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All questions of JEE Advanced 2011 for JEE Exam
A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, traveling with a velocity V m/s in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The velocity V of the bullet is
- a)250 m/s
- b)
- c)400 m/s
- d)500 m/s
Correct answer is option 'D'. Can you explain this answer?
A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, traveling with a velocity V m/s in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The velocity V of the bullet is
a)
250 m/s
b)
c)
400 m/s
d)
500 m/s
|
Vijay Kumar answered |
vball = 20 m/s
vbullet = 100 m/s
0.01 V = 0.01 x 100 + 0.2 x 20
v = 100 + 400 = 500 m/s
vbullet = 100 m/s
0.01 V = 0.01 x 100 + 0.2 x 20
v = 100 + 400 = 500 m/s
Among the following, the number of compounds than can react with PCl5 to give POCl3 is O2, CO2, SO2, H2O, H2SO4, P4O10
Correct answer is '5'. Can you explain this answer?
Among the following, the number of compounds than can react with PCl5 to give POCl3 is O2, CO2, SO2, H2O, H2SO4, P4O10
|
Mahi Sarkar answered |
Reactivity of Compounds with PCl5 to form POCl3
POCl3 is a commonly used reagent for the conversion of alcohols to alkyl chlorides. It is also used in the synthesis of various organic compounds. PCl5 is a strong electrophile and can react with various compounds to form POCl3.
Out of the given compounds:
1. O2: It is an inert gas and does not react with PCl5 to form POCl3.
2. CO2: It is also an inert gas and does not react with PCl5 to form POCl3.
3. SO2: It can react with PCl5 to form POCl3. The reaction is as follows:
SO2 + PCl5 → POCl3 + SOCl2
4. H2O: It can react with PCl5 to form POCl3. The reaction is as follows:
H2O + PCl5 → POCl3 + 2HCl
5. H2SO4: It can react with PCl5 to form POCl3. The reaction is as follows:
H2SO4 + PCl5 → POCl3 + 2HCl + SO2
6. P4O10: It is a compound of phosphorus and can react with PCl5 to form POCl3. The reaction is as follows:
P4O10 + 10PCl5 → 10POCl3 + PCl5
Therefore, out of the given compounds, 5 compounds can react with PCl5 to form POCl3.
POCl3 is a commonly used reagent for the conversion of alcohols to alkyl chlorides. It is also used in the synthesis of various organic compounds. PCl5 is a strong electrophile and can react with various compounds to form POCl3.
Out of the given compounds:
1. O2: It is an inert gas and does not react with PCl5 to form POCl3.
2. CO2: It is also an inert gas and does not react with PCl5 to form POCl3.
3. SO2: It can react with PCl5 to form POCl3. The reaction is as follows:
SO2 + PCl5 → POCl3 + SOCl2
4. H2O: It can react with PCl5 to form POCl3. The reaction is as follows:
H2O + PCl5 → POCl3 + 2HCl
5. H2SO4: It can react with PCl5 to form POCl3. The reaction is as follows:
H2SO4 + PCl5 → POCl3 + 2HCl + SO2
6. P4O10: It is a compound of phosphorus and can react with PCl5 to form POCl3. The reaction is as follows:
P4O10 + 10PCl5 → 10POCl3 + PCl5
Therefore, out of the given compounds, 5 compounds can react with PCl5 to form POCl3.
Water (with refractive index = 4/3 in a tank is 18 cm deep. Oil of refractive index 7/4 lies on water making a convex surface of radius of curvature ‘R = 6 cm’ as shown. Consider oil to act as a thin lens. An object ‘S’ is placed 24 cm above water surface. The location of its image is at ‘x’ cm above the bottom of the tank. Then ‘x’ is
Correct answer is '2'. Can you explain this answer?
Water (with refractive index = 4/3 in a tank is 18 cm deep. Oil of refractive index 7/4 lies on water making a convex surface of radius of curvature ‘R = 6 cm’ as shown. Consider oil to act as a thin lens. An object ‘S’ is placed 24 cm above water surface. The location of its image is at ‘x’ cm above the bottom of the tank. Then ‘x’ is
|
Yash Patel answered |
V2 = 16 cm
x = 18 - 16 = 2 cm
x = 18 - 16 = 2 cm
Let f(x) = x2 and g(x) = sinx for all x ε R. Then the set of all x satisfying (f o g o g o f) (x) = (g o g o f) (x),
where (f o g) (x) = f(g(x)), is- a)
- b)
- c)
- d)2nπ, n ε {...,-2, -1,0,1, 2, ....}
Correct answer is option 'A'. Can you explain this answer?
