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IMPORTANT BOARD QUESTIONS – MATH

👉 Jump to CBSE Class 11 Exam Prep Question Bank

Unit I – Some Basic Concepts of Chemistry (10 Questions)

1. Define mole and explain its importance.
2. Calculate empirical formula from % composition (C=40, H=6.7, O=53.3).
3. Case Study: Two labs prepare 1 M NaOH differently. Which is more accurate?
4. Why is limiting reagent concept important in industrial chemistry?
5. Numerical: Calculate molarity of solution with 5 g NaOH in 250 mL.
6. Explain difference between empirical and molecular formula.
7. Why is Avogadro’s number considered a “bridge constant”?
8. Case Study: A chemist dilutes concentrated H₂SO₄. Explain safety precautions.
9. Numerical: Calculate % purity of sample containing 8 g Na₂CO₃ neutralizing 0.1 M HCl.
10. Why is mass conserved in chemical reactions?

Unit II – Structure of Atom (12 Questions)

11. Derive energy expression for hydrogen atom (Bohr’s model).
12. Why does 4s orbital fill before 3d?
13. Explain Hund’s rule with example.
14. Case Study: Compare spectra of hydrogen and helium discharge tubes.
15. Why is ionization energy of oxygen lower than nitrogen?
16. Numerical: Calculate wavelength of electron transition n=3 → n=2 in hydrogen.
17. Explain significance of quantum numbers.
18. Why is Aufbau principle violated in Cr and Cu?
19. Case Study: Explain flame test colors of Na⁺ and K⁺ using electronic transitions.
20. Why is He stable with 2 electrons but H₂ unstable with 2 protons?
21. Explain difference between orbit and orbital.
22. Numerical: Calculate energy of photon with λ=400 nm.

Unit III – Classification of Elements & Periodicity (8 Questions)

23. Why is ionization enthalpy of oxygen lower than nitrogen?
24. Explain diagonal relationship between Li and Mg.
25. Case Study: Predict metallic/non-metallic character of element X (Z=15).
26. Why does atomic radius decrease across a period?
27. Explain anomalies in electron affinity trends across halogens.
28. Why is fluorine more electronegative than chlorine?
29. Case Study: Compare reactivity of alkali metals with water.
30. Predict properties of element with Z=37.

Unit IV – Chemical Bonding & Molecular Structure (10 Questions)

31. Explain shape of NH₃ vs H₂O using VSEPR.
32. Why is BF₃ planar but NH₃ pyramidal?
33. Case Study: Compare bond angles in CH₄, NH₃, H₂O.
34. Explain hybridization in CO₂.
35. Why is resonance important in benzene?
36. Case Study: Explain polarity of HCl vs HF.
37. Why is ionic bond stronger in MgO than NaCl?
38. Explain hydrogen bonding in ice.
39. Case Study: Predict geometry of SO₄²⁻.
40. Why is CO₂ non-polar but H₂O polar?

Unit V – Thermodynamics (12 Questions)

41. State First Law of Thermodynamics.
42. Why is enthalpy of neutralization constant for strong acid–strong base?
43. Numerical: Calculate ΔH for combustion of CH₄ using bond enthalpies.
44. Case Study: Why does sweating cool the body? Explain with entropy.
45. Define Gibbs free energy.
46. Why is ΔG negative for spontaneous reactions?
47. Numerical: Calculate ΔG at 298 K for ΔH=–40 kJ, ΔS=–100 J/K.
48. Case Study: Explain refrigeration in terms of thermodynamics.
49. Why is evaporation endothermic?
50. Explain Hess’s law with example.
51. Numerical: Calculate enthalpy change for formation of NaCl from Na and Cl₂.
52. Why is entropy higher in gases than solids?

Unit VI – Equilibrium (10 Questions)

53. Derive relation between Kc and Kp.
54. Numerical: Calculate pH of 0.01 M HCl.
55. Case Study: Industrial Haber process — effect of pressure and temperature.
56. Explain Le Chatelier’s principle with example.
57. Why is weak acid dissociation constant small?
58. Numerical: Calculate solubility of AgCl given Ksp=1.6×10⁻¹⁰.
59. Case Study: Explain buffer action in blood.
60. Why is ionic product of water temperature dependent?
61. Numerical: Calculate equilibrium constant for N₂ + 3H₂ ⇌ 2NH₃ at given concentrations.
62. Explain common ion effect with example.

