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All questions of 2012 for JEE Exam
Heat is produced at a rate given by H in a resistor when it is connected across a supply of voltage V. If now the resistance of the resistor is doubled and the supply voltage is made V/3 then the rate of production of heat in the resistor will be- a)H/18
- b)H/9
- c)6H
- d)18H
Correct answer is option 'A'. Can you explain this answer?
Heat is produced at a rate given by H in a resistor when it is connected across a supply of voltage V. If now the resistance of the resistor is doubled and the supply voltage is made V/3 then the rate of production of heat in the resistor will be
a)
H/18
b)
H/9
c)
6H
d)
18H
|
Rohit Jain answered |
Let f(x) = ax2 + bx + c, g(x) = px2 + qx + r, such that f(1) = g(1), f(2) = g(2) and f(3) – g(3) = 2. Then f(4) – g(4) is- a)4
- b)5
- c)6
- d)7
Correct answer is option 'C'. Can you explain this answer?
Let f(x) = ax2 + bx + c, g(x) = px2 + qx + r, such that f(1) = g(1), f(2) = g(2) and f(3) – g(3) = 2. Then f(4) – g(4) is
a)
4
b)
5
c)
6
d)
7
|
Ankita Das answered |
First of all make the equation with help of the given data. solving it u will find relation between a and p , b and q, c and r . putting it in fx ang gx u will get the ans to be 6
In a reversible chemical reaction at equilibrium, if the concentration of any one of the reactants is doubled, then the equilibrium constant will- a)also be doubled
- b)be halved
- c)remain the same
- d)become one-fourth
Correct answer is option 'C'. Can you explain this answer?
In a reversible chemical reaction at equilibrium, if the concentration of any one of the reactants is doubled, then the equilibrium constant will
a)
also be doubled
b)
be halved
c)
remain the same
d)
become one-fourth
|
Tejas Verma answered |
Equilibrium constant does not depend on conc. It is only a function of temperature
The number of solutions of the equation log2(x2 + 2x –1) = 1 is- a)0
- b)1
- c)2
- d)3
Correct answer is option 'C'. Can you explain this answer?
The number of solutions of the equation log2(x2 + 2x –1) = 1 is
a)
0
b)
1
c)
2
d)
3
|
Arnab Choudhary answered |
x2 + 2x –1 = 2
x2 + 2x – 3=0
(x + 3) (x – 1) = 0;
x = 1, –3
The total number of injections (one-one into mappings) from {a1, a2, a3 , a4} to {b1,b2 ,b3 ,b4 ,b5 ,b6 , b7 is}- a)400
- b)420
- c)800
- d)840
Correct answer is option 'D'. Can you explain this answer?
The total number of injections (one-one into mappings) from {a1, a2, a3 , a4} to {b1,b2 ,b3 ,b4 ,b5 ,b6 , b7 is}
a)
400
b)
420
c)
800
d)
840
|
Ananya Das answered |
So total = 7 × 6 × 5 × 4 = 840 one-one into functions
Identify the correct statement from the following in a chemical reaction.- a)The entropy always increases
- b)The change in entropy along with suitable change in enthalpy decides the fate of a reaction
- c)The enthalpy always decreases
- d)Both the enthalpy and the entropy remain constant
Correct answer is option 'B'. Can you explain this answer?
Identify the correct statement from the following in a chemical reaction.
a)
The entropy always increases
b)
The change in entropy along with suitable change in enthalpy decides the fate of a reaction
c)
The enthalpy always decreases
d)
Both the enthalpy and the entropy remain constant
|
Shahbaz Ahmad answered |
Option (b) is correct because the change in entropy Along with suitable change in enthalpy decides the fate of a reaction either it is spontaneous or non-spontaneous reaction .
Which of the following will show a negative deviation from Raoult’s law?- a)Acetone-benzene
- b)Acetone-ethanol
- c) Benzene-methanol
- d)Acetone-chloroform
Correct answer is option 'D'. Can you explain this answer?
Which of the following will show a negative deviation from Raoult’s law?
a)
Acetone-benzene
b)
Acetone-ethanol
c)
Benzene-methanol
d)
Acetone-chloroform
|
|
Tejas Verma answered |
Acetone – chloroform due to formation of intermolecular Hydrogen bonding
A spherical ball A of mass 4 kg, moving along a straight line strikes another spherical ball B of mass 1 kg at rest.
After the collision, A and B move with velocities v1 ms–1 and v2 ms–1 respectively making angles of 30o and 60o with respect to the original direction of motion of A. The ratio v1/v2 will be- a)√3/4
- b)4/√3
- c)1/√3
- d)√3
Correct answer is option 'A'. Can you explain this answer?