Let f(x) = x2 and g(x) = sinx for all x ε R. Then the set of all x satisfying (f o g o g o f) (x) = (g o g o f) (x),
where (f o g) (x) = f(g(x)), is
where (f o g) (x) = f(g(x)), is
a)
b)
c)
d)
2nπ, n ε {...,-2, -1,0,1, 2, ....}
|
Ananya Das answered |
(fogogof) (x) = sin2 (sin x2)
(gogof) (x) = sin (sin x2)
sin2 (sin x2) = sin (sin x2)
⇒ sin (sin x2) [sin (sin x2) - 1] = 0
(gogof) (x) = sin (sin x2)
sin2 (sin x2) = sin (sin x2)⇒ sin (sin x2) [sin (sin x2) - 1] = 0
⇒ sin (sin x2) = 0 or 1
⇒ sin x2 = nπ or 2mπ + π/2, where m, n ε I
⇒ sin x2 = 0
⇒ x2 = np x = ± np , n Î {0, 1, 2, …}.
⇒ sin x2 = nπ or 2mπ + π/2, where m, n ε I
⇒ sin x2 = 0
⇒ x2 = np x = ± np , n Î {0, 1, 2, …}.
The volume (in mL) of 0.1 M AgNO3 required for complete precipitation of chloride ions present in 30 mL
of 0.01 M solution of [Cr(H2O)5Cl]Cl2, as silver chloride is close to
Correct answer is '6'. Can you explain this answer?
The volume (in mL) of 0.1 M AgNO3 required for complete precipitation of chloride ions present in 30 mL
of 0.01 M solution of [Cr(H2O)5Cl]Cl2, as silver chloride is close to
of 0.01 M solution of [Cr(H2O)5Cl]Cl2, as silver chloride is close to
|
|
Anaya Patel answered |
Number of ionisable Cl- in [Cr(H2O)5Cl]Cl2 is 2
Millimoles of Cl- = 30 x 0.01 ´ 2 = 0.6
Millimoles of Ag+ required = 0.6
0.6 = 0.1 V
V = 6 ml
Millimoles of Cl- = 30 x 0.01 ´ 2 = 0.6 Millimoles of Ag+ required = 0.6 0.6 = 0.1 VV = 6 ml
A train is moving along a straight line with a constant acceleration ‘a’. A boy standing in the train throws a
ball forward with a speed of 10 m/s, at an angle of 60° to the horizontal. The boy has to move forward by
1.15 m inside the train to catch the ball back at the initial height. The acceleration of the train, in m/s2, is
Correct answer is '5'. Can you explain this answer?
A train is moving along a straight line with a constant acceleration ‘a’. A boy standing in the train throws a
ball forward with a speed of 10 m/s, at an angle of 60° to the horizontal. The boy has to move forward by
1.15 m inside the train to catch the ball back at the initial height. The acceleration of the train, in m/s2, is
ball forward with a speed of 10 m/s, at an angle of 60° to the horizontal. The boy has to move forward by
1.15 m inside the train to catch the ball back at the initial height. The acceleration of the train, in m/s2, is
|
Aryan Singh answered |
To determine the distance traveled by the train, we need to know the initial velocity of the train and the time it has been moving with the constant acceleration.
Let's assume the initial velocity of the train is u (m/s), the constant acceleration is a (m/s^2), and the time it has been moving is t (s).
The distance traveled by the train can be calculated using the equation:
s = ut + (1/2)at^2
where s is the distance traveled.
If the train starts from rest (u = 0), then the equation simplifies to:
s = (1/2)at^2
If you provide the values of the acceleration (a) and the time (t), we can calculate the distance traveled by the train.
Let's assume the initial velocity of the train is u (m/s), the constant acceleration is a (m/s^2), and the time it has been moving is t (s).
The distance traveled by the train can be calculated using the equation:
s = ut + (1/2)at^2
where s is the distance traveled.
If the train starts from rest (u = 0), then the equation simplifies to:
s = (1/2)at^2
If you provide the values of the acceleration (a) and the time (t), we can calculate the distance traveled by the train.
The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with
a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the
main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a
relative error of 2 %, the relative percentage error in the density is- a)0.9 %
- b)2.4 %
- c)3.1 %
- d)4.2 %
Correct answer is option 'C'. Can you explain this answer?
The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with
a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the
main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a
relative error of 2 %, the relative percentage error in the density is
a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the
main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a
relative error of 2 %, the relative percentage error in the density is
a)
0.9 %
b)
2.4 %
c)
3.1 %
d)
4.2 %
|
Baishali Tiwari answered |
Which of the following statement(s) is/are correct?- a)If the electric field due to a point charge varies as r-2.5 instead of r-2, then the Gauss law will still be valid.
- b)The Gauss law can be used to calculate the field distribution around an electric dipole
- c)If the electric field between two point charges is zero somewhere, then the sign of the two charges is the same.
- d)The work done by the external force in moving a unit positive charge from point A at potential VA to point B at potential VB is (VB - VA).
Correct answer is option 'C,D'. Can you explain this answer?