Unit VII – Redox Reactions (6 Questions)

63. Balance: Fe²⁺ + MnO₄⁻ → Fe³⁺ + Mn²⁺.
64. Case Study: Explain corrosion of iron in terms of redox.
65. Why is KMnO₄ a strong oxidizing agent?
66. Numerical: Calculate cell potential for Zn/Cu cell.
67. Explain difference between oxidation number and valency.
68. Case Study: Explain bleaching action of Cl₂.

Unit VIII – Organic Chemistry: Basic Principles (14 Questions)

69. Write IUPAC names of given compounds.
70. Explain difference between structural and geometrical isomerism.
71. Case Study: A chemist separates mixture using chromatography. Explain principle.
72. Why is carbon tetravalent?
73. Explain resonance in benzene.
74. Case Study: Explain purification of organic compounds using distillation.
75. Why is functional group important in classification?
76. Explain difference between homolytic and heterolytic bond fission.
77. Case Study: Explain principle of crystallization in purification.
78. Why is benzene aromatic?
79. Explain inductive effect with example.
80. Case Study: Explain difference between electrophiles and nucleophiles with examples.
81. Why is nomenclature important in organic chemistry?
82. Explain hyperconjugation with example.

Unit IX – Hydrocarbons (12 Questions)

83. Explain mechanism of electrophilic addition in ethene.
84. Why is benzene more stable

    👉 Jump to CBSE Class 11 Maths Exam Prep Question Bank

    📘 Plus One Mathematics – Important NCERT Questions
    🔗 Open Exam Prep Portal

    Chapter 1: Sets

    • Examples: 2, 5, 6(ii), 7, 9, 11, 13, 18, 22, 24
    • Exercise 1.1: 1(iii), 1(vi), 1(viii), 2, 3(iii), 3(iv), 4(ii), 4(iv), 5(iii), 5(vi)
    • Exercise 1.2: 1(i), 2(iii), 2(iv), 3(iv), 3(v), 4(iii), 4(iv), 6
    • Exercise 1.3: 1(ii), 1(iv), 1(v), 2(i), 2(iii), 2(v), 3, 4(ii), 4(iv), 5(ii), 5(iii), 6(ii), 6(iv), 8
    • Exercise 1.4: 1(iv), 3, 4, 5, 8(ii), 9, 12
    • Exercise 1.5: 1(iii), 1(vi), 3(iv), 3(ix), 4, 5, 7

    Chapter 2: Relations & Functions

    • Examples: 3, 4, 6, 8, 9, 11(ii), 11(iii), 14, 15, 17, 20, 21, 22
    • Exercise 2.1: 2, 4(i), 4(iii), 7, 8, 9, 10
    • Exercise 2.2: 1, 3, 4, 5, 8
    • Exercise 2.3: 1(ii), 1(iii), 2(ii), 5(i), 5(iii)

    Chapter 3: Trigonometric Functions

    • Examples: 2, 5, 6, 7, 9, 11, 16, 17, 18, 20, 21, 22
    • Exercise 3.1: 1(ii), 1(iv), 2(ii), 2(iv), 4, 6
    • Exercise 3.2: 1, 3, 7, 9, 10
    • Exercise 3.3: 1, 2, 3, 5(i), 6, 8, 9, 11, 13, 16, 18, 21, 22, 23

    Chapter 4: Complex Numbers

    • Examples: 2(ii), 5, 6(ii), 8
    • Exercise 4.1: 3, 6, 8, 10, 12, 14

    Chapter 5: Linear Inequalities

    • Examples: 2, 4, 8, 9, 11, 13
    • Exercise 5.1: 4, 6, 8, 10, 11, 16, 17, 20, 22, 23, 25

    Chapter 6: Permutations & Combinations

    • Examples: 3, 4, 8, 9, 11, 12(i), 14, 16, 19, 20, 21, 22, 23, 24
    • Exercise 6.1: 1(ii), 2, 4
    • Exercise 6.2: 1(ii), 4, 5(ii)
    • Exercise 6.3: 2, 4, 7(i), 9, 10, 11
    • Exercise 6.4: 1, 4, 5, 6

