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Questions and Answers
The angle, θ which mass m2 makes with the vertical is approximately
The angle, θ which mass m2 makes with the vertical is approximately
A horizontal disk of moment of inertia 4.25 kg – m2 with respect to its axis of symmetry is spinning counter clockwise at 15 revolutions per second about its axis. A second disk of moment of inertia 1.80 kg – m2 with respect to its axis of symmetry is spinning clockwise at 25 revolutions per second about the same axis and is dropped on top of the first disk. The new angular velocity of the system as viewed from above is close to
A horizontal disk of moment of inertia 4.25 kg – m2 with respect to its axis of symmetry is spinning counter clockwise at 15 revolutions per second about its axis. A second disk of moment of inertia 1.80 kg – m2 with respect to its axis of symmetry is spinning clockwise at 25 revolutions per second about the same axis and is dropped on top of the first disk. The new angular velocity of the system as viewed from above is close to
A boy standing on top of a tower of height 85 m throws a ball vertically upward with a certain speed. If 5.25 seconds later he hears the ball hitting the ground, then the speed with which the boy threw the ball is
A boy standing on top of a tower of height 85 m throws a ball vertically upward with a certain speed. If 5.25 seconds later he hears the ball hitting the ground, then the speed with which the boy threw the ball is
For a diode connected in parallel with a resistor, which is the most likely current (I) - voltage (V) characteristic?
For a diode connected in parallel with a resistor, which is the most likely current (I) - voltage (V) characteristic?
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The speed of an object when it returns to the surface of the plane is?
The speed of an object when it returns to the surface of the plane is?
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In the given circuit with identical inductors and resistors, the currents through the three resistors immediately after the key is switched off are?
In the given circuit with identical inductors and resistors, the currents through the three resistors immediately after the key is switched off are?
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The number of ordered pairs (x, y) of real numbers that satisfy the simultaneous equations x + y^2 = x^2 + y = 12 is
The number of ordered pairs (x, y) of real numbers that satisfy the simultaneous equations x + y^2 = x^2 + y = 12 is
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If z is a complex number satisfying |z^3 + z^-3| ≤ 2, then the maximum possible value of |z + z^–1| is
If z is a complex number satisfying |z^3 + z^-3| ≤ 2, then the maximum possible value of |z + z^–1| is
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The maximum temperature attained in the circular cycle of an ideal gas is closest to?
The maximum temperature attained in the circular cycle of an ideal gas is closest to?
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The heats of formation of NF3 and NCl3 in kJ mol⁻¹, respectively, closest to are?
The heats of formation of NF3 and NCl3 in kJ mol⁻¹, respectively, closest to are?
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The largest perfect square that divides 20143 – 20133 + 20123 – 20113 + ….+ 23 – 13 is
The largest perfect square that divides 20143 – 20133 + 20123 – 20113 + ….+ 23 – 13 is
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The ratio K1/K2 when the initial concentrations and degree of dissociation are the same for X = 2Y and Z = P + Q is?
The ratio K1/K2 when the initial concentrations and degree of dissociation are the same for X = 2Y and Z = P + Q is?
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Suppose OABC is a rectangle in the xy-plane where O is the origin and A, B lie on the parabola y = x^2. Then C must lie on the curve
Suppose OABC is a rectangle in the xy-plane where O is the origin and A, B lie on the parabola y = x^2. Then C must lie on the curve
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If R^2 = 2r^2, then ∠AOB equals
If R^2 = 2r^2, then ∠AOB equals
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The shortest distance from the origin to a variable point on the sphere (x - 2)^2 + (y - 3)^2 + (z - 6)^2 = 1 is
The shortest distance from the origin to a variable point on the sphere (x - 2)^2 + (y - 3)^2 + (z - 6)^2 = 1 is
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The number of real numbers λ for which a certain trigonometric equality holds is
The number of real numbers λ for which a certain trigonometric equality holds is
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Suppose ABCDEF is a hexagon such that AB = BC = CD = 1 and DE = EF = FA = 2. If the vertices A, B, C, D, E, F are concyclic, the radius of the circle passing through them is
Suppose ABCDEF is a hexagon such that AB = BC = CD = 1 and DE = EF = FA = 2. If the vertices A, B, C, D, E, F are concyclic, the radius of the circle passing through them is
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Let p(x) be a polynomial such that p(x) – p’(x) = x^n, where n is a positive integer. Then p(0) equals
Let p(x) be a polynomial such that p(x) – p’(x) = x^n, where n is a positive integer. Then p(0) equals
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The value of the limit lim[x->0] 6/(x^2 * sin(x)) is
The value of the limit lim[x->0] 6/(x^2 * sin(x)) is
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What is the most abundant transition metal in the human body?
What is the most abundant transition metal in the human body?
