Q1. Which of the following is an objective of Educational Psychology?
a) To provide knowledge of mental health
b) To understand and deal with the problems of discipline among children
c) To provide guidance for gifted and exceptional children
d) All the above
Answer: d) All the above
Explanation: Educational Psychology addresses mental health, discipline issues, and guidance for gifted children.
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Q2. Among Social adjustment, Social maturity, Social behaviour and Social interaction which one is not a factor influencing social development?
a) Social adjustment
b) Social maturity
c) Social interaction
d) Social behaviour
Answer: d) Social behaviour
Explanation: Social behaviour is a result, not a distinct influencing factor of social development.
Q3. Main causes of emotionality of adolescents are
a) Academic stress and peer pressure
b) Vocational problems, conflicts with family members, and needs of adolescents
c) Lack of social support
d) Media and hormonal changes
Answer: b) Vocational problems, conflicts with family members, and needs of adolescents
Explanation: Emotionality in adolescents arises mainly due to personal and social conflicts.
Q4. Which theory is popularly known as ‘trial and error’ theory of learning?
a) Pavlov’s Classical Conditioning
b) Skinner’s Operant Conditioning
c) Thorndike’s Theory
d) Gestalt Theory
Answer: c) Thorndike’s Theory
Explanation: Thorndike proposed the ‘Trial and Error’ theory of learning through repeated attempts.
Q5. The definition “A real integration of a change in a fact by a cue and anticipation of a future change in affect contingent upon certain actions” is given by
a) B.F. Skinner
b) Piaget
c) McClelland
d) Vygotsky
Answer: c) McClelland
Explanation: McClelland described motivation and behavior change through anticipation and action.
Q6. The development of personality mainly depends on
a) Genetic factors only
b) Environmental factors only
c) Environmental, Physique & Psychological factors
d) Heredity only
Answer: c) Environmental, Physique & Psychological factors
Explanation: Personality is shaped by multiple internal and external factors.
Q7. This tool of personality measurement was developed by Morgan and Murray in 1935
a) Rorschach Inkblot Test
b) Thematic Apperception Test
c) Minnesota Personality Inventory
d) Myers-Briggs Type Indicator
Answer: b) Thematic Apperception Test
Explanation: TAT helps in assessing underlying thoughts through storytelling based on pictures.
Q8. Which of the following statements is false?
a) Who is efficient in his work is mentally healthy
b) Over protecting the child causes abnormal mental health
c) Too much competition in school causes better mental health
d) The teacher who feels insecure is having poor mental health
Answer: c) Too much competition in school causes better mental health
Explanation: Excessive competition increases stress and harms mental health.
Q9. Educational Psychology is a systematic study of educational growth. This definition is given by
a) B.F. Skinner
b) Stephen
c) Piaget
d) Thorndike
Answer: b) Stephen
Explanation: Stephen provided this comprehensive definition of educational psychology.
Q10. Intelligence Quotient (I.Q.) between 80-90 is classified as
a) Average
b) Superior
c) Dullness
d) Genius
Answer: c) Dullness
Explanation: An IQ between 80–90 is considered below average or dull.
Q11. The factors upon which the design of a school depends are
a) Strength of students
b) Educational policy
c) Space, Type of school and finances of school
d) Number of teachers
Answer: c) Space, Type of school and finances of school
Explanation: Physical and economic factors determine school design.
Q12. Time-table of the school develops habit of
a) Creativity
b) Discipline
c) Regular study
d) Punctuality
Answer: d) Punctuality
Explanation: School timetables cultivate a habit of being on time.
Q13. Cumulative record of a pupil contains
a) His I.Q. only
b) Academic performance only
c) Medical record only
d) His I.Q., Attitudes and habit, his school to school record
Answer: d) His I.Q., Attitudes and habit, his school to school record
Explanation: Cumulative records are comprehensive profiles of a student’s development.
Q14. “School is a co-operative society or a society where cooperation is sought.” This definition is given by
a) W.M. Ryburn
b) S.K. Mitra
c) Rousseau
d) John Dewey
Answer: a) W.M. Ryburn
Explanation: Ryburn emphasized the collaborative nature of schooling.
Q15. A Headmaster must have the following qualities:
a) Good teacher
b) Optimistic outlook
c) Firmness and Creativity
d) All the above
Answer: d) All the above
Explanation: An ideal headmaster should be skilled, firm, creative, and positive.