    Chapter 7: Binomial Theorem

    • Examples: 2, 3
    • Exercise 7.1: 2, 4, 7, 10, 12, 13, 14

    Chapter 8: Sequences & Series

    • Examples: 3, 5, 7, 9, 10, 12, 13
    • Exercise 8.1: 2, 7, 9, 12, 14
    • Exercise 8.2: 3, 5(b), 7, 9, 11, 14, 16, 17, 18, 22, 23, 26, 27, 29, 30, 32

    Chapter 9: Straight Lines

    • Examples: 1(c), 2, 3, 4, 7(ii), 9, 12, 13, 15, 16
    • Exercise 9.1: 2, 3(ii), 5, 7, 8, 9, 10
    • Exercise 9.2: 1, 4, 6, 8, 10, 13, 14, 16, 17, 18
    • Exercise 9.3: 1(ii), 2(iii), 4, 5(i), 7, 8, 11, 13, 15, 16, 17

    Chapter 10: Conic Sections

    • Examples: 3, 4, 6, 7, 8, 10, 12, 13, 14(iii), 16, 18, 19
    • Exercise 10.1: 3, 5, 9, 12, 13, 15
    • Exercise 10.2: 2, 3, 5, 6, 8, 10, 12
    • Exercise 10.3: 2, 5, 7, 11, 12, 14, 16, 18, 19
    • Exercise 10.4: 3, 5, 7, 9, 11, 12, 14, 15

    Chapter 11: Introduction to 3D Geometry

    • Examples: 1, 4, 7, 8
    • Exercise 11.1: 3, 4
    • Exercise 11.2: 1(iii), 2, 3(i), 3(ii), 5

    Chapter 12: Limits & Derivatives

    • Examples: 2(ii), 2(iii), 3(i), 3(ii), 4(ii), 7, 10, 13, 15, 17, 19(i), 20(ii), 21(ii), 22(ii)
    • Exercise 12.1: 4, 6, 8, 10, 14, 15, 17, 19, 21, 22, 25, 28, 30, 32
    • Exercise 12.2: 4(i), 4(ii), 7(i), 7(iii), 9(ii), 9(iv), 10, 11(ii), 11(iii), 11(v), 11(vii)

    Chapter 13: Statistics

    • Examples: 3, 5, 6, 7, 9, 12, 14, 16
    • Exercise 13.1: 2, 4, 6, 8, 10, 11
    • Exercise 13.2: 2, 4, 6, 9

    Chapter 14: Probability

    • Examples: 3, 4, 5, 7, 8, 9, 10, 12
    • Exercise 14.1: 2, 4, 5(ii), 6, 7
    • Exercise 14.2: 3(i), 4, 5, 7, 8, 11, 12(ii), 14, 15, 16, 20, 21

    👉 Jump to Class 10 Maths Most Repeated Questions

    Most Repeated Questions – Class 10 Maths (Paul’s Coaching)

    Polynomials

    Q1) If the sum of the zeroes is 1 of the polynomial (k² – 14)x² – 2x – 12, find the value of k.

    Q2) If the sum of zeroes of the quadratic polynomial 3x² – kx + 6 is 3, then find the value of k.

    Q3) Form a quadratic polynomial whose zeroes are 3 + √2 and 3 – √2.

    Q4) Find a quadratic polynomial, the sum and product of whose zeroes are √3 and 1/√3 respectively.

    Q5) Find a quadratic polynomial whose zeroes are (3+15)/5 and (3-15)/5.

    Q6) Find the zeroes of the quadratic polynomial 6x² – 7x – 3 and verify the relationship between the zeroes and the coefficients.

    Real Numbers

    Q1) There are 104 students in class 10 and 96 students in class 9. In a house examination the students are to be evenly seated in parallel rows such that no two adjacent rows are of the same class. Find the maximum number of parallel rows of each class and the number of students in each row.

    Q2) Prove that 5 + √7 is irrational.

    Linear Equations in Two Variables

    Q1) For what value of k, the pair of equations 4x - 3y = 9, 2x + ky = 11 has no solution?