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The moral conductivities of HCI, NaCl, CH3COOH, and CH3COONa at infinite dilution follow the order:
The moral conductivities of HCI, NaCl, CH3COOH, and CH3COONa at infinite dilution follow the order:
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The spin only magnetic moment of [ZCl4] is 3.87 BM where Z is:
The spin only magnetic moment of [ZCl4] is 3.87 BM where Z is:
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If α-D-Glucose is dissolved in water and kept for a few hours, the major constituent(s) present in the solution is (are):
If α-D-Glucose is dissolved in water and kept for a few hours, the major constituent(s) present in the solution is (are):
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The pH of 1N aqueous solutions of HCl, CH3COOH, and HCOOH follows the order:
The pH of 1N aqueous solutions of HCl, CH3COOH, and HCOOH follows the order:
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The major product of the reaction is ___.
The major product of the reaction is ___.
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Schottky defect in a crystal arises due to:
Schottky defect in a crystal arises due to:
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What is x if x = 50 + 7^(1/3) - 50 - 7^(1/3)?
What is x if x = 50 + 7^(1/3) - 50 - 7^(1/3)?
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For the equation 1 + x + x^2 = a0 + a1x + a2x^2 + a3x^3 + ... + a4028x^4028, how are the variables A, B, and C related?
For the equation 1 + x + x^2 = a0 + a1x + a2x^2 + a3x^3 + ... + a4028x^4028, how are the variables A, B, and C related?
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Match the following mathematics terms with the correct descriptions:
Match the following mathematics terms with the correct descriptions:
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The angle, 𝜃 which mass m2 makes with the vertical is approximately
The angle, 𝜃 which mass m2 makes with the vertical is approximately
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A boy throws a ball vertically upward from a tower of height 85 m. If the ball hits the ground 5.25 seconds later, what was the speed with which the boy threw the ball?
A boy throws a ball vertically upward from a tower of height 85 m. If the ball hits the ground 5.25 seconds later, what was the speed with which the boy threw the ball?
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In a Young's Double Slit experiment using monoenergetic electrons, if the electrons are accelerated by a potential 4U, how does the fringe width change?
In a Young's Double Slit experiment using monoenergetic electrons, if the electrons are accelerated by a potential 4U, how does the fringe width change?
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In a circuit, the voltmeter reads 36 V between points A and B, 39 V between A and C, and 25 V between B and D. What will the voltmeter read when connected between points A and D?
In a circuit, the voltmeter reads 36 V between points A and B, 39 V between A and C, and 25 V between B and D. What will the voltmeter read when connected between points A and D?
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The Lewis acid strength of BBr3, BCl3, and BF3 is in the order
The Lewis acid strength of BBr3, BCl3, and BF3 is in the order
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What is the most abundant transition metal in the human body?
What is the most abundant transition metal in the human body?
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The moral conductivities of HCI, NaCl, CH3COOH, and CH3COONa at infinite dilution follow which order?
The moral conductivities of HCI, NaCl, CH3COOH, and CH3COONa at infinite dilution follow which order?
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The spin-only magnetic moment of [ZCl4] is 3.87 BM where Z is?
The spin-only magnetic moment of [ZCl4] is 3.87 BM where Z is?
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If α - D - Glucose is dissolved in water and kept for a few hours, the major constituent(s) present in the solution is?
If α - D - Glucose is dissolved in water and kept for a few hours, the major constituent(s) present in the solution is?
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The pH of 1N aqueous solutions of HCI, CH3COOH and HCOOH follows which order?
The pH of 1N aqueous solutions of HCI, CH3COOH and HCOOH follows which order?
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Schottky defect in a crystal arises due to?
Schottky defect in a crystal arises due to?
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The number of ordered pairs (x, y) of real numbers that satisfy the simultaneous equations x + y^2 = x^2 + y = 12 is:
The number of ordered pairs (x, y) of real numbers that satisfy the simultaneous equations x + y^2 = x^2 + y = 12 is:
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If z is a complex number satisfying |z^3 + z^(-3)| ≤ 2, then the maximum possible value of |z + z^(-1)| is:
If z is a complex number satisfying |z^3 + z^(-3)| ≤ 2, then the maximum possible value of |z + z^(-1)| is:
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The largest perfect square that divides 20143 – 20133 + 20123 – 20113 + ….+ 2^3 – 1^3 is:
The largest perfect square that divides 20143 – 20133 + 20123 – 20113 + ….+ 2^3 – 1^3 is:
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Suppose OABC is a rectangle in the xy-plane where O is the origin and A, B lie on the parabola y = x^2. Then C must lie on the curve:
Suppose OABC is a rectangle in the xy-plane where O is the origin and A, B lie on the parabola y = x^2. Then C must lie on the curve:
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In a specific configuration with two circles C1 and C2, if R^2 = 2r^2, then angle AOB is:
In a specific configuration with two circles C1 and C2, if R^2 = 2r^2, then angle AOB is:
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The shortest distance from the origin to a variable point on the sphere (x - 2)^2 + (y - 3)^2 + (z - 6)^2 = 1 is:
The shortest distance from the origin to a variable point on the sphere (x - 2)^2 + (y - 3)^2 + (z - 6)^2 = 1 is:
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The number of real numbers λ for which the equality sin(λα)/sin(α) - cos(λα)/cos(α) = λ - 1 holds for all real α which are not integral multiples of π/2 is:
The number of real numbers λ for which the equality sin(λα)/sin(α) - cos(λα)/cos(α) = λ - 1 holds for all real α which are not integral multiples of π/2 is:
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Suppose ABCDEF is a hexagon such that AB = BC = CD = 1 and DE = EF = FA = 2. If the vertices A, B, C, D, E, F are concyclic, the radius of the circle passing through them is:
Suppose ABCDEF is a hexagon such that AB = BC = CD = 1 and DE = EF = FA = 2. If the vertices A, B, C, D, E, F are concyclic, the radius of the circle passing through them is:
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Let p(x) be a polynomial such that p(x) – p'(x) = xn, where n is a positive integer. Then p(0) equals:
Let p(x) be a polynomial such that p(x) – p'(x) = xn, where n is a positive integer. Then p(0) equals:
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Evaluate the limit of (6/x^2) * (x/sin(x)) as x approaches 0:
Evaluate the limit of (6/x^2) * (x/sin(x)) as x approaches 0:
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Among all sectors of a fixed perimeter, choose the one with the maximum area. Then the angle at the center of this sector is:
Among all sectors of a fixed perimeter, choose the one with the maximum area. Then the angle at the center of this sector is:
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The speed of an object when it returns to the surface of the plane is?