Which of the following statement(s) is/are correct?
a)
If the electric field due to a point charge varies as r-2.5 instead of r-2, then the Gauss law will still be valid.
b)
The Gauss law can be used to calculate the field distribution around an electric dipole
c)
If the electric field between two point charges is zero somewhere, then the sign of the two charges is the same.
d)
The work done by the external force in moving a unit positive charge from point A at potential VA to point B at potential VB is (VB - VA).
|
Disha Kaur answered |
(D) is correct if we assume it is work done against electrostatic force
The correct functional group X and the reagent/reaction conditions Y in the following scheme are
- a)X = COOCH3, Y = H2/Ni/heat
- b)X = CONH2, Y = H2/Ni/heat
- c)X = CONH2, Y = Br2/NaOH
- d)X = CN, Y = H2/Ni/heat
Correct answer is option 'A,B,C,D'. Can you explain this answer?
The correct functional group X and the reagent/reaction conditions Y in the following scheme are
a)
X = COOCH3, Y = H2/Ni/heat
b)
X = CONH2, Y = H2/Ni/heat
c)
X = CONH2, Y = Br2/NaOH
d)
X = CN, Y = H2/Ni/heat
|
|
Sarita Yadav answered |
Condensation polymers are formed by condensation of a diols or diamine with dicarboxylic acids.
The number of distinct real roots of x4 - 4x3 + 12x2 + x - 1 = 0 is
Correct answer is '2'. Can you explain this answer?
The number of distinct real roots of x4 - 4x3 + 12x2 + x - 1 = 0 is
|
Pragati Mishra answered |
Problem:
Find the number of distinct real roots of the equation:
x^4 - 4x^3 + 12x^2 + x - 1 = 0
Solution:
To find the number of distinct real roots of the given equation, we can use the Descartes' rule of signs and the Intermediate Value Theorem.
Descartes' Rule of Signs:
The Descartes' rule of signs helps us determine the possible number of positive and negative roots in a polynomial equation by analyzing the signs of its coefficients.
In the given equation, the signs of the coefficients are:
- The coefficient of x^4 is positive.
- The coefficient of x^3 is negative.
- The coefficient of x^2 is positive.
- The coefficient of x is positive.
- The constant term is negative.
According to the Descartes' rule of signs, the number of positive roots of the equation is either the same as the number of sign changes in the coefficients or less than that by an even number.
In this case, there is only one sign change, so the number of positive roots is either 1 or 0.
Similarly, if we consider the equation f(-x), the number of negative roots is either 1 or 0.
Intermediate Value Theorem:
The Intermediate Value Theorem states that if a polynomial function f(x) is continuous on the interval [a, b] and f(a) and f(b) have opposite signs, then there exists at least one root of the equation f(x) = 0 in the interval (a, b).
Analysis:
To determine the number of distinct real roots, we need to find the number of sign changes in the coefficients and analyze the intervals where the function changes sign.
Let's analyze the equation:
f(x) = x^4 - 4x^3 + 12x^2 + x - 1
- There is one sign change from positive to negative between the terms -4x^3 and 12x^2, indicating that there is one negative root.
- There is no sign change between the terms 12x^2 and x, indicating that there are no positive roots.
- There is one sign change between the terms x and -1, indicating that there is one positive root.
Conclusion:
Based on the Descartes' rule of signs and the analysis of sign changes, we can conclude that the given equation has exactly 1 positive root and 1 negative root. Therefore, the total number of distinct real roots is 2.
Find the number of distinct real roots of the equation:
x^4 - 4x^3 + 12x^2 + x - 1 = 0
Solution:
To find the number of distinct real roots of the given equation, we can use the Descartes' rule of signs and the Intermediate Value Theorem.
Descartes' Rule of Signs:
The Descartes' rule of signs helps us determine the possible number of positive and negative roots in a polynomial equation by analyzing the signs of its coefficients.
In the given equation, the signs of the coefficients are:
- The coefficient of x^4 is positive.
- The coefficient of x^3 is negative.
- The coefficient of x^2 is positive.
- The coefficient of x is positive.
- The constant term is negative.
According to the Descartes' rule of signs, the number of positive roots of the equation is either the same as the number of sign changes in the coefficients or less than that by an even number.
In this case, there is only one sign change, so the number of positive roots is either 1 or 0.
Similarly, if we consider the equation f(-x), the number of negative roots is either 1 or 0.
Intermediate Value Theorem:
The Intermediate Value Theorem states that if a polynomial function f(x) is continuous on the interval [a, b] and f(a) and f(b) have opposite signs, then there exists at least one root of the equation f(x) = 0 in the interval (a, b).
Analysis:
To determine the number of distinct real roots, we need to find the number of sign changes in the coefficients and analyze the intervals where the function changes sign.
Let's analyze the equation:
f(x) = x^4 - 4x^3 + 12x^2 + x - 1
- There is one sign change from positive to negative between the terms -4x^3 and 12x^2, indicating that there is one negative root.
- There is no sign change between the terms 12x^2 and x, indicating that there are no positive roots.