Q16. The activities for aesthetic development of students include
a) Debate and quiz
b) School beautification
c) Sports activities
d) Yoga
Answer: b) School beautification
Explanation: Aesthetic development relates to sense of beauty and design.
Q17. Which of the following is not a function of supervision of schools?
a) Developing curriculum
b) Removing difficulties
c) To plan and formulate policies
d) Linking school with communities
Answer: c) To plan and formulate policies
Explanation: Planning policies is an administrative, not supervisory, function.
Q18. In the field of education, the state government has the following function(s):
a) Planning
b) Supervision
c) Preparing qualified and trained teachers
d) It specifies curriculum for schools of state
Answer: d) It specifies curriculum for schools of state
Explanation: State governments decide the curriculum for schools under their jurisdiction.
Q19. Which statement is false regarding external examination?
a) It suffers from subjectivity in Evaluation
b) It tests the real knowledge of the students
c) It encourages use of guides and cheap notes
d) It has an adverse effect on methods of teaching
Answer: b) It tests the real knowledge of the students
Explanation: External exams often fail to reflect true understanding.
Q20. Indiscipline in schools these days is due to
a) Attitude of students
b) Loss of leadership by teachers
c) Attitude of authorities
d) All the above
Answer: d) All the above
Explanation: Multiple social and institutional factors contribute to indiscipline.
Q21. “No religious instruction shall be provided in any educational institution wholly maintained out of state” is stated in one Constitution in
a) Article 28
b) Article 14
c) Article 30
d) Article 45
Answer: a) Article 28
Explanation: Article 28 prohibits religious instruction in state-funded institutions.
Q22. The Secondary Education Commission appointed by Govt. of India on Sept. 23, 1952 worked under the chairmanship of
a) Dr. S. Radhakrishnan
b) Dr. A. Lakshman Swami Mudaliar
c) Dr. Kothari
d) Maulana Azad
Answer: b) Dr. A. Lakshman Swami Mudaliar
Explanation: He chaired the important commission on secondary education reform.
Q23. Which one was not recommended by Kothari Commission regarding evaluation at the Secondary stage?
a) Certificate given by the Board
b) Establishment of experimental schools
c) Compartmental system
d) Internal assessment
Answer: c) Compartmental system
Explanation: Kothari Commission did not endorse compartment exams.
Q24. “By social education we mean an education for the complete man,” this definition of social education is given by
a) Gandhiji
b) Maulana Abul Kalam Azad
c) Tagore
d) John Dewey
Answer: b) Maulana Abul Kalam Azad
Explanation: He defined social education in terms of holistic development.
Q25. The proposals of NCERT for teacher education in the fifth plan do not include:
a) Raising the admission requirement
b) Emphasis on in-service training
c) Better facilities in teacher education institutions
d) Practical school experience
Answer: a) Raising the admission requirement
Explanation: The Fifth Plan emphasized training and infrastructure, not tougher entry.
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Q26. Which statement is false regarding public schools in India?
a) They are un-Indian in character
b) Undue emphasis is laid on the study of English language
c) They do not compel students to concentrate on cramming
d) They are highly undemocratic and unsocialistic
Answer: c) They do not compel students to concentrate on cramming
Explanation: Public schools often encourage rote learning and cramming.
Q27. The three language formula was evolved by
a) Ministry of Education
b) Kothari Commission
c) Secondary Education Board
d) Central Advisory Board of Education
Answer: d) Central Advisory Board of Education
Explanation: The three-language formula was proposed by CABE.
Q28. In which period did the education of women suffer badly?
a) Vedic period
b) Buddhist period
c) Medieval Muslim period
d) Modern period
Answer: c) Medieval Muslim period
Explanation: Restrictions during this time curtailed female education.
Q29. Causes of slow progress of vocational education according to the Secondary Education Commission (1952-53) include
a) Lack of funds
b) Lack of coordination
c) Lack of expert guidance
d) All of the above
Answer: d) All of the above
Explanation: Multiple systemic issues affected vocational education progress.
Q30. The broad aims of Navodaya Schools do not contain
a) All-round development
b) Admission based on merit
c) To give admission according to capacity to pay
d) Free boarding and lodging
Answer: c) To give admission according to capacity to pay
Explanation: Navodaya Schools are merit-based and free.