A spherical ball A of mass 4 kg, moving along a straight line strikes another spherical ball B of mass 1 kg at rest.
After the collision, A and B move with velocities v1 ms–1 and v2 ms–1 respectively making angles of 30o and 60o with respect to the original direction of motion of A. The ratio v1/v2 will be
After the collision, A and B move with velocities v1 ms–1 and v2 ms–1 respectively making angles of 30o and 60o with respect to the original direction of motion of A. The ratio v1/v2 will be
a)
√3/4
b)
4/√3
c)
1/√3
d)
√3
|
Siddharth Ghosh answered |
Apply conservation of momentum along Normal
The equation y2 + 4x + 4y + k = 0 represents a parabola whose latus rectum is- a)1
- b)2
- c)3
- d)4
Correct answer is option 'D'. Can you explain this answer?
The equation y2 + 4x + 4y + k = 0 represents a parabola whose latus rectum is
a)
1
b)
2
c)
3
d)
4
|
Maitri Das answered |
y2 + 4x + 4y + k = 0
⇒ (y + 2)2 = 4 (–x + 1 – k/4)
Latus rectum = 4
The stability of Me2C=CH2 is more than that of MeCH2CH = CH2 due to- a)inductive effect of the Me group
- b) resonance effect of the Me group
- c)hyperconjugative effect of the Me group
- d)resonance as well as inductive effect of the Me group
Correct answer is option 'C'. Can you explain this answer?
The stability of Me2C=CH2 is more than that of MeCH2CH = CH2 due to
a)
inductive effect of the Me group
b)
resonance effect of the Me group
c)
hyperconjugative effect of the Me group
d)
resonance as well as inductive effect of the Me group
|
Charvi Chopra answered |
Me2C = CH2 is more stable than MeCH2CH = CH2 due to hyperconjugative effect.
Two decks of playing cards are well schuffled and 26 cards are randomly distributed to a player. Then the probability that the player gets all distinct cards is- a)52C26 / 104C26
- b)2 X 52C26 / 104C26
- c)213 x 52C26 / 104C26
- d)226 x 52C26 / 104C26
Correct answer is option 'B'. Can you explain this answer?
Two decks of playing cards are well schuffled and 26 cards are randomly distributed to a player. Then the probability that the player gets all distinct cards is
a)
52C26 / 104C26
b)
2 X 52C26 / 104C26
c)
213 x 52C26 / 104C26
d)
226 x 52C26 / 104C26
|
Bhaskar Saha answered |
Total no. of way of distribution = 104 C26 Favourable no. of ways of ditribution =
(selecting any one decki) × (selecting 26 cards out of it) = 2 x 52 C26
In a slide calipers, (m + 1) number of vernier divisions is equal to m number of smallest main scale divisions. If d unit is the magnitude of the smallest main scale division, then the magnitude of the vernier constant is- a)d/(m+1) unit
- b)d/m unit
- c)md/(m+1) unit
- d)(m+1)d/m unit
Correct answer is option 'D'. Can you explain this answer?
In a slide calipers, (m + 1) number of vernier divisions is equal to m number of smallest main scale divisions. If d unit is the magnitude of the smallest main scale division, then the magnitude of the vernier constant is
a)
d/(m+1) unit
b)
d/m unit
c)
md/(m+1) unit
d)
(m+1)d/m unit
|
Shreya Sengupta answered |
A body when fully immersed in a liquid of specific gravity 1.2 weighs 44 gwt. The same body when fully immersed in water weighs 50 gwt. The mass of the body is- a)36 g
- b)48 g
- c)64 g
- d)80 g
Correct answer is option 'D'. Can you explain this answer?
A body when fully immersed in a liquid of specific gravity 1.2 weighs 44 gwt. The same body when fully immersed in water weighs 50 gwt. The mass of the body is
a)
36 g
b)
48 g
c)
64 g
d)
80 g
|
|
Sanskriti Dasgupta answered |
mg – σvg = 44, σ = density of liquid,
mg –1.2
ρvg = 44 ..............(1),
ρ = density of water
mg – ρvg = 50.............(2),
(1) – 1.2 x(2)
M = 80 g
mg –1.2
ρvg = 44 ..............(1),
ρ = density of water
mg – ρvg = 50.............(2),
(1) – 1.2 x(2)
M = 80 g
There are 100 students in a class. In an examination, 50 of them failed in Mathematics, 45 failed in Physics, 40 failed in Biology and 32 failed in exactly two of the three subjects. Only one student passed in all the subjects. Then the number of students failing in all the three subjects- a)is 12
- b)is 4
- c)is 2
- d)cannot be determined from given information
Correct answer is option 'C'. Can you explain this answer?