- There is one sign change between the terms x and -1, indicating that there is one positive root.
Conclusion:
Based on the Descartes' rule of signs and the analysis of sign changes, we can conclude that the given equation has exactly 1 positive root and 1 negative root. Therefore, the total number of distinct real roots is 2.
A block of mass 0.18 kg is attached to a spring of force-constant 2 N/m. The coefficient of friction between the block and the floor is 0.1. Initially the block is at rest and the spring is unstretched. An impulse is given to the block as shown in the figure. The block slides a distance of 0.06 m and comes to rest for the first time. The initial velocity of the block m/s is V = N/10. Then N is:
Correct answer is '4'. Can you explain this answer?
A block of mass 0.18 kg is attached to a spring of force-constant 2 N/m. The coefficient of friction between the block and the floor is 0.1. Initially the block is at rest and the spring is unstretched. An impulse is given to the block as shown in the figure. The block slides a distance of 0.06 m and comes to rest for the first time. The initial velocity of the block m/s is V = N/10. Then N is:
|
Maulik Khanna answered |
Let ν be the speed of the block just after impulse. At B, the block comes to rest.
Therefore: Loss in K.E. of the block = Gain in P.E. of the spring + Work done against friction
A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in freespace.
It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the
sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the
sphere is A x 10z (where 1 < A < 10). The value of ‘Z’ is
Correct answer is '7'. Can you explain this answer?
A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in freespace.
It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the
sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the
sphere is A x 10z (where 1 < A < 10). The value of ‘Z’ is
It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the
sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the
sphere is A x 10z (where 1 < A < 10). The value of ‘Z’ is
|
Ishani Bajaj answered |
Let L be a normal to the parabola y2 = 4x. If L passes through the point (9, 6), then L is given by- a)y - x + 3 = 0
- b)y + 3x - 33 = 0
- c)y + x - 15 = 0
- d)y - 2x + 12 = 0
Correct answer is option 'A,B,D'. Can you explain this answer?
Let L be a normal to the parabola y2 = 4x. If L passes through the point (9, 6), then L is given by
a)
y - x + 3 = 0
b)
y + 3x - 33 = 0
c)
y + x - 15 = 0
d)
y - 2x + 12 = 0
|
Anisha Deshpande answered |
y2 = 4x
Equation of normal is y = mx – 2m – m3.
It passes through (9, 6)
⇒ m3 – 7m + 6 = 0
⇒ m = 1, 2, – 3
⇒ y – x + 3 = 0, y + 3x – 33 = 0, y – 2x + 12 = 0.
Equation of normal is y = mx – 2m – m3.
It passes through (9, 6)
⇒ m3 – 7m + 6 = 0
⇒ m = 1, 2, – 3
⇒ y – x + 3 = 0, y + 3x – 33 = 0, y – 2x + 12 = 0.
A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, x1(t) = A sinωt and
Adding a third sinusoidal displacement x3(t) = B sin (ωt + φ) brings the mass to a complete rest. The values of B and φ are- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, x1(t) = A sinωt and
Adding a third sinusoidal displacement x3(t) = B sin (ωt + φ) brings the mass to a complete rest. The values of B and φ are
Adding a third sinusoidal displacement x3(t) = B sin (ωt + φ) brings the mass to a complete rest. The values of B and φ area)
b)
c)
d)
|
Bhavya Joshi answered |
SECTION – I (Total Marks : 24)(Single Correct Answer Type)This Section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of
which ONLY ONE is correct.Q. The freezing point (in oC) of a solution containing 0.1 g of K3[Fe(CN)6 (Mol. Wt. 329) in 100 g of water
(Kf = 1.86 K kg mol-1) is- a)-2.3 x 10-2
- b)-5.7 x 10-2
- c)-5.7 x 10-3
- d)-1.2 x 10-2
Correct answer is option 'A'. Can you explain this answer?
SECTION – I (Total Marks : 24)
(Single Correct Answer Type)
This Section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of
which ONLY ONE is correct.
which ONLY ONE is correct.
Q. The freezing point (in oC) of a solution containing 0.1 g of K3[Fe(CN)6 (Mol. Wt. 329) in 100 g of water
(Kf = 1.86 K kg mol-1) is
(Kf = 1.86 K kg mol-1) is
a)
-2.3 x 10-2
b)
-5.7 x 10-2
c)
-5.7 x 10-3
d)
-1.2 x 10-2
|
|
Lakshmi Mishra answered |
SECTION – II (Total Marks : 16)(Multiple Correct Answer(s) Type)This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of
which ONE OR MORE may be correct.Q. Reduction of the metal centre in aqueous permanganate ion involves- a)3 electrons in neutral medium
- b)5 electrons in neutral medium
- c)3 electrons in alkaline medium
- d)5 electrons in acidic medium
Correct answer is option 'A,D'. Can you explain this answer?