The speed of an object when it returns to the surface of the plane is?
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In the circuit shown, the currents through the three resistors immediately after the key is switched off are?
In the circuit shown, the currents through the three resistors immediately after the key is switched off are?
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The maximum temperature attained in the circular cycle of the ideal gas is close to?
The maximum temperature attained in the circular cycle of the ideal gas is close to?
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The heats of formation of NF3 and NCI3 are closest to?
The heats of formation of NF3 and NCI3 are closest to?
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The geometry and the number of unpaired electrons of [MnBr4]2-, respectively, are?
The geometry and the number of unpaired electrons of [MnBr4]2-, respectively, are?
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The standard cell potential for Zn Zn2+ Cu2+ Cu is 1.10V. When the cell is completely discharged, the ratio log[Zn2+]/[Cu2+] is closest to?
The standard cell potential for Zn Zn2+ Cu2+ Cu is 1.10V. When the cell is completely discharged, the ratio log[Zn2+]/[Cu2+] is closest to?
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In the reaction x, y, and z are?
In the reaction x, y, and z are?
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An organic compound having molecular formula C2H6O undergoes oxidation to produce X, which contains 40% carbon, 6.7% hydrogen, and 53.3% oxygen. The molecular formula of the compound X is?
An organic compound having molecular formula C2H6O undergoes oxidation to produce X, which contains 40% carbon, 6.7% hydrogen, and 53.3% oxygen. The molecular formula of the compound X is?
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The most abundant transition metal in the human body is?
The most abundant transition metal in the human body is?
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The moral conductivities at infinite dilution of HCI, NaCI, CH3COOH, and CH3COONa follow which order?
The moral conductivities at infinite dilution of HCI, NaCI, CH3COOH, and CH3COONa follow which order?
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The spin only magnetic moment of [ZCl4] is 3.87 BM where Z is?
The spin only magnetic moment of [ZCl4] is 3.87 BM where Z is?
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If α-D-Glucose is dissolved in water and kept for a few hours, the major constituent(s) present in the solution is (are)?
If α-D-Glucose is dissolved in water and kept for a few hours, the major constituent(s) present in the solution is (are)?
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The pH of 1N aqueous solutions of HCI, CH3COOH, and HCOOH follows the order?
The pH of 1N aqueous solutions of HCI, CH3COOH, and HCOOH follows the order?
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The angle, θ which mass m2 makes with the vertical is approximately
The angle, θ which mass m2 makes with the vertical is approximately
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A boy standing on top of a tower of height 85 m throws a ball vertically upward. If he hears the ball hitting the ground 5.25 seconds later, what was the speed with which the boy threw the ball?
A boy standing on top of a tower of height 85 m throws a ball vertically upward. If he hears the ball hitting the ground 5.25 seconds later, what was the speed with which the boy threw the ball?
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For a diode connected in parallel with a resistor, what is the most likely current (I) - voltage (V) characteristic?
For a diode connected in parallel with a resistor, what is the most likely current (I) - voltage (V) characteristic?
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When a point charge Q rotates uniformly in a vertical circle aligned along the magnetic axis of the earth, at what angular speed ω will the effective magnetic field at the center of the circle be reduced to zero?
When a point charge Q rotates uniformly in a vertical circle aligned along the magnetic axis of the earth, at what angular speed ω will the effective magnetic field at the center of the circle be reduced to zero?
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The speed of an object when it returns to the surface of the plane is given by the formula: $rac{2GM}{5R}$. What is the correct answer choice for this question?
The speed of an object when it returns to the surface of the plane is given by the formula: $rac{2GM}{5R}$. What is the correct answer choice for this question?
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In the circuit shown, the currents through the resistors immediately after the key is switched off are: 2I upwards, I downwards, and I downwards. What is the correct answer choice?
In the circuit shown, the currents through the resistors immediately after the key is switched off are: 2I upwards, I downwards, and I downwards. What is the correct answer choice?