Q31. Intervening variable in structure of teaching comprises
a) Educational objectives
b) Teaching strategies
c) Content of Teaching & Strategies
d) Both a and b
Answer: c) Content of Teaching & Strategies
Explanation: These elements mediate between input and outcome in teaching.
Q32. According to B.S. Bloom, education has three poles:
a) Knowledge, Skill, Values
b) Cognitive, Affective, Psychomotor
c) Educational objectives, Change in behaviour, Learning experiences
d) Teaching, Learning, Assessment
Answer: c) Educational objectives, Change in behaviour, Learning experiences
Explanation: Bloom’s taxonomy defines learning in terms of outcomes and experience.
Q33. Educational technology can be conceived as a science of techniques and methods by which goals be realized.” This definition is given by
a) S.S. Chauhan
b) S.K. Mitra
c) Sara Blackwell
d) B.F. Skinner
Answer: b) S.K. Mitra
Explanation: S.K. Mitra emphasized practical strategies in educational technology.
Q34. Programmed Learning is not
a) An instructional strategy
b) An audio-visual aid
c) Based on operant conditioning
d) Self-paced learning
Answer: b) An audio-visual aid
Explanation: Programmed learning is method-based, not a visual medium.
Q35. Scaled down teaching includes
a) To reduce size of lesson
b) To reduce class size
c) To reduce the teaching skill
d) All of the above
Answer: d) All of the above
Explanation: It’s a simplified version of real classroom situations.
Q36. Components of “Skill of probing questions” do not include
a) Prompting
b) Redirecting
c) Seeking further information
d) Testing pupil’s understanding
Answer: d) Testing pupil’s understanding
Explanation: It focuses on deepening thought, not direct evaluation.
Q37. According to Flander’s system for interaction analysis, teacher’s indirect talk does not involve
a) Accepting feelings
b) Praising
c) Encouraging
d) Criticising or justifying
Answer: d) Criticising or justifying
Explanation: Indirect talk avoids negative or judgmental feedback.
Q38. “Action research is the research concerned with school problems carried on by school personnel to improve school practices” is defined by
a) Corey
b) Sara Blackwell
c) Kurt Lewin
d) B.F. Skinner
Answer: b) Sara Blackwell
Explanation: Sara Blackwell emphasized practical application in educational improvement.
Q39. Among the following, which is not a Philosophical Teaching Model?
a) Computer-based teaching model
b) Rule model
c) Insight model
d) Impression model
Answer: a) Computer-based teaching model
Explanation: It is technical, not philosophical.
Q40. The affective purposes are satisfied in the value of
a) Beauty
b) Truth
c) Utility
d) Clarity
Answer: a) Beauty
Explanation: Aesthetic appreciation relates to emotional and affective learning.
Q41. The community influences the child’s growth and development
a) Negatively only
b) Positively only
c) Formally
d) In many ways
Answer: d) In many ways
Explanation: Community affects learning socially, emotionally, and behaviorally.
Q42. What is the ultimate value of science?
a) Beauty
b) Truth
c) Goodness
d) Wealth
Answer: b) Truth
Explanation: Science seeks to uncover objective truths.
Q43. The teachings of Muhammad, the Holy Prophet taught mankind
a) Rules governing social life
b) Rules governing monetary dealing
c) Moral values
d) Ways to govern a government
Answer: c) Moral values
Explanation: His teachings emphasized ethical conduct and spirituality.
Q44. “Value is that which satisfies human desire.” This statement is given by
a) Plato
b) Aristotle
c) W.M. Urban
d) Spencer
Answer: c) W.M. Urban
Explanation: Urban’s value theory links desire with fulfillment.
Q45. The General Assembly of United Nations adopted and proclaimed the Universal Declaration of Human Rights on
a) October 24, 1945
b) December 10, 1948
c) June 26, 1946
d) November 20, 1947
Answer: b) December 10, 1948
Explanation: This marks International Human Rights Day.
Q46. Which complaints are entertained by the National Human Rights Commission?
a) Civil disputes
b) Political matters
c) With regard to review the safeguards under law
d) Tax evasion
Answer: c) With regard to review the safeguards under law
Explanation: NHRC ensures protection of basic rights enshrined in law.
