statement II explanation of Statement I. is not the correct explanation of Statement I.
(c) Statement I is false, Statement II is true.
Q.11
(d) Statement I is the true, Statement II is false.
An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range (a) 200 J - 500 J (b) 2 x 105 J - 3 x 105 J (c) 20000 J - 50000 J
(d) 2000 J - 5000 J
Q.12
A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc (a) Continuously decreases (b) Continuously increases (c) First increases and then decreases (d) Remains unchanged
Q.13
A pulley of radius 2 m is rotated about its axis by a force F = (20 t = 5t2)N ( where t is measured in seconds) applied tangentially. It the moment of intertia of the pulley about its axis of rotation is 10 kg-m2 the number of rotations made by the pulley before its direction of motion if reserved, is (a) More than 3 but less than 6 (b) More than 6 but less than 9 (c) More than 9
Q.14
The height at which the acceleration due to gravity becomes in terms of R, the radius of the earth is
(d) Less than 3
g 9
(where g = the acceleration due to gravity on the surface of the earth) (b)
(a) 2R (c)
Q.15
Q.16
–
R
(d) √2R
2
A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 kms-1, the escape velocity from the surface of the planet would be (a) 1.1 km s-1
(b) 11 km s-1
(c) 110 km s-1
(d) 0.11 km s-1
If gE and gM are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan oil drop experiment could be performed on the two surfaces, one will find the ratio (a) 1 (c)
Q.18
to be
electronic charge on the earth
(d)
E
g
g
M
g
E
Two mercury drops (each of radius r) merge to form a bigger drop. The surface energy of the bigger drop, If T is the surface tension, is (a) 25/3 πr2T
(b) 4πr2T
(c) 2πr2T
(d) 28/3πr2T
If a ball of steel (density ρ = 7.8 g cm-3) attains a terminal velocity of 10 cm-1 when falling in a tank of water (coefficient of viscosity ηwater = 8.5 x 10-4 Pa -s) then its terminal velocity in glycerine (ρ = 12 g cm-3 , η = 13.2 Pa -s) would be nearly (a) 1.6 x 10-5 cms-1 (c) 6.45 x
Q.19
electronic charge on the moon
(b) Zero
g
M
Q.17
R √3
10-4 cms-1
(b) 6.25 x 10-4 cms-1 (d) 1.5 x 10-5 cms-1
3
The specific heat capacity of a metal at low temperature (T) is given as Cp(kJK-1 kg-1) = 32( 400 ). A 100 g vessel of this metal is to T
be cooled from 20 K to 4 K by a special refrigerator operating at room temperature (270C). The amount of work required to cool the vessel is
(a) Equal to 0.002 kJ (c) Between 0.148 kJ and 0.028 kJ
Q.20
A container with insulating walls is divided into two equal parts by a partition fitted with a valve. One part is filled with an ideal gas at a pressure p and temperature T, whereas the other part is completely evacuated. If the valve is suddenly opened, the pressure and temperature of the gas will be p
p
(a) , T 2
(b) ,
T
(d) p ,
T
2
(c) p, T
Q.21
(b) Greater than 0.148 kJ (d) Less than 0.028 kJ
2
2
Three perfect gases at absolute temperatures T1, T2 and T3 are mixed. The masses of molecules are m1, m2 and m3 and the number of molecules are n1, n2 and n3 respectively . Assuming no loss of energy, the final temperature of the mixture is (a)
(b)
n 1+n 2+n 3 2
(c)
2
n 1T1 +n 2T2 +n 3T3
2
2
2
2
2
n T1 +n T2 +n T3 1
2
3
n 1T1 +n 2T2 +n 3T3
(d)
2
2
n 1T1 +n 2T2 +n 3T3 n 1T1 +n 2T2 +n 3T3 (T1 +T2 +T3 ) 3
Q.22
Statement I Two longitudinal waves given by equations -y1 (x,t) = 2a sin(ω - kx) and y2(x,t) = asin(2ωt - 2kx) will have equal intensity. Statement II Intensity of waves of given frequency in same medium is proportional to square of amplitude only. (a) Statement I is false, Statement II is true (b) Statement I is true, Statement II is false (c) Statement I is true, Statement II true; Statement II is the correct (d) Statement I is true, Statement II is true; Statement II explanation of Statement I is not correct explanation of Statement I
Q.23
^ ^ An electric charge +q moves with velocity v ⃗ = 3^ i + 4j + k ,in an electromagnetic field given by The y component of the source experienced by +q is (a) 2q (b) 11q (c) 5q (d) 3q
Q.24
If 400Ω of resistance is made by adding four Ω resistance of tolerance 5% , then the tolerance of the combination is (a) 20% (b) 5% (c) 10% (d) 15%
Q.25
A thin rectangular magnet suspended freely has a period of oscillation equal to T. Now, it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. It its period of oscillation is T', the ration T'/T is 1
(a)
2√2
(c) 2
(b)
1
(d)
1
⃗ E
=
^ ^ ^ ⃗ 3 i + j + 2k B
,
=
^ ^ ^ i + j − 3k
.