There are 100 students in a class. In an examination, 50 of them failed in Mathematics, 45 failed in Physics, 40 failed in Biology and 32 failed in exactly two of the three subjects. Only one student passed in all the subjects. Then the number of students failing in all the three subjects
a)
is 12
b)
is 4
c)
is 2
d)
cannot be determined from given information
|
|
Maheshwar Unni answered |
n(MUPUB) = n(M) + n(P) + n(B) -n(M ∩ P) - n(PMB) - n(B ∩ P) + n(M ∩ P ∩ B)
given n(M) = 50 , n (P) = 45, n(B) = 40;
n(M∩ P) + n(P∩ B) + n(B∩ M) - 3(M∩ P ∩ B) = 32
99 = 50 + 45 + 40 – (32 + 3 n (M ∩ P∩ B) )+ n(M ∩ P∩ B) ;
2 n(M ∩ P ∩ B) = 36 – 32;
n(M∩ P ∩ B) = 2
A vehicle registration number consists of 2 letters of English alphabets followed by 4 digits, where the first digit is not zero. Then the total number of vehicles with distinct registration numbers is- a)262 x 104
- b)26P2 x 10 P4
- c)26 P2 x 9 x 10 P3
- d)262 x 9 x 103
Correct answer is option 'D'. Can you explain this answer?
A vehicle registration number consists of 2 letters of English alphabets followed by 4 digits, where the first digit is not zero. Then the total number of vehicles with distinct registration numbers is
a)
262 x 104
b)
26P2 x 10 P4
c)
26 P2 x 9 x 10 P3
d)
262 x 9 x 103
|
|
Khaja Moinuddin answered |
By passing excess Cl2(g) in boiling toluene, which one of the following compounds is exclusively formed?
- a)A
- b)B
- c)C
- d)D
Correct answer is option 'D'. Can you explain this answer?
By passing excess Cl2(g) in boiling toluene, which one of the following compounds is exclusively formed?
a)
A
b)
B
c)
C
d)
D
|
|
Ashfaque Usmani answered |
In excess of Cl2 all the Hydrogen atom in CH3 are removed and chlorine take the place in toluene
Under identical conditions, the SN1 reaction will occur most efficiently with- a)tert-butyl chloride
- b)1-chlorobutane
- c)2-methyl-1-chloropropane
- d)2-chlorobutane
Correct answer is option 'A'. Can you explain this answer?
Under identical conditions, the SN1 reaction will occur most efficiently with
a)
tert-butyl chloride
b)
1-chlorobutane
c)
2-methyl-1-chloropropane
d)
2-chlorobutane
|
|
Lavanya Menon answered |
Reactivity order for SN1 reaction in case of alkyl halide is 3°> 2°> 1°
then the value of the determinant of Q is equal to
The line x = 2y intersects the ellipse x2/4 + y2 = 1 at the points P and Q. The equation of the circle with PQ as diameter is- a)x2 + y2 = 1/2
- b)x2 + y2 = 1
- c)x2 + y2 = 2
- d)x2 + y2 = 5/2
Correct answer is option 'D'. Can you explain this answer?
The line x = 2y intersects the ellipse x2/4 + y2 = 1 at the points P and Q. The equation of the circle with PQ as diameter is
a)
x2 + y2 = 1/2
b)
x2 + y2 = 1
c)
x2 + y2 = 2
d)
x2 + y2 = 5/2
|
|
Srestha Iyer answered |
Solving the given equations then common points are 
Eqn. of Circle PQ as
diameter
diameter
The equations x2 +x +a=0 and x2 +ax +1=0 have a common real root- a)for no value of a
- b)for exactly one value of a
- c)for exactly two values of a
- d)for exactly three values of a
Correct answer is option 'B'. Can you explain this answer?
The equations x2 +x +a=0 and x2 +ax +1=0 have a common real root
a)
for no value of a
b)
for exactly one value of a
c)
for exactly two values of a
d)
for exactly three values of a
|
Kirti Mehta answered |
The Common Real Root of Two Quadratic Equations
To find the common real root of two quadratic equations, we need to equate the two equations and solve for the common value of x. Let's analyze the given equations and find the common real root.
