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Find magnetic field at O.
Position of particle as a function of time is given as . Choose correct statement about and whereare velocity and acceleration of particle at time t.
= ω (–sinωt cosωt + cosωt sinωt) = 0
so
A Carnot engine, having an efficiency of η = 1/10 as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is
For Carnot engine using as refrigerator
It is given η = 1/10
⇒
⇒
So, Q_{2} = 90 J (as W = 10 J)
Two uniformly charged solid spheres are such that E_{1 }is electric field at surface of 1st sphere due to itself. E_{2} is electric field at surface of 2^{nd} sphere due to itself. r_{1}, r_{2} are radius of 1^{st} and 2^{nd} sphere respectively. If then ratio of potential at the surface of spheres 1^{st} and 2^{nd} due to their self charges is:
Output at terminal Y of given logic circuit.
Velocity of a wave in a wire is v when tension in it is 2.06 × 10^{4} N. Find value of tension in wire when velocity of wave become v/2
= 0.515 × 10^{4} N
n mole of He and 2n mole of O_{2} is mixed in a container. Then will be
A uniform solid sphere of radius R has a cavity of radius 1m cut from it if centre of mass of the system lies at the periphery of the cavity then
_{
}
Alternative:
A solid sphere of mass m= 500gm is rolling without slipping on a horizontal surface. Find kinetic energy of a sphere if velocity of centre of mass is 5 cm/sec.
K.E. of the sphere = Translational K.E + Rotational K.E.
K = Radius of gyration
Two liquid columns of same height 5m and densities ρ and 2ρ are filled in a container of uniform cross sectional area. Then ratio of force exerted by the liquid on upper half of the wall to lower half of the wall is.
Two square plates of side 'a' are arranged as shown in the figure. The minimum separation between plates is 'd' and one of the plate is inclined at small angle α with plane parallel to another plate. The capacitance of capacitor is (given α is very small)
In YDSE path difference at a point on screen is λ/8. Find ratio of intensity at this point with maximum
intensity.
In the given circuit switch is closed at t = 0. The charge flown in time t = T_{C} (where T_{C} is time constant).
A particle is dropped from height h = 100 m, from surface of a planet. If in last 1/2 sec of its journey it covers 19 m. Then value of acceleration due to gravity that planet is :
Area of shaded trapezium
........(i)
......... (ii)
g = 8 m/s^{2}
A charge particle of mass m and charge q is released from rest in uniform electric field. Its graph between velocity (v) and distance travelled (x) will be :
An object is moving away from concave mirror of focal length f starting from focus. The distance of an object from pole of mirror is x. The correct graph of magnitude of magnification(m) verses distance x is:
At focus, magnification is ∞
In full scale deflection current in galvanometer of 100 Ω resistance is 1 mA. Resistance required in series to convert it into voltmeter of range 10 V.
There are two identical particles A and B. One is projected vertically upward with speed √2gh from ground and other is dropped from height h along the same vertical line. Collision between them is perfectly inelastic. Find time taken by them to reach the ground after collision in terms of .
time for collision
After t_{1}
and
at the time of collision
and height from ground
so time
Length of a simple pendulum is 25.0 cm and time of 40 oscillation is 50 sec. If resolution of stop watch is 1 sec then accuracy is g is (in %)
An electron is moving initially with velocityin uniform electric field . If initial wavelength of electron is λ_{0} and mass of electron is m. Find wavelength of electron as a function of time.
Initially m
Velocity as a function of time =
so wavelength
An asteroid of mass m (m << m_{E}) is approaching with a velocity 12 km/s when it is at distance of 10 R from the centre of earth (where R is radius of earth). When it reaches at the surface of Earth, its velocity is (Nearest Integer) in km/s.
= 16.028 km/s
In H–spectrum wavelength of 1^{st} line of Balmer series is λ = 6561Å. Find out wavelength of 2^{nd} line of same series in nm.