2
4
Q.26
In a transformer, number of turns in the primary are 140 and that in the secondary are 280. If current in primary is 4A, then that in the secondary is (a) 04:00 am (b) 02:00 am (c) 06:00 am (d) 10:00 am
Q.27
A radiation of energy E falls normally on a perfectly reflecting surface. The momentum transferred to the surface is (a)
E c
(c) Ec
Q.28
(b)
2E
(d)
E
c
c
2
A youngs double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen is
(a) Hyperbola (c) Straight line
(b) Circle (d) Parabola
Q.29
Sodium and copper have work functions 2.3 eV and 4.5 eV respectively. Then the ratio of the wavelengths is nearest to (a) 1:2 (b) 4:1 (c) 2:1 (d) 1:4
Q.30
After absorbing a slowly moving neutron of mass mN (momentum ∼ 0) a nucleus of mass M breaks into two nuclei of masses m1 and 5m1(6m1 = M + mN), respectively. If the de-Broglie wavelength of the nucleus with mass m1 is λ, then de-broglie wavelength of the other nucleus will be (a) 25λ (b) 5λ (c)
λ
(d) λ
5
CHEMISTRY Q.31
The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1:4. The ratio of number of their molecule is (a) 1:4 (b) 7:32 (c) 1:8 (d) 3:16
Q.32
The molarity of a solution obtained by mixing 750 mL of 0.5 M HCl with 250mL of 2M HCl will be (a) 0.875 M (b) 1.00 M (c) 1.75 M (d) 0.0975 M
Q.33
Which of the following exists as covalent crystal in the solid state? (a) Iodine
(b) Silicon
(c) Sulphur
(d) Phosphorous
Q.34
Q.35
Q.36
Experimentally, it was found that a metal oxide has formula M0.98O. Metal M, present as M2+ and M2+ in its oxide. Fraction of the metal which exists as M3+ would be (a) 7.01%
(b) 4.08%
(c) 6.05%
(d) 5.08%
The correct set of four quantum numbers for the valence electrons of rubidium atom [Z=37] is (a) 5,0,0, +
1
(c) 5,1,1, +
1
(b) 5,1,0, +
2
2 1
(d) 5,0,1, + 2
2
Energy of an electron is given by E =
1
−2.178 × 10
−18
J (
Z
2
. Wavelength of light required to excite an electron in an hydrogen )
n
2
atom from level n=1 to n=2 will be (h = 6.62 × 10-34Js and c = 3.0 × 108 ms-1 )
Q.37
(a) 1.214 × 10-7 m
(b) 2.816 × 10-7 m
(c) 6.500 × 10-7 m
(d) 8.500 × 10-7 m
The correct statement for the molecule CsI3 is (a) It is a covalent molecule
(b) It contains Cs+ and I3−
(c) It contains Cs3+ and I- ions
(d) It contains Cs+, I- and lattice I2 molecule
Q.38
For which of the following molecule significant μ = 0?