    Q2) Represent graphically: x + 3y = 6, 2x - 3y = 12. Write coordinates where lines intersect y-axis.

    Q3) Solve: a²/x - b²/y = 0 ; a²b/x + b²a/y = a+b.

    Q4) Solve: 10/(x+y) + 2/(x-y) = 4 ; 15/(x+y) - 5/(x-y) = -2.

    Q5) Solve: 141x + 93y = 189 ; 93x + 141y = 45.

    Q6) The sum of the digits of a two-digit number is 8 and the difference with reversed digits is 18. Find the number.

    Q7) The age of the father is twice the sum of the ages of his 2 children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.

    Q8) The taxi charges in a city comprise fixed charges together with the charge for the distance covered. For a journey of 12 km, the charge paid is ₹89 and for 20 km, the charge paid is ₹145. What will a person have to pay for travelling a distance of 30 km?

    Q9) A boat takes 4 hours to go 44 km downstream and it can go 20 km upstream in the same time. Find the speed of the stream and that of the boat in still water.

    Coordinate Geometry

    Q1) Find the ratio in which the y-axis divides the line segment joining the points A(5, -6) and B(-1, -4). Also find the coordinates of the point of division.

    Q2) The points A(4, 7), B(p, 3) and C(7, 3) are the vertices of a right triangle, right-angled at B. Find the value of p.

    Q3) If A(4,3), B(-1, y) and C(3,4) are the vertices of a right triangle ABC, right-angled at A, then find the value of y.

    Q4) If the point P(k-1, 2) is equidistant from the points A(3, k) and B(k, 5), find the values of k.

    Q5) Find a point P on the y-axis which is equidistant from the points A(4, 8) and B(-6, 6). Also find the distance AP.

    Q6) If the points A(x, y), B(3, 6) and C(-3, 4) are collinear, show that x - 3y + 15 = 0.

    Applications of Trigonometry

    Q1) From the top of a 100 m high lighthouse, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

    Q2) The angle of elevation of the top of a vertical tower from a point on the ground is 60°. From another point 10 m vertically above the first, its angle of elevation is 30°. Find the height of the tower.

    Q3) From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of a 10 m high building are 30° and 60° respectively. Find the height of the tower.

    Q4) From the top of a vertical tower, the angles of depression of two cars at an instant are found to be 45° and 60°. If the cars are 100 m apart and are on the same side of the tower, find the height of the tower.

    Q5) The angles of depression of the top and bottom of a 12 m tall building, from the top of a multi-storeyed building are 30° and 60° respectively. Find the height of the multi-storeyed building.

    Q6) The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of depression from the top of the tower of the foot of the hill is 30°. If the tower is 50 m high, find the height of the hill.

    Circles

    Q1) PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the length TP.

    Q2) A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that BD = 8 cm and DC = 6 cm. Find the sides AB and AC.

    Q3) In the figure, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersects XY at A and X'Y' at B. Prove that ∠AOB = 90°.

    Q4) In Figure, a right triangle ABC circumscribes a circle of radius r. If AB = 8 cm and BC = 6 cm, find the value of r.

    Q5) From an external point P, two tangents PT and PS are drawn to a circle with centre O and radius r. If OP = 2r, show that ∠OTS = ∠OST = 30°.

    Q6) In the given figure, PA and PB are tangents to the circle with centre O such that ∠APB = 50°. Write the measure of ∠OAB.

    Q7) In the figure, O is the centre of a circle of radius 5 cm. T is a point such that OT = 13 cm and OT intersects circle at E. If AB is a tangent to the circle at E, find the length of AB.

    Q8) In the figure, two equal circles with centres O and O' touch each other at X. OO' produced meets the circle with centre O' at A. AC is tangent to the circle with centre O at C. O'D ⟂ AC. Find DO'/CO.

    Q9) In the figure, the sides AB, BC and CA of triangle ABC touch a circle with centre O and radius r at P, Q and R respectively. Prove that: (i) AB + CQ = AC + BQ (ii) Area(ΔABC) = ½ (Perimeter of ΔABC) × r.

    Q10) In Fig, two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2∠OPQ.