= 4860 Å = 486 nm
There are three containers C_{1}, C_{2} and C_{3} filled with same material at different constant temperature. When we mix then for different volume then we get some final temperature as shown in the below table. So find value of final temperature θ as shown in the table.
............(i)
.......(ii)
.........(iii)
and θ_{1} + θ_{2} + θ_{3} = (1 + 1 + 1)θ....(iv)
from (1) + (2) + (3)
3θ_{1} + 3θ_{2} + 3θ_{3} = 450
⇒ θ_{1} + θ_{2} + θ_{3} = 150
from (4) equation 150 = 3θ
θ = 50ºC
Two batteries (connected in series) of same emf 10 V of internal resistances 20Ω and 5Ω are connected to a load resistance of 30Ω. Now an unknown resistance x is connected in parallel to the load resistance. Find value of x so that potential drop of battery having internal resistance 20Ω becomes zero.
An EMW is travelling along zaxis.
& Frequency of wave is 25 Hz, then electric field in volt/m.
E/B = c
E = B × c
= 15 N/c
Correct bond energy order of following is
Determine Bohr's radius of Li^{2+} ion for n = 2. Given (Bohr's radius of Hatom = a_{0})
For Li^{2+}
Given the following reaction sequence
A & B are respectively
Correct order of magnetic moment (spin only) for the following complexes
(a) [Pd(PPh_{3})_{2}Cl_{2}]
(b) [Ni(CO)_{4}]
(c) [Ni(CN)_{4}]^{2– }
(d)[Ni(H_{2}O)_{6}]^{2+}
Determine total number of neutrons in three isotopes of hydrogen.
Number of neutrons
Compare E_{a} (activation energy) for a, b, c and d.
log k = log A –
slope
⇒ E_{b} > E_{c} > E_{d} > E_{a }
Which of the following exhibit both Frenkel & Schottky defect?
Only AgBr can exhibit both Schottky and Frenkel defect.
Given:
Basicity of B is:
Basicity = 1
Which reaction does not occurs in the blast furnace in the metallurgy of Fe
(A) CaO + SiO_{2} → CaSiO_{3}
(B) Fe_{2}O_{3} + CO → Fe_{3}O_{4} + CO_{2}
(C) FeO + SiO_{2} → FeSiO_{3}
(D)
Theory based
Correct order of radius of elements is:
C, O, F, Cl, Br
Amongs the following which will show geometrical isomerism.
(a) [Ni(NH_{3})_{5}Cl]^{+}
(b) [Ni(NH_{3})_{4}ClBr]
(c) [Ni(NH_{3})_{3}Cl]^{+}
(d) [Ni(NH_{3})_{2}(NO_{2})_{2}]
Ma_{4}bc can show 2 G.I.
Ma_{2}b_{2} can show 2 G.I.
(Square planar)
Assertion: pH of water increases on increasing temperature.
Reason: H_{2}O → H^{+} + OH^{–} is an exothermic process.
Assertion: It has been found that for hydrogenation reaction the catalytic activity increases from group5 to group11 metals with maximum activity being shown by groups 79 elements of the periodic table.
Reason: For 79 group elements adsorption rate is maximum.
The major product of the following reactions is
(Aromatic)
Find the final major product of the following reactions
On prototaoon, OH dispatches as H_{2}O making a carbocation. The H+ will shift to 3° carbon for a more stable carbocation and then elimination will occur to form.
There are two compounds A and B of molecular formula C_{9}H_{18}O_{3}. A has higher boiling point than B. What are the possible structures of A and B?
In (A), extensive intermolecular Hbonding is possible while in (B) there is no Intermolecular Hbonding.
Kjeldahl method cannot be used for :
Kjeldahl method is not applicable to nitro or diazo groups present in the ring, as nitrogen atom can't be converted to ammonium sulfate under the reaction conditions.
A compound X that adds 2 hydrogen molecules on hydrogenation. The compound X also gives 3  oxohexanedioic acid on oxidative ozonolysis. The compound 'X' is:
Formation of Bakelite follows:
Formation of Bakelite follows electrophilic substitution reaction of phenol with formaldehyde followed by condensation.