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For the reaction N2 + 3X2 -> 2NX, the heats of formation of NF3 and NCI3 are closest to: (-226 kJ mol–1, +467 kJ mol–1). What is the correct answer choice?
For the reaction N2 + 3X2 -> 2NX, the heats of formation of NF3 and NCI3 are closest to: (-226 kJ mol–1, +467 kJ mol–1). What is the correct answer choice?
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The equilibrium constants for the reactions X = 2Y and Z = P + Q are K1 and K2, respectively. If the initial concentrations and the degree of dissociation of X and Z are the same, what is the correct ratio: K1 / K2?
The equilibrium constants for the reactions X = 2Y and Z = P + Q are K1 and K2, respectively. If the initial concentrations and the degree of dissociation of X and Z are the same, what is the correct ratio: K1 / K2?
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The standard cell potential for Zn Zn2+ Cu2+ Cu is 1.10V. When the cell is completely discharged, log[Zn2+]/[Cu2+] is closest to which value?
The standard cell potential for Zn Zn2+ Cu2+ Cu is 1.10V. When the cell is completely discharged, log[Zn2+]/[Cu2+] is closest to which value?
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In the reaction shown, x = Mg, dry ether; y = CO2; z = dil. HCl. What is the correct answer choice?
In the reaction shown, x = Mg, dry ether; y = CO2; z = dil. HCl. What is the correct answer choice?
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An organic compound with molecular formula C2H6O undergoes oxidation to produce X. The molecular formula of X with 40% carbon, 6.7% hydrogen, and 53.3% oxygen is:
An organic compound with molecular formula C2H6O undergoes oxidation to produce X. The molecular formula of X with 40% carbon, 6.7% hydrogen, and 53.3% oxygen is:
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The maximum number of cyclic isomers of a compound with molecular formula C3H2Cl2 is:
The maximum number of cyclic isomers of a compound with molecular formula C3H2Cl2 is:
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The volume vs. temperature graph for 1 mole of an ideal gas is given. The pressure of the gas at X, Y, and Z, respectively, are:
The volume vs. temperature graph for 1 mole of an ideal gas is given. The pressure of the gas at X, Y, and Z, respectively, are:
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When MnO2 is fused with KOH and oxidized in air, it gives a dark green compound X. In acidic solution, X undergoes disproportionation to give a purple compound Y and MnO2. What are the compounds X and Y, respectively?
When MnO2 is fused with KOH and oxidized in air, it gives a dark green compound X. In acidic solution, X undergoes disproportionation to give a purple compound Y and MnO2. What are the compounds X and Y, respectively?
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A metal (X) dissolves in dilute HCl and dilute NaOH to liberate H2. Addition of NH4Cl and NH4OH to an HCl solution of X produces Y as a precipitate. The species X and Y, respectively, are:
A metal (X) dissolves in dilute HCl and dilute NaOH to liberate H2. Addition of NH4Cl and NH4OH to an HCl solution of X produces Y as a precipitate. The species X and Y, respectively, are:
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The number of ordered pairs(x, y) of real numbers that satisfy the simultaneous equations x + y^2 = x^2 + y = 12 is
The number of ordered pairs(x, y) of real numbers that satisfy the simultaneous equations x + y^2 = x^2 + y = 12 is
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If z is a complex number satisfying |z^3 + z^(-3)| ≤ 2, then the maximum possible value of |z + z^(-1)| is
If z is a complex number satisfying |z^3 + z^(-3)| ≤ 2, then the maximum possible value of |z + z^(-1)| is
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The largest perfect square that divides 20143 – 20133 + 20123 – 20113 + ….+ 23 – 13 is
The largest perfect square that divides 20143 – 20133 + 20123 – 20113 + ….+ 23 – 13 is
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Suppose OABC is a rectangle in the xy-plane where O is the origin and A, B lie on the parabola y = x^2. Then C must lie on the curve
Suppose OABC is a rectangle in the xy-plane where O is the origin and A, B lie on the parabola y = x^2. Then C must lie on the curve
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Circle C1 and C2 of radii r and R respectively, touch each other. If R^2 = 2r^2, then angle AOB equals
Circle C1 and C2 of radii r and R respectively, touch each other. If R^2 = 2r^2, then angle AOB equals
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The shortest distance from the origin to a variable point on the sphere (x - 2)^2 + (y - 3)^2 + (z - 6)^2 = 1 is
The shortest distance from the origin to a variable point on the sphere (x - 2)^2 + (y - 3)^2 + (z - 6)^2 = 1 is
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The number of real numbers λ for which the equality sin(λα)cos(λα) / sin(α)cos(α) = λ - 1 holds for all real α which are not integral multiples of π/2 is
The number of real numbers λ for which the equality sin(λα)cos(λα) / sin(α)cos(α) = λ - 1 holds for all real α which are not integral multiples of π/2 is
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Suppose ABCDEF is a hexagon such that AB = BC = CD = 1 and DE = EF = FA = 2. If the vertices A, B, C, D, E, F are concyclic, the radius of the circle passing through them is