(i)
(ii)
(iii)
(iv) (a) Only (i) (c) Only (iii)
Q.39
(b) (i) and (ii) (d) (iii) and (iv)
For the complete combustion of ethanol, C2H5OH(l) + 3O2(g) → 2CO2 (g) + 3H2O (l) the amount of heat produced as measured in bomb calorimeter is 1364.47 kJ mol-1 at 250C. Assuming ideality, the ehthalpy of combustion, ΔCH for the reaction will be (a) -1366.95 kJ mol-1
(b) -1361.95 kJ mol-1
(c) -1460.50 kJ mol-1
(d) -1350.50 kJ mol-1
Q.40
Consider the separate solution of 0.500 M C2H5 (aq), 0.100 M Mg3(PO4)2 (aq), 0.250 M KBr (aq) and 0.125 M Na3PO4 (aq) at 250C. What statement is true about these solutions, assuming all salts to be strong electrolytes. (b) 0.100 M Mg3(PO4)2 (aq) has the highest osmotic (a) They all have same osmotic pressure pressure (d) 0.5000 M C2H5OH (aq) has the highest osmotic (c) 0.125 M Na3PO4(aq) has the highest osmotic pressure pressure
Q.41
Kf for water is 1,86 K kg mol-1. If your automobile radiator holds 1.0 kg of water, then how many grams of ethylene glycol (C2H6O2) must you add to get the freezing point of the solution lowered to -2.80 C ? (a) 72 g (c) 39 g
Q.42
For the reaction SO2 (g) + 1 O2 2
If Kp = KC (a) -1 (c)
1 2
(b) 93 g (d) 27 g
SO3(g),
(g) ⇌
(RT)x where
the symbols have usual meanings the, the value of x is (assuming ideality). 1
(b) − 2 (d) 1
Q.43
How many litres of water must be added to 1 L of an aqueous solution of HCl with a pH of 1 to create an aqueous solution with pH of 2? (a) 0.1 L (b) 0.9 L (c) 2.0 L
Q.44
Q.45
(d) 9.0 L
Resistance of 0.2M solutions of an electrolyte in 50Ω . The specific conductance of the solution is 1.4 Sm-. The resistance of 0.5M solution of the same electrolyte is 280Ω . The molar conductivity of 0.5 M solution of the electrolyte in S mol-1 is (a) 5 x 10-4
(b) 5 x 10-3
(c) 5 x 103
(d) 5 x 102
The equivalent consuctance of NaCl at concentration C and at infinite dilution are λc and λ∞, respectively . The correct relationship between λc and λ∞ is given as (a) λc = λ∞ + (B)C (c) λc = λ∞
Q.46
Q.47
(b) λc = λ∞ - (B)C
− − − (B) √C
− −
(d) λc = λ∞ + (B) √C
The rate of a reaction double when its temperature changes from 300K to 310 K. Activation energy of such a reaction will be (R = 8.314 JK-1 mol-1 and log 2 = 0.301) (a) 53.6 kJ mol-1
(b) 58.6 kJ mol-1
(c) 58.5 kJ mol-1
(d) 60.5kJ mol-1
Which of the following represents the correct order of increasing first ionization enthalpy for Ca, Ba, S, Se and Ar? (a) Ca < S < Ba < Se < Ar (b) S < Se < Ca < Ba < Ar (c) Ba < Ca < Se < S < Ar
Q.48
(d) Ca < Ba < S < Se < Ar
The first ionisation potential of Na is 5.1 ev. The value of electron gain enthalpy of Na+ will be (a) -2.55 eV (b) -5.1 eV (c) -10.2 eV
Q.49
Which series of reactions correctly represent chemical relations related to iron and its compound? (a) F e (c) F e
Q.50
Q.51
Q.52
(d) +2.55 eV
Dil.H2 SO4
→
H2 SO4 .O2