Products formed by hydrolysis of maltose are
Maltose on hydrolysis gives 2 moles of αDglucose.
Temperature of 4 moles of gas increases from 300 K to 500 K find 'Cv' if ΔU = 5000 J.
Given :
Determine at equilibrium
For cell reaction Sn  Sn ^{2+}  Pb^{ 2+}  Pb
take = 0.06 V
At Equilibrium state.
E_{cell }= 0 ; Eº_{cell} = 0.01 V
= 10^{1/3} = 2.1544
Given following reaction,
NaClO_{3} + Fe → O_{2 }+ FeO + NaCl
In the above reaction 492 L of O_{2} is obtained at 1 atm & 300 K temperature.
Determine mass of NaClO_{3} required (in kg).
(R = 0.082 L atm mol^{–1} K^{–1} )
mol of NaClO_{3} = mol of O_{2}
mol of O_{2 }=
= 20 mL
mass of NaClO_{3}= 20 × 106.5 = 2130 g
Complex [ML_{5}] can exhibit trigonal bipyramidal and square pyramidal geometry. Determine total number of 180º, 90º & 120º LML bond angles.
∠120º = 3; ∠90º = 6; ∠180º = 1
→Total = 10
∠90º = 8; ∠180º = 2 ⇒ Total = 10
How many atoms lie in the same plane in the major product (C)?
(Where A is the alkyne of lowest molecular mass)
Number of atoms in one plane = 13
Let and is nonzero vector and find
Let coefficient of x^{4} and x^{2} in the expansion of is α and β then α β is equal to
α = – 96 and β = 36
∴ α  β = 132
Differential equation of x^{2 }= 4b(y + b), where b is a parameter, is
2x = 4by'
So. differential equation is
Image of (1, 2, 3) w.r.t a plane is then which of the following points lie on the plane
d.r of normal to the plane
10/3, 10/3, 10/3
1, 1, 1
midpoint of P and Q is
equation of plane x + y + z = 1
Using L’Hospital
Let P be the set of points (x, y) such that x^{2} ≤ y ≤ – 2x + 3. Then area of region bounded by points in set P is
Point of intersection of y = x^{2} & y = – 2x + 3 is
obtained by x^{2} + 2x – 3 = 0
⇒ x =  3, 1
So, Area =
= 12 + 8 – 28/3 = 32/3
Let f(x) = → R then range of f(x) is (where [ . ] denotes greatest integer function)
∴ f(x) is a decreasing function
∴
Let A = and I = then value of 10 A^{–1} is –
Characteristics equation of matrix ‘A’ is
x^{2} – 6x – 10 = 0
∴ A^{2}  6A  10I = 0
⇒ 10A^{–1} = A – 6I
Solution set of 3^{x}(3^{x }–1) + 2 = 3^{x} –1 + 3^{x} – 2 contains
Let 3^{x} = t
t(t –1) + 2 = t –1 + t –2
t^{2} – t + 2 = t –1 + t –2
are positive solution
t = a
3^{x} = a
x = log_{3} a so singleton set
Mean and variance of 20 observation are 10 and 4. It was found, that in place of 11, 9 was taken by mistake find correct variance.
................... (1)
................... (2)
= 104 × 20 = 2080
Actual mean =
Variance =
= = 106 – 102.01 = 3.99
λx + 2y + 2z = 5
2λx + 3y + 5z = 8
4x + λy + 6z = 10
for the system of equation check the correct option.
D = (λ + 8) ( 2  λ)
for λ = 2
= 5[18 – 10] – 2 [48 – 50] + 2 (16 – 30]
= 40 + 4 – 28 ≠ 0
No solutions for λ = 2
For an A.P. T_{10} = 1/20; T_{20 }= 1/10 Find sum of first 200 term.