Suppose ABCDEF is a hexagon such that AB = BC = CD = 1 and DE = EF = FA = 2. If the vertices A, B, C, D, E, F are concyclic, the radius of the circle passing through them is
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Let p(x) be a polynomial such that p(x) - p'(x) = x^n, where n is a positive integer. Then p(0) equals
Let p(x) be a polynomial such that p(x) - p'(x) = x^n, where n is a positive integer. Then p(0) equals
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The value of the limit lim (6/x^2 * integral from x to 0 of sin t dt) as x approaches 0 is
The value of the limit lim (6/x^2 * integral from x to 0 of sin t dt) as x approaches 0 is
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Among all sectors of a fixed perimeter, choose the one with maximum area. Then the angle at the center of this sector is
Among all sectors of a fixed perimeter, choose the one with maximum area. Then the angle at the center of this sector is
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Define a function f: by f(x) = max {|x|, |x - 1|, …, |x - 2n|}, where n is a fixed natural number. The integral of f from 0 to 2n is
Define a function f: by f(x) = max {|x|, |x - 1|, …, |x - 2n|}, where n is a fixed natural number. The integral of f from 0 to 2n is
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If p(x) is a cubic polynomial with p(1) = 3, p(0) = 2, and p(-1) = 4, then the integral of p(x) from -1 to 1 is
If p(x) is a cubic polynomial with p(1) = 3, p(0) = 2, and p(-1) = 4, then the integral of p(x) from -1 to 1 is
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Let x > 0 be a fixed real number. Then the integral from 0 to infinity of e^(-t)|x - t| dt is equal to
Let x > 0 be a fixed real number. Then the integral from 0 to infinity of e^(-t)|x - t| dt is equal to
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An urn contains marbles of four colors: red, white, blue, and green. When four marbles are drawn without replacement, the following events are equally likely. The smallest total number of marbles satisfying the given condition is
An urn contains marbles of four colors: red, white, blue, and green. When four marbles are drawn without replacement, the following events are equally likely. The smallest total number of marbles satisfying the given condition is
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There are 6 boxes labeled B1, B2, …, B6. In each trial, two fair dice D1, D2 are thrown. If D1 shows j and D2 shows k, then j balls are put into the box Bk. After n trials, what is the probability that B1 contains at most one ball?
There are 6 boxes labeled B1, B2, …, B6. In each trial, two fair dice D1, D2 are thrown. If D1 shows j and D2 shows k, then j balls are put into the box Bk. After n trials, what is the probability that B1 contains at most one ball?
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Let a = 6i - 3j - 6k and d = i + j + k. Suppose that a = b + c where b is parallel to d and c is perpendicular to d. Then c is
Let a = 6i - 3j - 6k and d = i + j + k. Suppose that a = b + c where b is parallel to d and c is perpendicular to d. Then c is
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If log(3x - 1)(x - 2) = log(9x^2 - 6x + 1)^(2x^2 - 10x - 2), then x equals
If log(3x - 1)(x - 2) = log(9x^2 - 6x + 1)^(2x^2 - 10x - 2), then x equals
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Suppose a, b, c are positive integers such that 2a + 4b + 8c = 328. Then the value of a + 2b + 3c / abc is equal to
Suppose a, b, c are positive integers such that 2a + 4b + 8c = 328. Then the value of a + 2b + 3c / abc is equal to
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The sides of a right-angled triangle are integers. The length of one of the sides is 12. The largest possible radius of the incircle of such a triangle is
The sides of a right-angled triangle are integers. The length of one of the sides is 12. The largest possible radius of the incircle of such a triangle is
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Study Notes
Mathematics
- Simultaneous Equations: Solve simultaneous equations x + y2 = x2 + y = 12.
- Complex Numbers: Find the maximum possible value of |z + z^-1| given |z3 + z - 3| ≤ 2.
- Perfect Squares: Find the largest perfect square that divides 20143 - 20133 + ... + 23 - 13.
- Parabola: Find the equation of the curve on which point C lies given that OABC is a rectangle, A and B lie on the parabola y = x2, and C lies on the curve.
Calculus
- Limits: Evaluate the limit of (6/x) / sin(x) as x approaches 0.
- Polynomials: Find the value of p(0) where p(x) - p'(x) = xn.
- Integrals: Find the value of the integral of f(x) from 0 to 1, where f(x) = max{|x|, |x - 1|, ..., |x - 2n|}.
- Optimization: Maximize the area of a sector with fixed perimeter.
Probability
- Random Variables: Find the probability that a box contains at most one ball given that the probability of drawing a red, white, blue, or green marble is equally likely.
Physics
- Mechanics: Find the coefficient of kinetic friction between a box and a table given that the box slides 1m in 2 seconds.
- Nuclear Physics: Find the energy released when 1μg of Carbon-11 decays into Boron-11, given that the energy released per decay is 0.96 MeV.
- Electromagnetism: Find the angular velocity of a system consisting of two disks spinning in the same direction.
Chemistry
- Radioactivity: Find the half-life of Carbon-11 given that the decay formula is 11C → 11B + e+ + νe.