Q47. Who do the social and economic conditions affect in the child considerably?
a) Intelligence
b) Socialisation
c) Health
d) Emotions
Answer: b) Socialisation
Explanation: A child’s behavior and adaptability are shaped socially and economically.
Q48. The dimensional formula for Surface Tension is
a) [M L⁰ T⁻²]
b) [M T⁻²]
c) [M L⁻¹ T⁻²]
d) [M⁰ L² T⁻²]
Answer: a) [M L⁰ T⁻²]
Explanation: Surface tension = Force/Length → MLT⁻² / L = [M L⁰ T⁻²]
Q49. Among Displacement, Distance covered, and Speed, which one can be zero when the particle is in motion for some time?
a) Displacement
b) Distance
c) Speed
d) None of the above
Answer: a) Displacement
Explanation: A round trip ends in zero displacement.
Q50. Two projectiles are fired at different angles with the same magnitude of velocity such that they have the same range. At what angles they might have been projected?
a) 30° and 60°
b) 15° and 75°
c) 45° and 45°
d) 25° and 65°
Answer: d) 25° and 65°
Explanation: Complementary angles give equal ranges for identical speed.
Q51. A cricket player catches a ball of mass 100g moving with a velocity of 25 m/s. If the ball is caught in 0.1 sec, the force exerted on the hand of the player is:
a) 2.5 N
b) 25 N
c) 250 N
d) 0.25 N
Answer: b) 25 N
Explanation: Force = change in momentum / time = (0.1×25)/0.1 = 25 N.
Q52. A circular disc of mass ‘M’ and radius ‘R’ is rotating about its axis with uniform speed ‘v’. What is its kinetic energy?
a) 1/2 Mv²
b) 1/4 Mv²
c) 1/2 Iω²
d) 1/4 Iω²
Answer: b) 1/4 Mv²
Explanation: For rotation, KE = 1/2 Iω²; for a disc, I = 1/2 MR² → KE = 1/4 Mv².
Q53. If the mass and radius of a planet are doubled, then acceleration due to gravity on its surface will become
a) Same
b) Half
c) Double
d) One fourth
Answer: b) Half
Explanation: g ∝ M/R² → (2M)/(2R)² = 2/4 = 1/2.
Q54. The densities of two materials X and Y are in the ratio 1:3. Their specific heats are in the ratio 3:1. If we take same volumes of the two substances, the ratio of their thermal capacities will be:
a) 1:1
b) 1:3
c) 3:1
d) 1:9
Answer: a) 1:1
Explanation: Thermal capacity ∝ density × specific heat → (1×3):(3×1).
Q55. A particle executes SHM with a time period of 2 seconds and amplitude 5 cm. Its maximum velocity will be:
a) 10π cm/sec
b) 5π cm/sec
c) 5 cm/sec
d) 2.5 cm/sec
Answer: b) 5π cm/sec
Explanation: Maximum velocity in SHM is A⋅ωA \cdot \omegaA⋅ω, which equals 5π5\pi5π cm/sec here.
Q56. Fundamental frequency of a Sonometer wire is ‘n’. If its length, diameter, and tension are doubled, the new fundamental frequency will be:
a) √2 n
b) 2n
c) n/√2
d) n/2
Answer: c) n/√2
Explanation: Frequency is inversely proportional to length and directly proportional to the square root of tension and inversely to square root of mass per unit length.
Q57. As one penetrates a uniformly charged conducting sphere, what happens to the electric field strength?
a) Increases
b) Remains constant
c) Becomes zero
d) Decreases
Answer: c) Becomes zero
Explanation: Inside a conductor, electric field is zero.
Q58. The masses of the wires of copper are in the ratio 1:3:5 and their lengths are in the ratio 5:3:1. The ratio of their electrical resistances is:
a) 125:15:1
b) 5:3:1
c) 1:1:1
d) 1:3:5
Answer: a) 125:15:1
Explanation: R = ρL/A; since mass ∝ volume ∝ L × A → A = mass/L, so R ∝ L²/mass.
Q59. Charge carriers in the thermocouple are:
a) Protons
b) Neutrons
c) Electrons
d) Holes
Answer: c) Electrons
Explanation: Electrons flow due to temperature difference in thermocouples.
Q60. A voltmeter has resistance R₀ and range V. What resistance should be connected in series to increase its range to nV?
a) R₀/n
b) nR₀
c) (n-1)R₀
d) (n+1)R₀
Answer: c) (n-1)R₀
Explanation: Series resistance required is (n−1)R₀ to increase range to nV.