Let α = and a = . If a and b are roots of quadratic equation then quadratic equation is
α = ω, b = 1 + ω^{3} + ω^{6} + .......... = 101
a = (1 + ω) (1 + ω^{2} + ω^{4} + ......... ω^{198} + ω^{200})
=
Equation: x^{2} – (101 +1)x + (101) × 1 = 0
⇒ x^{2}  102x + 101 = 0
Let f(x) is a three degree polynomial for which f '(–1) = 0, f ''(1) = 0, f(–1) = 10, f(1) = 6 then local minima of f(x) exist at
Let f(x) = ax^{3} + bx^{2} + cx + d
a = 1/4 d = 35/4
b = 3/4 c = 9/4
⇒ f(x) = a(x^{3} – 3x^{2} – 9x) + d
f ' (x) = 3/4 (x^{2 }– 2x – 3)
⇒ f ' (x) = 0 ⇒ x = 3, –1
local minima exist at x = 3
Let A and B are two events such that P(exactly one) = 2/5, P(A ∪ B) = then P(A ∩ B) =
P(exactly one) = 2/5
⇒ P(A) + P(B)  2P(A ∩ B) = 2/5
P (A ∪ B) = 1/2
⇒ P(A) + P(B) – P(A ∩ B) = 1/2
∴ P(A ∩ B) = 1/2  2/5 = (54)/10 = 1/10
1/3 < I < 1/√8
Normal at (2, 2) to curve x^{2} + 2xy – 3y^{2} = 0 is L. Then perpendicular distance from origin to line L is
x^{2} + 2xy – 3y^{2} = 0
x^{2} + 3xy – xy – 3y^{2} = 0
(x – y) (x + 3y) = 0
x – y = 0 x + 3y = 0
(2, 2) satisfy x – y = 0
Normal : x + y = λ
λ = 4
Hence x + y =4
perpendicular distance from origin = = 2√2
Which of the following is tautology
(~p ∧ q) → (p ν q)
~{(~p ∧ q) ∧ (~p ∧ ~q)}
~{~p ∧ f}
If a hyperbola has vertices (±6, 0) and P(10, 16) lies on it, then the equation of normal at P is
Vertex is at (±6, 0)
∴ a = 6
Let the hyperbola is
Putting point P(10, 16) on the hyperbola
⇒ b^{2 }= 144
∴ hyperbola is
∴ equation of normal is
∴ putting we get 2x + 5y = 100
If y = mx + c is a tangent to the circle (x – 3)^{2} + y^{2} = 1 and also the perpendicular to the tangent to the circle x^{2} + y^{2} = 1 at , then
Slope of tangent to x^{2} + y^{2} = 1 at
x^{2} + y^{2 }= 1
2x + 2yy' = 0
y = mx + c is tangent of x^{2} + y^{2} = 1
so m = 1
y = x + c
now distance of (3, 0) from y = x + c is
= 1
c^{2} + 6c + 9 = 2
c^{2} + 6c + 7 = 0
Let = 1/7 and = 1/√10 where α, β ∈ . Then tan (α + 2β) is equal to
and = 1/√10
tan α = 1/7
sin β = 1/√10
tanβ = 1/3
tan2β =
tan (α + 2β) = =
The number of four letter words that can be made from the letters of word "EXAMINATION" is
EXAMINATION
2N, 2A, 2I, E, X, M, T, O
Case I All are different so = 8.7.6.5 = 1680
Case II 2 same and 2 different so
= 3.21.12 = 756
Case III 2 same and 2 same so = 3.6 = 18
Total = 1680 + 756 + 18 = 2454
Let the line y = mx intersects the curve y^{2} = x at P and tangent to y^{2} = x at P intersects xaxis at Q. If area (ΔOPQ) = 4, find m (m > 0)
2ty = x + t^{2}
Q(–t^{2}, 0)
= 4
t^{3 }= 8
t = ± 2 (t > 0)
m = 2
1/4 [1568 + 420 + 28] = 504
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