Others
- Electronics: Find the current-voltage characteristic of a diode connected in parallel with a resistor.
- Black Holes: Find the dimensions of the area of a black hole in terms of the universal gravitational constant G, its mass M, and the speed of light C.Here are the study notes for the provided text:
Chemistry
- Lewis acid strength of BBr3, BCI3, and BF3 is in the order of BF3 > BCI3 > BBr3.
- O2- is isoelectronic with Zn2+.
- Bond angles in methane, ammonia, and water are respectively 109.5, 104.5, and 107.1 degrees.
- The oxidation state of Mn in the reaction of hydrogen peroxide with potassium permanganate in alkaline medium is +2.
- The rate constant of a chemical reaction at a very high temperature will approach the Arrhenius frequency factor.
- The reducing strength of metals follows the order of Cr > Pb > Ag > Cu.
- Optical activity can be exhibited by 2-bromobutane.
- The structure of the polymer obtained by the reaction is III.
- The major product of the reaction between CH3CH2ONa and (CH3)3CCI in ethanol is CH3CH2OC(CH3)3.
- When H2S gas is passed through a hot acidic aqueous solution containing AI3+, Cu2+, Pb2+, and Ni2+, a precipitate is formed which consists of PbS and CuS.
- The electronic configuration of an element with the largest difference between the 1st and 2nd ionization energies is 1s2 2s2 2p6.
- The order of electronegativity of carbon is sp > sp2 > sp3 in hybridized states.
- The most abundant transition metal in the human body is iron.
- The moral conductivities of HCl, NaCl, CH3COOH, and CH3COONa at infinite dilution follow the order of HCl > CH3COOH > NaCl > CH3COONa.
Mathematics
- The value of x = 50 + 7 - (50 - 7) is a rational number, but not an integer.
- The coefficients of the equation 1 + x + x2 = a0 + a1x + a2x2 + ... follow a specific pattern.
- The slope of the incident beam in the given graph is 13/8.
- The series C(θ) = ∑(n=0 to ∞)cos(nθ)/n! has certain properties.
- The limit of a specific function as x approaches 0 is 2.
- The probability that 1 is an element of A, when A is a subset of Xn, is p, and the probability that 2 is an element of A is q, where p > q and p - q = 1/6.
Physics
- The height to which water should be poured in a cubical vessel so that an object at the bottom can be seen is 16 cm.
- The moments of inertia of a non-uniform circular disc about four mutually perpendicular tangents are related to the distance of the center of mass of the disc from its geometrical center.
- The stress on a horizontal steel railroad track on a hot summer day is 6.6 × 10^7 Pa.
- Electromagnetic waves can travel from air to a medium with a refractive index very nearly equal to zero.
- The ratio of the masses of two small metal balls connected by strings of equal length to a fixed point is close to 0.58.
- Diamagnetic particles scattered on a horizontal table accumulate around regions such as C.
- The distance between the vertex and the center of mass of a uniform solid planar circular segment of angular size θ and radius R is R(4sin(θ/2))/(3θ).
- The speed of an object when it returns to the surface of a planet is √(2GM/R).
- The currents through the three resistors in the given circuit are I downwards, I downwards, and I downwards.
Miscellaneous
- There are 60 questions in the provided text, divided into three parts: Chemistry, Mathematics, and Physics.### Cyclic Isomers
- The maximum number of cyclic isomers (positional and optical) of a compound having molecular formula C3H2CI2 is 4.
Ideal Gas
- The volume vs. temperature graph of 1 mole of an ideal gas is given, and the pressure of the gas at X, Y, and Z, respectively, are 0.328, 0.820, and 0.820 atm.
Oxidation of MnO2
- When fused with KOH and oxidized in air, MnO2 gives a dark green compound X.
- In acidic solution, X undergoes disproportionation to give an intense purple compound Y and MnO2.
- Compound X is K2MnO4, and compound Y is KMnO4.
Metal Reaction
- A metal (X) dissolves both in dilute HCl and dilute NaOH to liberate H2.
- Addition of NH4Cl and excess NH4OH to an HCl solution of X produces Y as a precipitate.
- Y is also produced by adding NH4Cl to the NaOH solution of X.
- The species X and Y, respectively, are Al and Al(OH)3.
FIITJEE Answer Keys
- The answer keys for KVPY 2015 are provided for questions 1-110.