Q61. A current ‘i’ passes through a wire of length ‘l’, radius ‘r’ and resistivity ‘ρ’. The rate of heat generated is:
a) i²R
b) i²ρl/(πr²)
c) (i²ρl)/(πr²)
d) (i²r²)/(ρl)
Answer: c) (i²ρl)/(πr²)
Explanation: R = ρl/A = ρl/πr², Heat = i²R.
Q62. A convex lens of focal length 16 cm forms a virtual image of double the size of the object. What is the distance of the object from the lens?
a) 16 cm
b) 8 cm
c) 32 cm
d) 24 cm
Answer: b) 8 cm
Explanation: Using lens and magnification formulas, the object is placed 8 cm from the convex lens to produce a virtual image double its size.
Q63. If R₁ and R₂ are the radii of curvature of a double convex lens, which one will have the largest power?
a) R₁ = R₂ = 10 cm
b) R₁ = R₂ = 5 cm
c) R₁ = 10 cm, R₂ = 20 cm
d) R₁ = 5 cm, R₂ = 10 cm
Answer: b) R₁ = R₂ = 5 cm
Explanation: Smaller radius gives higher curvature and hence more power.
Q64. The luminous flux from a 100 watt electric lamp is 6830 lumen. What is the efficiency of the lamp?
a) 10%
b) 50%
c) 68.3%
d) 6.83%
Answer: d) 6.83%
Explanation: Efficiency = (6830/100×683) = 6.83%.
Q65. What is the nature of path of an electron when it moves in a transverse electric field?
a) Circular
b) Straight line
c) Parabola
d) Ellipse
Answer: c) Parabola
Explanation: Electric force acts like uniform gravity, forming a parabolic path.
Q66. The shortest wavelength of X-Rays emitted from an X-Ray tube depends upon:
a) Current in the tube
b) Nature of gas
c) Voltage applied to tube
d) Material of target
Answer: c) Voltage applied to tube
Explanation: Higher voltage → more energy → shorter wavelength.
Q67. The work function for a photoelectric material is 3.3 eV. The threshold frequency will be equal to:
a) 3 × 10¹⁴ Hz
b) 5 × 10¹⁴ Hz
c) 8 × 10¹⁴ Hz
d) 10 × 10¹⁴ Hz
Answer: c) 8 × 10¹⁴ Hz
Explanation: f = φ/h = 3.3/(6.63×10⁻³⁴) ≈ 8×10¹⁴ Hz.
Q68. The main distinction between conductors, semiconductors and insulators is concerned with:
a) Band gap
b) Number of valence electrons
c) Atomic mass
d) Width of forbidden band
Answer: d) Width of forbidden band
Explanation: The wider the gap, the poorer the conductivity.
Q69. There are 210 members in a club, 100 of them drink tea and 65 drink tea but not coffee. Each member drinks tea or coffee. How many drink coffee?
a) 145
b) 110
c) 100
d) 105
Answer: a) 145
Explanation: Coffee drinkers = 210 – 65 = 145.
Q70. Let f(x) = √(x – 1) and g(x) = √(4 – x²). Then the domain of f∘g is:
a) (−1, 2)
b) [1, 2]
c) (1, 2)
d) [0, 2]
Answer: c) (1, 2)
Explanation: Composite function is defined where g(x) ∈ domain of f, i.e. g(x) ≥ 1.
Q71. If α, β, γ are the cube roots of unity, then (1 + α)(1 – β)(1 – β²) is equal to:
a) 0
b) 1
c) -1
d) 3
Answer: a) 0
Explanation: Since one factor becomes zero due to cube roots of unity relation, the whole expression equals zero.
Q72. The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an A.P. The three numbers are:
a) 8, 16, 32
b) 7, 14, 28
c) 6, 12, 24
d) 9, 18, 36
Answer: a) 8, 16, 32
Explanation: G.P. – (1, 7, 21) = A.P. confirms the answer.
Q73. The number of divisors of the number 36000 is:
a) 72
b) 90
c) 100
d) 120
Answer: b) 90
Explanation: Prime factorization gives exponent pattern (2⁶ × 3² × 5³) → (6+1)(2+1)(3+1) = 7×3×4 = 84.
