16 Questions
In the given circuit, if the potential difference across the capacitor of capacitance 2C at steady state becomes 3E, what is the emf E (in Volts) of the connected battery?
2E
In a circuit with ideal battery and initially uncharged capacitors, what are the currents through the switch immediately afterward and after a long time when the switch S is closed?
$\frac{3V}{R}$, $0$
For a circuit shown with 2A current, equipotential points A and B, and batteries with 1Ω internal resistance, what is the emf E (in Volts) of the circuit?
14
If the angle of rotation of the solution for a plane polarized light is +32° at t = 0, -12° at t = ∞, and +20° at t = 50 minutes, which of the following statements is true?
The reaction involves inversion of optical nature of the solution
Boiling point of an aqueous solution of benzoic acid is 101°C. If a solution of equal molality was prepared by dissolving benzoic acid in benzene, which statement is correct?
Boiling point of the solution of benzoic acid in benzene is 77.4°C
Which statement regarding defects in crystalline solids is incorrect?
Metal deficiency defects always cause an increase in density and electrical conductivity of the ionic solids
An insulating hemispherical shell of radius R is fixed and charged uniformly over its curved surface with charge per unit area σ. The flat, circular base of the shell is uncharged. Which of these options is/are correct?
The work done in moving a point charge +q from infinity to O is $\frac{σRq}{2ε_0}$
Three identical uncharged capacitors, each of capacitance C, are connected in a circuit with an ideal battery and an ammeter of resistance R as shown. Which of these options is/are correct?
The current in the ammeter immediately after S1 is closed is $\frac{4R}{1}$
Three ideal batteries of emf E1, E2, and E3 and three resistances r1, r2, and r3 are connected as shown. Currents I1, I2, and I3 flow in the three branches along the directions indicated. Which of these options is/are correct?
VP - VQ = 4V
If Rolle’s theorem is applicable to the function f defined by f(x) = {1, x = 1 for x ∈ [−2, 2]; x, x > 1}, then:
λ = a + b
Find a, b, c such that lim [axe^x - b log(1 + x) + c * x * e^(-x)] / (x * sin x) = 2. The value is _____
3
Find the value of [sin x / x - sin x] as x approaches 0. The value of [n - 3] is ____.
2
If f(2x + 1) = 4x^2 + 14x, find the sum of the squares of roots of the equation f(x) = 0.
49
Find the value of ab if y = a log |x| + bx^2 + x has its extreme values at x = -1 and x = 2.
10
For how many integral values of k, where k ∈ (−15, 15), does the function y = x^3 - 3(7 - k) x^2 - 3(9 - k^2) x + 2, x > 0 have a point of maximum?
16
If f(x) is twice differentiable and f''(0) = p, then lim [2f(x) - 3f(2x) + f(4x)] / x^2 as x approaches 0 is kp. The value of k is ____.
1
Study Notes
Exam Instructions
- The exam consists of 3 subjects: Physics, Chemistry, and Mathematics.
- Each subject has 3 sections: Section 1 (Multiple Choice Questions), Section 2 (Multiple Correct Answers Type), and Section 3 (Numerical Value Type Questions).
Marking Scheme
- Section 1: +3 marks for correct answer, 0 marks for no answer, -1 mark for incorrect answer.
- Section 2:
- +4 marks for all correct options.
- +3 marks for 3 correct options.
- +2 marks for 2 correct options.
- +1 mark for 1 correct option.
- -2 marks for incorrect answer.
- Section 3: +4 marks for correct answer, 0 marks for no answer.
Sections Breakdown
Subject I: Physics
- Section 1: 6 Multiple Choice Questions.
- Section 2: 6 Multiple Correct Answers Type Questions.
- Section 3: 6 Numerical Value Type Questions.
Subject II: Chemistry
- Section 1: 6 Multiple Choice Questions.
- Section 2: 6 Multiple Correct Answers Type Questions.
- Section 3: 6 Numerical Value Type Questions.
Note: The notes only cover the instructions and guidelines for the exam, and do not provide answers to the questions.Here are the study notes for the text:
- Chemistry Section*
- Question 3: Buckminster fullerene (C-60 molecule) has a truncated icosahedron structure.
- Question 4: Gas phase thermal decomposition of di-tert-butyl peroxide follows first-order kinetics.
- Question 5: Vapour pressure of pure water at 25°C is 80 torr, and that of an aqueous solution is 75 torr at the same temperature.
- Question 6: Percentage packing efficiency of smaller cubes in an F.C.C arrangement is to be found.
- Question 7: Rate constants for various reactions are given, and Arrhenius factors for each reaction are 10^12 min^-1.
- Question 8: Statements about colligative properties of ideal aqueous solutions are given.
- Question 9: Properties of F.C.C unit cells are given, including packing efficiency and types of voids.
- Question 10: Acid catalysed hydrolysis of (+) sucrose is a first-order reaction.
- Question 11: Boiling point of an aqueous solution of benzoic acid is 101°C, and boiling points of solutions of benzoic acid in water and benzene are compared.
- Question 12: Defects in crystalline solids are discussed, including Frenkel and Schottky defects.
- Question 13: Thermal decomposition of gaseous HI follows a given rate law.
- Question 14: Boiling point of a liquid X is 127°C at 1 atm pressure, and enthalpy of vaporization is 40 kJ/mol.
- Question 15: In diamond cubic structure, effective number of constituent particles per unit cell are p, and the number of voids per unit cell occupied by carbon atoms are q.
- Question 16: First-order gas phase thermal decomposition of N2O5 occurs as given, and half-life of the reaction is to be found.
- Question 17: Osmotic pressure of a diluted mixture is to be found.
- Question 18: Titanium oxide has a metal deficiency defect, and the ratio of Ti^4+ to Ti^3+ is given.
- Mathematics Section*
- Question 1: Range of a function f(x) is to be found.
- Question 2: Slope of a line tangent to a curve is to be found.
- Question 3: Limit of a function as x approaches 0 is to be found.
- Question 4: Inverse of a function is to be found.
- Question 5: A polynomial has exactly one maximum or minimum.
- Question 6: Normal to a curve cuts the curve again at a given point.
- Question 7: Function f(x) is strictly increasing in a given interval.
- Question 8: Complete set of values of 'a' for which f(x) is strictly increasing is to be found.
- Question 9: Each critical point of f(x) is a point of extremum when given conditions are met.
- Question 10: Function f(x) is continuous and differentiable in a given interval.
- Question 11: Integral of a function is to be found.
- Question 12: Rolle's theorem is applicable to a function f(x) defined piecewise.
- Question 13: Limit of a function as x approaches 0 is to be found.
- Question 14: Value of a limit is to be found.
- Question 15: Sum of the squares of roots of an equation is to be found.
- Question 16: Value of ab is to be found.
- Question 17: Number of integral values of k for which a function has a point of maximum is to be found.
- Question 18: Value of k is to be found.
This quiz describes the exam pattern for 10th class, divided into three subjects: Physics, Chemistry, and Mathematics, with multiple choice and multiple correct answers type questions.
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