KVPY – XII Class - Stream – SB/SX
Part I – Mathematics
- Question 1: Simultaneous equations x + y² = x² + y = 12
- Number of ordered pairs (x, y) of real numbers that satisfy the equations
- Question 2: Complex number satisfying |z³ + z - 3| ≤ 2
- Maximum possible value of |z + z⁻¹|
- Question 3: Largest perfect square that divides 20143 - 20133 + ... + 23 - 13
- Largest perfect square that divides the given expression
- Question 4: Parabola y = x²
- Coordinates of point C where the parabola intersects the line λ, which is parallel to the line joining the centres of C₁ and C₂
- Question 5: Circle C₁ and C₂ of radii r and R respectively, touch each other
- Angle ∠AOB where λ is tangent to C₁ at P and intersects C₂ at A and B
- Question 6: Shortest distance from the origin to a variable point on the sphere (x - 2)² + (y - 3)² + (z - 6)² = 1
- Shortest distance from the origin to the sphere
- Question 7:Equality sin(λα) cos(λα) = λ - 1, holds for all real α which are not integral multiples of π/2
- Number of real numbers λ for which the equality holds
- Question 8: Hexagon ABCDEF with sides AB = BC = CD = 1 and DE = EF = FA = 2
- Radius of the circle passing through the vertices A, B, C, D, E, F
- Question 9: Polynomial p(x) such that p(x) - p'(x) = xⁿ, where n is a positive integer
- Value of p(0)
- Question 10: Limit lim (x → 0) (6/x²) sin x
- Value of the limit
- Question 11: Maximum area sector
- Angle at the centre of the sector with maximum area
- Question 12: Function f(x) = max{|x|, |x - 1|, ..., |x - 2n|}
- Integral ∫ f(x) dx from 0 to 2n
- Question 13: Cubic polynomial p(x) with p(1) = 3, p(0) = 2 and p(-1) = 4
- Integral ∫ p(x) dx from -1 to 1
- Question 14: Integral ∫ |x - t| dt from 0 to ∞
- Value of the integral
- Question 15: Urn contains marbles of four colours
- Smallest total number of marbles satisfying the given condition
- Question 16: Probability that B₁ contains at most one ball
- Probability expression
- Question 17: Vectors a = 6i - 3j - 6k and d = i + j + k
- Vector c, where a = b + c, b is parallel to d and c is perpendicular to d
- Question 18: Equality log(3x - 1) = log(9x² - 6x + 2)
- Value of x
- Question 19: Positive integers a, b, c such that 2a + 4b + 8c = 328
- Value of (a + 2b + 3c) / abc
- Question 20: Right-angled triangle with integer sides, one of which is 12
- Largest possible radius of the incircle of such a triangle### Chemistry
- The Lewis acid strength of BBr3, BCI3, and BF3 is in the order of BF3 < BCI3 < BBr3.
- O2- is isoelectronic with Zn2+.
- The bond angles (in degrees) in methane, ammonia, and water are respectively closest to 109.5, 104.5, 107.1.
- In alkaline medium, the reaction of hydrogen peroxide with potassium permanganate produces a compound in which the oxidation state of Mn is +3.
- The rate constant of a chemical reaction at a very high temperature will approach the Arrhenius frequency factor.
- The reducing strength of the metals follows the order of Cr > Pb > Ag > Cu based on their standard reduction potentials.
- The molecule that can exhibit optical activity is 2-bromobutane.
- The structure of the polymer obtained by a reaction is a branched polymer.
- The major product of the reaction between CH3CH2ONa and (CH3)3CCI in ethanol is CH3CH2OC(CH3)3.
Mathematics
- The limit of a function involving the series expansion of cos(θ) is related to the limit of a function involving the series expansion of sin(θ).
- The smallest α for which f(x) ≥ 0 for all x > 0 is 3.
- The graph of y = 2x - 4x^3 has a line y = c such that the areas of the regions marked I and II are equal.
- The probability that 1 ∈ A is greater than the probability that 2 ∈ A, and the difference between the two probabilities is 1/6.
- The remainder when the determinant of a 3x3 matrix is divided by 5 is 1.
Physics
- The moments of inertia of a non-uniform circular disc about four mutually perpendicular tangents are related to the distance of the center of mass of the disc from its geometrical center.
- The stress on a horizontal steel railroad track on a hot summer day is 6.6 × 10^7 Pa.
- Electromagnetic waves emanating from a point A in air are incident on a rectangular block of material M and emerge from the other side.
- The ratio of the masses of two small metal balls connected by strings of equal length to a fixed point is close to 3.0.
- The distance between the vertex and the center of mass of a uniform solid planar circular segment of angular size θ and radius R is given by R sin(θ/2) / θ.
Let me know if you would like me to clarify or expand on any of these points!### Questions and Answers
- The maximum number of cyclic isomers (positional and optical) of a compound having molecular formula C3H2CI2 is 4.
Ideal Gas Volume vs Temperature Graph
- The pressure of the gas at X, Y, and Z, respectively, are 3.28, 8.20, 3.28 atm.
Compound X and Y
- MnO2 when fused with KOH and oxidized in air gives a dark green compound X.
- In acidic solution, X undergoes disproportionation to give an intense purple compound Y and MnO2.
- The compound X and Y, respectively, are K2MnO4 and KMnO4.
Metal X and Y
- Metal X dissolves both in dilute HCI and dilute NaOH to liberate H2.
- Addition of NH4CI and excess NH4O to an HCI solution of X produces Y as a precipitate.
- Y is also produced by adding NH4CI to the NaOH solution of X.
- The species X and Y, respectively, are Zn and Zn(OH)2.
KVPY 2015 Official Answer Keys
- The answer keys for questions 1-110 are provided, with the correct answers labeled A, B, C, or D.
KVPY – XII Class - Stream – SB/SX
Mathematics
- There are 15 questions in the mathematics section, each with 4 options.