Given Equations:
1) x^2 + x + a = 0
2) x^2 + ax + 1 = 0
Equating the Equations:
Let's equate the two equations to find the common root x:
x^2 + x + a = x^2 + ax + 1
Simplifying the Equation:
By rearranging the terms, we get:
x + a = ax + 1
Isolating the Variables:
To isolate x, we subtract ax from both sides of the equation:
x - ax + a = 1
Factoring Out x:
Next, we factor out x from the left side of the equation:
x(1 - a) + a = 1
Simplifying the Equation:
Now, we simplify the equation:
x(1 - a) = 1 - a
Dividing Both Sides by (1 - a):
To solve for x, we divide both sides of the equation by (1 - a):
x = (1 - a) / (1 - a)
Final Conclusion:
We can see that x is equal to 1 for all values of a except when a = 1. In this case, the denominator becomes 0, which is undefined. Therefore, for all other values of a, the common real root of the given equations is x = 1.
Answer:
The given equations have a common real root for exactly one value of a, which is option 'B'.
To find the common real root of two quadratic equations, we need to equate the two equations and solve for the common value of x. Let's analyze the given equations and find the common real root.
Given Equations:
1) x^2 + x + a = 0
2) x^2 + ax + 1 = 0
Equating the Equations:
Let's equate the two equations to find the common root x:
x^2 + x + a = x^2 + ax + 1
Simplifying the Equation:
By rearranging the terms, we get:
x + a = ax + 1
Isolating the Variables:
To isolate x, we subtract ax from both sides of the equation:
x - ax + a = 1
Factoring Out x:
Next, we factor out x from the left side of the equation:
x(1 - a) + a = 1
Simplifying the Equation:
Now, we simplify the equation:
x(1 - a) = 1 - a
Dividing Both Sides by (1 - a):
To solve for x, we divide both sides of the equation by (1 - a):
x = (1 - a) / (1 - a)
Final Conclusion:
We can see that x is equal to 1 for all values of a except when a = 1. In this case, the denominator becomes 0, which is undefined. Therefore, for all other values of a, the common real root of the given equations is x = 1.
Answer:
The given equations have a common real root for exactly one value of a, which is option 'B'.
Let C1 and C2 denote the centres of the circles x2 + y2 = 4 and (x – 2)2 + y2 = 1 respectively and let P and Q be their points of intersection. Then the areas of triangles C1PQ and C2PQ are in the ratio- a)3 : 1
- b)5 : 1
- c)7 : 1
- d)9 : 1
Correct answer is option 'C'. Can you explain this answer?
Let C1 and C2 denote the centres of the circles x2 + y2 = 4 and (x – 2)2 + y2 = 1 respectively and let P and Q be their points of intersection. Then the areas of triangles C1PQ and C2PQ are in the ratio
a)
3 : 1
b)
5 : 1
c)
7 : 1
d)
9 : 1
|
|
Asif Ali answered |
An object placed in front of a concave mirror at a distance of x cm from the pole gives a 3 times magnified real image.If it is moved to a distance of (x + 5) cm, the magnification of the image becomes 2. The focal length of the mirror is- a)15 cm
- b)20 cm
- c)25 cm
- d)30 cm
Correct answer is option 'D'. Can you explain this answer?
An object placed in front of a concave mirror at a distance of x cm from the pole gives a 3 times magnified real image.If it is moved to a distance of (x + 5) cm, the magnification of the image becomes 2. The focal length of the mirror is
a)
15 cm
b)
20 cm
c)
25 cm
d)
30 cm
|
Parth Majumdar answered |
so f = 30 cm
If four distinct points (2k, 3k), (2, 0), (0, 3) (0, 0) lie on a circle, then- a)k < 0
- b)o < k < 1
- c)k = 1
- d)k > 1
Correct answer is option 'C'. Can you explain this answer?
If four distinct points (2k, 3k), (2, 0), (0, 3) (0, 0) lie on a circle, then
a)
k < 0
b)
o < k < 1
c)
k = 1
d)
k > 1
|
Nilotpal Ghosh answered |
Equation of circle x(x – 2) + y (y – 3) = 0
(2k, 3k) will satisfy
So, K = 1
(2k, 3k) will satisfy
So, K = 1
The number of real values of for which the system of equationsx + 3y+5z = αx
5x+y+3z =α y
3x+5y+z = αz- a)1
- b)2
- c)4
- d)6
Correct answer is option 'A'. Can you explain this answer?
The number of real values of for which the system of equations
x + 3y+5z = αx
5x+y+3z =α y
3x+5y+z = αz
5x+y+3z =α y
3x+5y+z = αz
a)
1
b)
2
c)
4
d)
6
|
|
Sneha Sengupta answered |
Understanding the System of Equations
- Given system of equations:
1. x + 3y + 5z = α
2. 5x + y + 3z = α
3. 3x + 5y + z = α
Analysis of the System
- To find the number of real values of α for which the system has a solution, we need to analyze the system of equations.