F eSO4
H eat,air
Cl2 .heat
→
→
F eC l 3
→
H eat
F e2 (SO4 ) 3
→ Fe
Zn
F eC l 2 → F e
(b) F e (d) F e
O2 ,heat
→
dil.H2 SO4
F eO
H eat
F eSO4 0
F e3 O4
→
→ Fe 0
CO,600 C
O2 .heat
→
→
CO,700 C
F eO
→
Fe
Among the following oxoacids, the correct decreasing order of acid strength is (a) HOCL > HClO2 > HClO3 > HClO4 (b) HClO4 > HOCl > HClO2 > HClO3 (c) HClO4 > HClO3 > GClO2 > HOCl
(d) HClO2 > HClO4 > HClO3 > HOCl
Which one of the following properties is not shown by NO? (a) It is diagmagnetic in gaseous state (c) It combines with oxygen to form nitrogen dioxide
(b) It is neutral oxide (d) Its bond order is 2.5
The octahedral complex of a metal ion M3+ with four monodentate ligands L1, L2, L3 and L4 absorb wavelengths in the region of red, green, yellow and blue, respectively. The increasing order of ligands strength of the four ligands is (a) L 4 < L 3 < L 2 < L 1 (b) L 1 < L 3 < L 2 < L 4 (c) L 3 < L 2 < L 4 < L 1
(d) L 1 < L 2 < L 4 < L 3
Q.53
The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was (a) Methylisocyanate (b) Methylamine (c) Ammonia
Q.54
Q.55
(d) Phosgene
The order of stability of the following carbocations
(a) III > II > I
(b) II > III > I
(c) I > II > III
(d) III > I > II
The major organic compound formed by the reaction of 1,1.1-trichloroethane with silver powder is (a) acetylene (b) ethene (c) 2-butyne
Q.56
(d) 2-butene
Sodium phenoxide when heated with CO2 under pressure at 1250C yields a product which on acetylation produces C.
The major product C would be
(a)
(b)
(c)
Q.57
(d)
On heating an aliphiatic primary amine with chloroform and ethanolic potassium hydroxide , the organic compound formed is (a) An alkanol (b) An alkanediol (c) A alkyl cyanide
Q.58
Q.59
Q.60
(d) An alkyl isocyanide
Considering the basic strength of amines in aqueous solution , which one has the smallest pKb value? (a) (CH3)2NH
(b) CH3NH2
(c) (CH3)3N
(d) C6H5NH2
Which one is classified as a condensation polymer? (a) Dacron
(b) Neoprene
(c) Teflon
(d) Acrylonitrile
For the estimation of nitrogen , 1.4 g of an organic compound was digested by kjeldahls method and the evolved ammonia was M
M
absorbed in 6 mL of M sulphuric acid .The unreacted acid required 20 mL of M sodium hydroxide for the complete neutralization 10 10 .The percentage of nitrogen in the compound is (a) 6% (b) 10% (c) 3%
(d) 5%
MATHEMATICS Q.61
Let R be the set of real numbers. Statement I A = {(x,y) ε R x R : y - x is an integer} is an equivalent relation on R. Statement II B = {(x,y) ε R x R : x = αy for some rational number α } is an equivalence relation on R. (a) Statement I is true, Statement II is true ; Statement II is not a correct (b) Statement I is true, Statement II is false explantion for Statement I. (d) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
(c) Statement I is false, Statement II is true.