- Questions cover various topics, including algebra, geometry, and calculus.
- Question 1 involves solving a system of equations, while question 2 deals with complex numbers.
- Question 3 asks for the largest perfect square that divides a given expression.
- Question 4 involves a parabola and a rectangle, while question 5 deals with circles and tangents.
- Question 6 asks for the shortest distance from the origin to a point on a sphere.
- Question 7 involves trigonometry and equalities.
- Question 8 deals with a hexagon and circles.
- Question 9 involves polynomials and derivatives.
- Question 10 asks for the value of a limit.
- Question 11 deals with the maximum area of a sector.
- Question 12 involves a function and an integral.
- Question 13 asks for the value of an integral.
- Question 14 deals with an exponential function and an integral.
- Question 15 involves probability and marbles.
Physics
- There are 25 questions in the physics section, each with 4 options.
- Questions cover various topics, including mechanics, electromagnetism, and thermodynamics.
- Question 21 involves friction and a box sliding off a table.
- Question 22 deals with nuclear physics and energy release.
- Question 23 involves a composite body and center of mass.
- Question 24 deals with two spherical objects and strings.
- Question 25 involves a disk and angular momentum.
- Question 26 involves a ball thrown upward from a tower.
- Question 27 deals with a diode and current-voltage characteristics.
- Question 28 involves an interference pattern and electrons.
- Question 29 deals with a point charge and a magnetic field.
- Question 30 involves a bottle of water on the moon.
- Question 31 deals with a simple pendulum and its time period.
- Question 32 involves a circuit and an ac voltmeter.
- Question 33 deals with a donor atom in a semiconductor.
- Question 34 involves an ideal gas and isobaric lines.
- Question 35 deals with a metallic ring and a magnetic field.
- Question 36 involves a black hole and its area.
- Question 37 deals with an infrared source and photon flux.
- Question 38 involves a wire bent in a polygonal shape and a magnetic field.
- Question 39 deals with sound intensity and decibel levels.
- Question 40 involves a wire, a block, and a rigid wall.### Chemistry Questions
- Question 41: The Lewis acid strength of BBr3, BCI3, and BF3 is in the order of BF3 < BCI3 < BBr3.
- Question 42: O2– is isoelectronic with Mg2+.
- Question 43: The H-C-H, H-N-H, and H-O-H bond angles in methane, ammonia, and water are closest to 109.5°, 107.1°, and 104.5°, respectively.
- Question 44: In alkaline medium, the reaction of hydrogen peroxide with potassium permanganate produces a compound in which the oxidation state of Mn is +3.
Optics and Magnetism
- Question 91: A cubical vessel has opaque walls. An observer can see only the wall CD but not the bottom. Nearly to what height should water be poured so that she can see an object placed at the bottom at a distance of 10 cm from the corner C?
Thermodynamics
- Question 88: The figure shows a portion of the graph y = 2x – 4x3. The line y = c is such that the areas of the regions marked I and II are equal. If a, b are the x-coordinates of A, B respectively, then a + b equals 3/7.
Physics
- Question 92: The moments of inertia of a non-uniform circular disc (of mass M and radius R) about four mutually perpendicular tangents AB, BC, CD, DA are I1, I2, I3, and I4, respectively.
- Question 93: A horizontal steel railroad track has a length of 100 m when the temperature is 25°C. The track is constrained from expanding or bending. The stress on the track on a hot summer day, when the temperature is 40°C, is 6.6 × 10^7 Pa.
Mathematics
- Question 81: Let x = (50 + 7)^(-1/3). Then x = 2.
- Question 82: Let 1 + x + x2 = a0 + a1x + a2x2 + ... + a4028x4028. Then A = a0 - a3 + a6 - ... + a4026, B = a1 - a4 + a7 - ... - a4027, C = a2 - a5 + a8 - ... + a4028.### Molecular Formula and Isomers
- The maximum number of cyclic isomers (positional and optical) of a compound having molecular formula C3H2CI2 is 4.
Ideal Gas and Pressure
- The volume vs. temperature graph of 1 mole of an ideal gas is given, with points X, Y, and Z.
- The pressure of the gas at X, Y, and Z, respectively, are 0.328 atm, 0.820 atm, and 0.820 atm.
Manganese Compounds
- MnO2 when fused with KOH and oxidized in air gives a dark green compound X.
- In acidic solution, X undergoes disproportionation to give an intense purple compound Y and MnO2.
- The compound X is K2MnO4 and the compound Y is KMnO4.
Metal Reactivity
- A metal (X) dissolves both in dilute HCl and dilute NaOH to liberate H2.
- Addition of NH4CI and excess NH4O to an HCl solution of X produces Y as a precipitate.
- Y is also produced by adding NH4CI to the NaOH solution of X.
- The species X is Al and the species Y is Al(OH)3.
KVPY 2015 Official Answer Keys
- The answer keys for the KVPY 2015 examination are provided, with answers for questions 1-110.
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This quiz contains mathematics questions for KVPY XII Class Stream SB/SX, held on 1st November 2015.