SECTION – II (Total Marks : 16)
(Multiple Correct Answer(s) Type)
This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of
which ONE OR MORE may be correct.
which ONE OR MORE may be correct.
Q. Reduction of the metal centre in aqueous permanganate ion involves
a)
3 electrons in neutral medium
b)
5 electrons in neutral medium
c)
3 electrons in alkaline medium
d)
5 electrons in acidic medium
|
Hansa Sharma answered |
In acidic medium
In neutral medium
Hence, number of electron loose in acidic and neutral medium 5 and 3 electrons respectively.
SECTION – I (Total Marks : 24)(Single Correct Answer Type)This Section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of
which ONLY ONE is correct.Q. Which of the field patterns given below is valid for electric field as well as for magnetic field?- a)
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
SECTION – I (Total Marks : 24)
(Single Correct Answer Type)
This Section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of
which ONLY ONE is correct.
which ONLY ONE is correct.
Q. Which of the field patterns given below is valid for electric field as well as for magnetic field?
a)
b)
c)
d)
|
|
Prakash answered |
Option c is correct as you know magnetic field form circular loop
and INDUCED electric field (not electrostatic electric field ) also form close circular loop
A light ray travelling in glass medium is incident on glass-air interface at an angle of incidence θ. The reflected (R) and transmitted (T) intensities, both as function of θ, are plotted. The correct sketch is- a)
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
A light ray travelling in glass medium is incident on glass-air interface at an angle of incidence θ. The reflected (R) and transmitted (T) intensities, both as function of θ, are plotted. The correct sketch is
a)
b)
c)
d)
|
|
Disha Tiwari answered |
After total internal reflection, there is no refracted ray.
A series R-C circuit is connected to AC voltage source. Consider two cases; (A) when C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current IR through the resistor and voltage VC across the capacitor are compared in the two cases. Which of the following is/are true?- a)
- b)
- c)
- d)
Correct answer is option 'B,C'. Can you explain this answer?
A series R-C circuit is connected to AC voltage source. Consider two cases; (A) when C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current IR through the resistor and voltage VC across the capacitor are compared in the two cases. Which of the following is/are true?
a)
b)
c)
d)
|
Tanuja Kapoor answered |
If the normal at the point P intersects the x-axis at (9,
where be is a constant such that 0 < b < 1. Then
A satellite is moving with a constant speed ‘V’ in a circular orbit about the earth. An object of mass ‘m’ is
ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its
ejection, the kinetic energy of the object is- a)
- b)mV2
- c)
- d)2mV2
Correct answer is option 'B'. Can you explain this answer?
A satellite is moving with a constant speed ‘V’ in a circular orbit about the earth. An object of mass ‘m’ is
ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its
ejection, the kinetic energy of the object is
ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of its
ejection, the kinetic energy of the object is
a)
b)
mV2
c)
d)
2mV2
|
|
Krishna Iyer answered |
Let y'(x) + y(x)g'(x) = g(x)g'(x), y(0) = 0, x ε R, where f'(x) denotes 
and g(x) is a given nonconstantdifferentiable function on R with g(0) = g(2) = 0. Then the value of y(2) is
Correct answer is '0'. Can you explain this answer?
Let y'(x) + y(x)g'(x) = g(x)g'(x), y(0) = 0, x ε R, where f'(x) denotes and g(x) is a given nonconstant
and g(x) is a given nonconstantdifferentiable function on R with g(0) = g(2) = 0. Then the value of y(2) is
|
Samarth Singh answered |
y'(x) + y(x) g'(x) = g(x) g'(x)
⇒ eg(x) y'(x) + eg(x) g'(x) y(x) = eg(x) g(x) g'(x)
Let f : [-1, 2] → [0, ∞) be a continuous function such that f(x) = f(1 - x) for all x ε[-1, 2]. Let 
and R2 be the area of the region bounded by y = f(x), x = -1, x = 2, and the x-axis. Then- a)R1 = 2R2
- b)R1 = 3R2
- c)2R1 = R2
- d)3R1 = R2
Correct answer is option 'C'. Can you explain this answer?
Let f : [-1, 2] → [0, ∞) be a continuous function such that f(x) = f(1 - x) for all x ε[-1, 2]. Let and R2 be the area of the region bounded by y = f(x), x = -1, x = 2, and the x-axis. Then
and R2 be the area of the region bounded by y = f(x), x = -1, x = 2, and the x-axis. Thena)
R1 = 2R2
b)
R1 = 3R2
c)
2R1 = R2
d)
3R1 = R2
|
Prasenjit Sen answered |
The number of hexagonal faces that are present in a truncated octahedron is
Correct answer is '8'. Can you explain this answer?
The number of hexagonal faces that are present in a truncated octahedron is
|
|
Divya Menon answered |
Truncated Octahedron and Hexagonal Faces:
The truncated octahedron is a polyhedron with 14 faces, 36 edges, and 24 vertices. It is created by truncating an octahedron by cutting off its corners. This results in a solid shape with hexagonal and square faces.