Q.62
Q.63
The domain of the function f(x) = f rac1sqrt|x| −isx (a) (o,∞)
(b) (-∞,0)
(c) (-∞,∞)-(0)
(d) (-∞,∞)
Let α, β be real and z be a complex number. If z2 + az + β = 0 has two distinct roots on the line Re z = 1, then it is necessary that (a) β ∈ (-1,0) (b) |β| = 1 (c) β ∈ (1,∞)
(d) β ∈ (0,1)
Q.64
If ω (≠ 1) is a cube root of unity and (1 + ω)7 = A + Bω . Then , (A,B) equals to (a) (1,1) (b) (1,0) (c) (-1,1) (d) (0,1)
Q.65
The number of values of k for which the linear equations 4x + ky + z = 0, kx + 4y + z = 0 and 2x + 2y + z = 0 posses a non-zero solution is (a) 2 (b) 1 (c) zero
Q.66
Q.67
If ω ≠ 1 is the complex cube root of unity and matrix H - [
(d) 3
ω
0
0
ω
, then H70 is equal to
]
(a) H
(b) 0
(c) -H
(d) H2
There are 10 points in a plane. Out of these 6 are collinear. If N is the number of triangles formed by joining these points, then (a) n > 190 (b) N ≤ 100 (c) 100 < N ≤ 140
(d) 140 < N ≤ 190
Q.68
Let s(k) = 1 + 3 + 5 + ...... + (2k - 1) = 3 + k2. Then which of the following is true? (b) s(k) ⇒ S(k+1) (a) S(1) is correct (d) Principle of mathematical induction can be used to (c) S(k) ⇒ S(k+1) prove the formula.
Q.69
A man saves Rs. 200 in each of the first three months of his service. In each of the subsquent months his saving increases by Rs. 40 more than the saving of immediately previous month . His total saving from the start of service will be Rs. 11040 after (a) 19 months (b) 20 months
(c) 21 months
Q.70
(d) 18 months
100
Let an be the nth term of an AP. If ∑r=1 (a)
α−β
(c)
α−β
100
a
a2r = α and ∑2r-1 r=1
(b) α − β
200
(d) β - α
100
Q.71
√1−{cos2(x−2)}
lim x→2 (
)
x−2
–
–
(a) Equals √2
(b) Equals −√2
1
(c) Equals
(d) Does not exist
√2
Q.72
= β , then the common difference of the AP is
The values of p and q for which the function ⎧ ⎪ ⎪ ⎪
sin(p+1)x+sinx
x < 0
x
f(x) = ⎨
q
⎪ ⎪ ⎩ ⎪
x = 0
√x+x2 −√x
x > 0
x3/2
is continuous for all x in R, are
Q.73
Q.74
(a) p = 52 , q =
1
(c) p = 12 , q =
3
For ∈ (0,
5π 2
3
(b) p = − 2, q =
2
(d) p = 12 , q = -
2
x
m define f(x) = ∫0
)
.
(b) Local minimum at π and local maximum at 2π
(c) Local maximum at π and local minimum at 2π
(d) Local maximum at π and 2π
1
The value of ∫0 π
8log(1+x) 2
1+x
is
dx
(b)
log2
8
The area of the region enclosed by the curves y = x , x = e, y = (a) 1 sq unit (c)
5 2
sq. unit
The area bounded by the curve y2 = 4x and x2 = 4y is (a) 0 (c)
Q.77
2
√t sintdt
(c) log 2
Q.76
2 3
then, f has (a) Local minimum at π and 2π
(a)
Q.75
1
If
16 3
dy dx
π
log2
2
(d) π log 2
1 x
and the positive x - axis is (b)
3
(d)
1
(b)
32
(d)
8
2
2
sq. unit sq. unit
3
3
= y + 3 > 0 and y(0) = 2, then y (log 2) is equal to
(a) 5
(b) 13
(c) -2
(d) 7
Q.78
Let I be the purchase value of an equipment and v(t) be the value after it has been used for t years . The value V(t) depreciates at a rate given by differential equation
dV (t) dt
= -k(T -t), where k > 0 is a constant and T is the total life in years of the equipment . Then ,
the scrap value V(T) of the equipment is (a) I −
kT
2
(b) I −
2
(c) e-kT
Q.79
(d) T 2
k(T −t)
2
2 1
−
k
The line L1 : y - x = 0 and L2 : 2x + y = 0intersect the line L3 : y + 2 = 0 at P and Q respectively. The bisector of the acute angle between L1 and L2 intersects L3 at R. –
–
Statement I The ratio PR ; RQ equals 2√2 : √5 Statement II In any triangle, bisector of an angle divides the triangle into two similar triangles. (a) Statement I is true, Statement II is true; Statement II is not a correct (b) Statement I is true, Statement II is false. explanation for Statement I. (d) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
(c) Statement I is false, Statement II is true.