- We can represent the system in matrix form as AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.
Determinant of Coefficient Matrix
- The determinant of the coefficient matrix A is given by |A| = -144.
- If |A| ≠ 0, then the system has a unique solution for any value of α.
Calculating the Determinant
- Since |A| ≠ 0, the system of equations has a unique solution for any value of α.
- Therefore, the number of real values of α for which the system has a solution is 1.
Therefore, the correct answer is option 'A'.
If f is a real-valued differentiable function such that f(x) f’(x) < 0 for all real x, then- a) f(x) must be an increasing function
- b) f(x) must be a decreasing function
- c)|f (x )| must be an increasing function
- d)|f (x)| must be a drecreasing function
Correct answer is option 'D'. Can you explain this answer?
If f is a real-valued differentiable function such that f(x) f’(x) < 0 for all real x, then
a)
f(x) must be an increasing function
b)
f(x) must be a decreasing function
c)
|f (x )| must be an increasing function
d)
|f (x)| must be a drecreasing function
|
Nayanika Dey answered |
f(x) f (x) < 0 ....(i)
f(x) < 0 ; f (x) > 0 or f(x) > 0 ; f (x) < 0 ............... (ii)
f(x) < 0 ; f (x) > 0 or f(x) > 0 ; f (x) < 0 ............... (ii)
So possible graphs of f(x) are
|f(x)| is decreasing function in both cases.
When a certain metal surface is illuminated with light of frequency ν , the stopping potential for photoelectric current is νo When the same surface is illuminated by light of frequency v/2 the stopping potential is v0/4 The threshold frequency for photoelectric emission is- a)v/6
- b)v/3
- c)2v/3
- d)4v/3
Correct answer is option 'B'. Can you explain this answer?
When a certain metal surface is illuminated with light of frequency ν , the stopping potential for photoelectric current is νo When the same surface is illuminated by light of frequency v/2 the stopping potential is v0/4 The threshold frequency for photoelectric emission is
a)
v/6
b)
v/3
c)
2v/3
d)
4v/3
|
Parth Yadav answered |
solving equation (1) and (2) ,v/3
Four speakers will address a meeting where speaker Q will always speak after speaker P. Then the number of ways in which the order of speakers can be prepared is- a)256
- b)128
- c)24
- d)12
Correct answer is option 'D'. Can you explain this answer?
Four speakers will address a meeting where speaker Q will always speak after speaker P. Then the number of ways in which the order of speakers can be prepared is
a)
256
b)
128
c)
24
d)
12
|
|
Anand Kumar answered |
Let P,Q,R and S are four speakers.As mentioned Q will speak after P.So, exclude P and Q then we left with only two i.e, R and S.
Now, here we have 3 position
(1) before R
(2) Between R and S
(3) after S
selection of 2 positions out of 3 can be done in 3C2 and arrangement of P and Q is fixed(Q speaks after P) so, it can be done in only one ways
Therefore ,answer of this part is 3C2×1
Now, remaining two R and S can be arranged in 2!
Therefore ,total required order= 3C2×1×2! =12
A Wheatstone bridge has the resistances 10 Ω , 10 Ω , 10Ω and 30 Ω in its four arms. What resistance joined in parallel to the 30 resistance will bring it to the balanced condition?- a)2Ω
- b)5Ω
- c)10Ω
- d)15Ω
Correct answer is option 'D'. Can you explain this answer?
A Wheatstone bridge has the resistances 10 Ω , 10 Ω , 10Ω and 30 Ω in its four arms. What resistance joined in parallel to the 30 resistance will bring it to the balanced condition?
a)
2Ω
b)
5Ω
c)
10Ω
d)
15Ω
|
|
Kiran Nair answered |
for a balanced bridge. R = 10 Ω
The equivalent weight of K2Cr2O7 in acidic medium is expressed in terms of its molecular weight (M) as- a)M/3
- b)M/4
- c)M/6
- d)M/7
Correct answer is option 'C'. Can you explain this answer?
The equivalent weight of K2Cr2O7 in acidic medium is expressed in terms of its molecular weight (M) as
a)
M/3
b)
M/4
c)
M/6
d)
M/7
|
Navya Hegde answered |
Because k2Cr2O7 loses 6 elections. equivalent weight is the mass divided by the no of electrons lost or gained. that is why M/6 is the correct answer.
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