Number of Hexagonal Faces:
- The truncated octahedron has a total of 8 hexagonal faces.
- Each hexagonal face is formed by truncating the corners of the original octahedron.
- Since there are 8 corners in an octahedron, each corner truncation results in a hexagonal face.
- Therefore, the truncated octahedron has 8 hexagonal faces in total.
In conclusion, the number of hexagonal faces present in a truncated octahedron is 8.
The truncated octahedron is a polyhedron with 14 faces, 36 edges, and 24 vertices. It is created by truncating an octahedron by cutting off its corners. This results in a solid shape with hexagonal and square faces.
Number of Hexagonal Faces:
- The truncated octahedron has a total of 8 hexagonal faces.
- Each hexagonal face is formed by truncating the corners of the original octahedron.
- Since there are 8 corners in an octahedron, each corner truncation results in a hexagonal face.
- Therefore, the truncated octahedron has 8 hexagonal faces in total.
In conclusion, the number of hexagonal faces present in a truncated octahedron is 8.
(Matrix-Match Type)This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with ONE or MORE statement(s) given in Column II. Q. One mole of a monatomic gas is taken through a cycle ABCDA as shown in the P-V diagram. Column II give the characteristics involved in the cycle. Match them with each of the processes given in Column I.
- a)(A) → (p, r, t)(B) → (p, r)(C) → (q, s)(D) → (r, t)
- b)(A) → ( t)(B) → (p, r)(C) → (q, r)(D) → (r, a)
- c)(A) → (p, r, )(B) → (p, r, s)(C) → (q, s)(D) → (p, r, t)
- d)(A) → (r, t)(B) → (q, r)(C) → (s)(D) → ( t)
Correct answer is option 'A'. Can you explain this answer?
(Matrix-Match Type)
This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with ONE or MORE statement(s) given in Column II.
Q. One mole of a monatomic gas is taken through a cycle ABCDA as shown in the P-V diagram. Column II give the characteristics involved in the cycle. Match them with each of the processes given in Column I.
a)
(A) → (p, r, t)
(B) → (p, r)
(C) → (q, s)
(D) → (r, t)
b)
(A) → ( t)
(B) → (p, r)
(C) → (q, r)
(D) → (r, a)
c)
(A) → (p, r, )
(B) → (p, r, s)
(C) → (q, s)
(D) → (p, r, t)
d)
(A) → (r, t)
(B) → (q, r)
(C) → (s)
(D) → ( t)
|
|
Anagha Reddy answered |
Process A → B → Isobaric compression
Process B → C → Isochoric process
Process C → D → Isobaric expansion
Process D → A → Polytropic with TA = TD
Process B → C → Isochoric process
Process C → D → Isobaric expansion
Process D → A → Polytropic with TA = TD
For the first order reaction
2N2O5(g) → 4NO2(g) + O2(g)- a)the concentration of the reactant decreases exponentially with time
- b)the half-life of the reaction decreases with increasing temperature
- c)the half-life of the reaction depends on the initial concentration of the reactant
- d)the reaction proceeds to 99.6% completion in eight half-life duration
Correct answer is option 'A,B,D'. Can you explain this answer?
For the first order reaction
2N2O5(g) → 4NO2(g) + O2(g)
2N2O5(g) → 4NO2(g) + O2(g)
a)
the concentration of the reactant decreases exponentially with time
b)
the half-life of the reaction decreases with increasing temperature
c)
the half-life of the reaction depends on the initial concentration of the reactant
d)
the reaction proceeds to 99.6% completion in eight half-life duration
|
Nisha Sen answered |
For first order reaction
[A] = [A]0e–kt
Hence concentration of [NO2] decreases exponentially.
Hence concentration of [NO2] decreases exponentially.
Also, t1/2 =
. Which is independent of concentration and t1/2 decreases with the increase of
temperature.
. Which is independent of concentration and t1/2 decreases with the increase oftemperature.
Oxidation states of the metal in the minerals haematite and magnetite, respectively, are- a)II, III in haematite and III in magnetite
- b)II, III in haematite and II in magnetite
- c)II in haematite and II, III in magnetite
- d)III in haematite and II, III in magnetite
Correct answer is option 'D'. Can you explain this answer?