Q.80
Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (-3,1) and has eccentricity
− − √
2 5
is
Q.81
Q.82
Q.83
(a) 5x2 + 3y2 - 48 = 0
(b) 3x2 + 5y2 - 15 = 0
(c) 5x2 + 3y22 - 32 = 0
(d) 3x2 + 5y22 + 5y2 - 32 = 0
The two circles x2 + y2 = ax and x2 + y2 = c2 (c > 0) touch each other if (a) |a| = c (c) |a| = 2c
(b) a = 2c (d) 2|a| = c
If the angle between the line x = (a)
3
(c)
5
y−1
z−3
2
3
=
and the plane x+2y+3z= 4 is cos−1
2
3
–
(d)
2
5
3
–
–
⃗ If a=
1 10
(d)
^ ^ (3 i + k)
⃗ and b=
(a) -3 (c) 3
Q.86
2
then λ equals to )
(b) 10√3
(c) 5√3
Q.85
(b)
5
14
The distance of the point (1, -5, 9) from the plane x - y + z = 5 measured along a straight line x = y = z is (a) 3√5
Q.84
−− (√
1 7
− − 3√10
^ ^ ^ (2 i + 3k − 6k)
⃗ ⃗ ⃗ then the value of (2a⃗ − b) isb)] ⋅ [(a⃗ × b ) × (a⃗ + 2
(b) 5 (d) -5
The vactor a⃗ and b ⃗ are not perpendicular and c ⃗ and d ⃗ are two vectors satisfying equal to (a) c ⃗ + (
a⃗ ⋅c ⃗
(c) c ⃗ − (
a⃗ ⋅c ⃗
⃗ a ⃗ ⋅b
⃗ a ⃗ ⋅b
)b
)b
⃗
⃗
⃗ ⃗ ⃗ b × c ⃗ b × d
(b) b ⃗ + ( (d) b ⃗ − (
and a⃗ × d =⃗ 0. Then the vectors
=
⃗ b ⋅c ⃗ ⃗ a⃗ ⋅b ⃗ b ⋅c ⃗ ⃗ a⃗ ⋅b
) c ⃗
) c ⃗
If C and D are two events such that the C ⊂ D and P(D) ≠ 0, then the correct statement among the following is (a) P(C|D) ≥ P(C) (b) P(C|D) < P(C) P (D)
d
⃗
is
Q.87
(d) P(C|D) = P(C)
P (D)
(c) P(C|D) =
P (C)
If the mean deviations about the median of the number a, 2a, .......5a is 50, than |a| equals to (a) 3 (b) 4 (c) 5
Q.88
Q.89
Q.90
(d) 2
If A =sin2x + cos4x , then for all real x (a)
13
(c)
3 4
(b) 1 ≤ A ≤ 2
≤ A ≤ 1
6
≤ A ≤
13 6
(d)
3
(b)
π
(d)
2π
4
≤ A ≤ 1
The possible values of θ ∈ (0,π) such that sin(θ) + sin(4θ) + sin(7θ) = 0 are (a)
2π
(c)
2π
9
9
, ,
π 4 π 4
, ,
4π 9 π 2
,
,
π 2
2π 2
, ,
3π 4 3π 4
, ,
8π 9 35π 36
4
9
,
5π 12
,
π 4
, ,
π 2 π 2
, ,
2π 3 2π 3
, ,
3π 4 3π 4
, ,
8π 9 8π 9
Consider the following statements P : Suman is brilliant. Q : Suman is rich. R : Suman is honest. The negative of the statement. Suman is brilliant and dishonest if and only if Suman is rich can be expressed as (a) ∼ (Q ↔ (O P ∼ R) (b) ∼ Q ↔ P ^ R (c) ∼ (P ^ ∼ R) ↔ Q
(d) ∼ P ^ (Q ↔ ∼ R)
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