Oxidation states of the metal in the minerals haematite and magnetite, respectively, are
a)
II, III in haematite and III in magnetite
b)
II, III in haematite and II in magnetite
c)
II in haematite and II, III in magnetite
d)
III in haematite and II, III in magnetite
|
|
Hansa Sharma answered |
Haematite : Fe2O3 : 2x + 3 × (-2) = 0
x =3
Magnetite : Fe3O4 [an equimolar mixture of FeO and Fe2O3]
FeO : x – 2 = 0 ⇒ x = 2
Fe2O3 : x = 3
x =3
Magnetite : Fe3O4 [an equimolar mixture of FeO and Fe2O3]
FeO : x – 2 = 0 ⇒ x = 2
Fe2O3 : x = 3
A value of b for which the equationsx2 + bx - 1 = 0x2 + x + b = 0,have one root in common is- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
A value of b for which the equations
x2 + bx - 1 = 0
x2 + x + b = 0,
have one root in common is
a)
b)
c)
d)
|
|
Anjali Sharma answered |
x2 + bx - 1 = 0
x2 + x + b = 0 … (1)
Common root is
(b - 1) x - 1 - b = 0
where each of a, b, and c is either ω or ω2. Then the number of distinct matrices in the set S is
and the
If P(T) denotes the probability of occurrence of the event T,
SECTION-IV (Total Marks : 16)(Matrix-Match Type)This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with ONE or MORE statement(s) given in Column II.Q. Match the statements given in Column I with the values given in Column II
- a)(A) → (p)(B) → (p)(C) → (r)(D) → (t)
- b)(A) → (q)(B) → (p)(C) → (s)(D) → (t)
- c)(A) → (r)(B) → (p)(C) → (q)(D) → (t)
- d)(A) → (s)(B) → (p)(C) → (q)(D) → (r)
Correct answer is option 'B'. Can you explain this answer?
SECTION-IV (Total Marks : 16)
(Matrix-Match Type)
This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with ONE or MORE statement(s) given in Column II.
Q. Match the statements given in Column I with the values given in Column II
a)
(A) → (p)
(B) → (p)
(C) → (r)
(D) → (t)
b)
(A) → (q)
(B) → (p)
(C) → (s)
(D) → (t)
c)
(A) → (r)
(B) → (p)
(C) → (q)
(D) → (t)
d)
(A) → (s)
(B) → (p)
(C) → (q)
(D) → (r)
|
|
Snehal Sharma answered |
then the number of point(s) in S lying inside the smaller part is
Let ω = eiπ/3, and a, b, c, x, y, z be non-zero complex numbers such that
a + b + c = x
a + bω + cω2 = y
a + bω2 + cω = z.
Correct answer is '3'. Can you explain this answer?
Let ω = eiπ/3, and a, b, c, x, y, z be non-zero complex numbers such that
a + b + c = x
a + bω + cω2 = y
a + bω2 + cω = z.
a + b + c = x
a + bω + cω2 = y
a + bω2 + cω = z.
|
|
Megha Ahuja answered |
The expression may not attain integral value for all a, b, c
If we consider a = b = c, then
x = 3a
SECTION-III (Total Marks : 24)(Integer Answer Type)This section contains 6 questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9.Enter only the numerical value in the space provided below.Q. Let 
be three given vectors. If 
and 
then the value of 
is
Correct answer is '9'. Can you explain this answer?
SECTION-III (Total Marks : 24)
(Integer Answer Type)
This section contains 6 questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9.
Enter only the numerical value in the space provided below.
Q. Let be three given vectors. If and then the value of is
be three given vectors. If and then the value of is
|
Maitri Das answered |
Passing H2S gas into a mixture of Mn2+, Ni2+, Cu2+ and Hg2+ ions in an acidified aqueous solution precipitates- a)CuS and HgS
- b)MnS and CuS
- c)MnS and NiS
- d)NiS and HgS
Correct answer is option 'A'. Can you explain this answer?
Passing H2S gas into a mixture of Mn2+, Ni2+, Cu2+ and Hg2+ ions in an acidified aqueous solution precipitates
a)
CuS and HgS
b)
MnS and CuS
c)
MnS and NiS
d)
NiS and HgS
|
|
Sneha Pillai answered |
H2S in presence of aqueous acidified solution precipitates as sulphide of Cu and Hg apart from Pb+2, Bi+3, Cd+2, As+3, Sb+3 and Sn+2.
Let (x, y) be any point on the parabola y2 = 4x. Let P be the point that divides the line segment from (0, 0)
to (x, y) in the ratio 1 : 3. Then the locus of P is- a)x2 = y
- b)y2 = 2x
- c)y2 = x
- d)x2 = 2y
Correct answer is option 'C'. Can you explain this answer?
Let (x, y) be any point on the parabola y2 = 4x. Let P be the point that divides the line segment from (0, 0)
to (x, y) in the ratio 1 : 3. Then the locus of P is
to (x, y) in the ratio 1 : 3. Then the locus of P is
a)
x2 = y
b)
y2 = 2x
c)
y2 = x
d)
x2 = 2y
|
Hrishikesh Singh answered |
y2 = 4x and Q will lie on it
(4k)2 = 4 ´ 4h
k2 = h
y2 = x (replacing h by x and k by y)
(4k)2 = 4 ´ 4h
k2 = h
y2 = x (replacing h by x and k by y)
SECTION – II (Total Marks : 16)(Multiple Correct Answer(s) Type)This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of
which ONE OR MORE may be correct.Q. Two solid spheres A and B of equal volumes but of different densities dA and dB are connected by a string. They are fully immersed in a fluid of density dF. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if- a)dA < dF
- b)dB > dF
- c)dA > dF
- d)dA + dB = 2dF
Correct answer is option 'A,C,D'. Can you explain this answer?
SECTION – II (Total Marks : 16)
(Multiple Correct Answer(s) Type)
This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of
which ONE OR MORE may be correct.
which ONE OR MORE may be correct.
Q. Two solid spheres A and B of equal volumes but of different densities dA and dB are connected by a string. They are fully immersed in a fluid of density dF. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if
a)
dA < dF
b)
dB > dF
c)
dA > dF
d)
dA + dB = 2dF
|
|
Gauri Rane answered |
A thin ring of mass 2 kg and radius 0.5 m is rolling without on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision
- a)the ring has pure rotation about its stationary CM.
- b)the ring comes to a complete stop.
- c)friction between the ring and the ground is to the left.
- d)there is no friction between the ring and the ground.
Correct answer is option 'C'. Can you explain this answer?
A thin ring of mass 2 kg and radius 0.5 m is rolling without on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision
a)
the ring has pure rotation about its stationary CM.
b)
the ring comes to a complete stop.
c)
friction between the ring and the ground is to the left.
d)
there is no friction between the ring and the ground.
|
|
Anjali Sharma answered |
During collision friction is impulsive and immediately after collision the ring will have a clockwise angular
velocity hence friction will be towards left.
velocity hence friction will be towards left.
Match the statements given in Column I with the intervals/union of intervals given in Column II
- a)(A) → (s)(B) → (t)(C) → (r)(D) → (r)
- b)(A) → (r)(B) → (t)(C) → (s)(D) → (q)
- c)(A) → (p)(B) → (q)(C) → (r)(D) → (s)
- d)(A) → (s)(B) → (p)(C) → (r)(D) → (q)
Correct answer is option 'A'. Can you explain this answer?
Match the statements given in Column I with the intervals/union of intervals given in Column II
a)
(A) → (s)
(B) → (t)
(C) → (r)
(D) → (r)
b)
(A) → (r)
(B) → (t)
(C) → (s)
(D) → (q)
c)
(A) → (p)
(B) → (q)
(C) → (r)
(D) → (s)
d)
(A) → (s)
(B) → (p)
(C) → (r)
(D) → (q)
|
|
Anjali Sharma answered |
Column I shows four systems, each of the same length L, for producing standing waves. The lowest
possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as
λf. Match each system with statements given in Column II describing the nature and wavelength of the
standing waves.
- a)(A) → (p, t)(B) → (p, r)(C) → (q, r)(D) → (r)
- b)(A) → (q, t)(B) → (s)(C) → (r, s)(D) → (q, r)
- c)(A) → (q, t)(B) → (r, s)(C) → (s)(D) → (p, q, r)
- d)(A) → (p, t)(B) → (p, s)(C) → (q, s)(D) → (q, r)
Correct answer is option 'D'. Can you explain this answer?
Column I shows four systems, each of the same length L, for producing standing waves. The lowest
possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as
λf. Match each system with statements given in Column II describing the nature and wavelength of the
standing waves.
possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as
λf. Match each system with statements given in Column II describing the nature and wavelength of the
standing waves.
a)
(A) → (p, t)
(B) → (p, r)
(C) → (q, r)
(D) → (r)
b)
(A) → (q, t)
(B) → (s)
(C) → (r, s)
(D) → (q, r)
c)
(A) → (q, t)
(B) → (r, s)
(C) → (s)
(D) → (p, q, r)
d)
(A) → (p, t)
(B) → (p, s)
(C) → (q, s)
(D) → (q, r)
|
|
Anilchoudhary answered |
D
SECTION – II (Total Marks : 16)(Multiple Correct Answer(s) Type)This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of
which ONE OR MORE may be correct.Q. 
- a)f(x) is continuous at x = - π/2
- b)f(x) is not differentiable at x = 0
- c)f(x) is differentiable at x = 1
- d)f(x) is differentiable at x = -3/2
Correct answer is option 'A,B,C,D'. Can you explain this answer?
SECTION – II (Total Marks : 16)
(Multiple Correct Answer(s) Type)
This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of
which ONE OR MORE may be correct.
which ONE OR MORE may be correct.
Q.
a)
f(x) is continuous at x = - π/2
b)
f(x) is not differentiable at x = 0
c)
f(x) is differentiable at x = 1
d)
f(x) is differentiable at x = -3/2
|
Aarav Roy answered |
Clearly, f (x) is not differentiable at x = 0 as f´(0-) = 0 and f´(0+) = 1.
f (x) is differentiable at x = 1 as f' (1–) = f'(1+) = 1.
f (x) is differentiable at x = 1 as f' (1–) = f'(1+) = 1.
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