Q74. The term which is independent of x in the expansion of (x² + 1/x)⁹ is:
a) 84
b) 126
c) 72
d) 108
Final Answer: a) 84
Explanation: The independent term in the expansion is the one where the power of xxx is 0, which occurs at r=6r = 6r=6, giving the term (96)=84\binom{9}{6} = 84(69)=84.
Q75. The sum of the series ∑ (1/((2n−1)·n!)) from n=1 to ∞ is:
a) e
b) 1/2(e − 1/e)
c) ln(2)
d) 1
Answer: b) 1/2(e − 1/e)
Explanation: It is a standard exponential series identity.
Q76. If cos A = 1/7 and cos B = 13/14 (A, B are acute angles), then A − B is equal to:
a) π/6
b) π/3
c) π/4
d) π/2
Answer: b) π/3
Explanation: Based on trigonometric identities and values, A−B = π/3.
Q77. The coordinates of the orthocenter of the triangle whose angular points are (1, 2), (2, 3) and (4, 3) is:
a) (1, 6)
b) (2, 3)
c) (3, 1)
d) (4, 2)
Answer: a) (1, 6)
Explanation: Calculated using intersection of altitudes in coordinate geometry.
Q78. The equation of the circle which passes through the origin and makes intercepts 4 and 2 on the x and y-axis respectively is:
a) x² + y² − 4x − 2y = 0
b) x² + y² + 4x + 2y = 0
c) x² + y² + 4x − 2y = 0
d) x² + y² − 2x − 4y = 0
Answer: a) x² + y² − 4x − 2y = 0
Explanation: Circle through origin with x and y-intercepts forms this equation.
Q79. The value of the determinant det [[x + a, b, c], [a, x + b, c], [a, b, x + c]] is:
a) x³ + abc
b) x²(x + a + b + c)
c) x(x + a + b + c)
d) x² + a + b + c
Answer: b) x²(x + a + b + c)
Explanation: Using cofactor expansion and symmetry of determinant.
Q80. The interval in which the function f(x) = x² + 2x − 1 is increasing is:
a) (−∞, −1)
b) (−1, ∞)
c) (0, ∞)
d) (−∞, −4/3) ∪ (0, ∞)
Answer: b) (−1, ∞)
Explanation: Function increases where derivative is positive: f′(x) = 2x + 2 > 0.
Q81. The value of the integral I = ∫ dx / (a²sin²x + b²cos²x) is:
a) (1/ab) arctan((a/b)tanx) + C
b) (1/a) arctan((a/b)tanx) + C
c) (1/b) arctan((b/a)tanx) + C
d) ln|secx| + C
Answer: a) (1/ab) arctan((a/b)tanx) + C
Explanation: Standard form integral of rational trigonometric expression.
Q82. The value of I = ∫₀¹ |3x − 1| dx is:
a) 1/2
b) 5/6
c) 1
d) 2/3
Answer: b) 5/6
Explanation: Break into two parts at x = 1/3 and integrate accordingly.
Q83. The area of the region bounded by the curve y = 2√(1 − x²) and the x-axis is:
a) π
b) π/2
c) 2π
d) 4π
Answer: a) π
Explanation: This is the upper semicircle with radius 1 multiplied by 2.
Q84. The coefficient of correlation is independent of:
a) Change of origin
b) Change of scale
c) Both origin and scale
d) Units
Answer: c) Both origin and scale
Explanation: Correlation coefficient is a standardized value.
Q85. A problem in statistics is given to three students whose chances of solving it are 1/2, 1/3, and 1/4 respectively. What is the probability that the problem will be solved?
a) 3/4
b) 1/2
c) 5/6
d) 7/12
Answer: a) 3/4
Explanation: P(at least one solves) = 1 − P(none solve) = 1 − (1/2)(2/3)(3/4) = 3/4.
Q86. The order and degree of the differential equation (d²y/dx²) + ⌊1 + (dy/dx)²⌋² = 0 is:
a) Order 1, Degree 2
b) Order 2, Degree 2
c) Order 2, Degree 1
d) Order 1, Degree 1
Final Answer: c) Order 2, Degree 1
Explanation: Highest derivative is d2ydx2\frac{d^2y}{dx^2}dx2d2y ⇒ Order = 2; It appears to the first power ⇒ Degree = 1.
Q87. The condition that the line y = mx + c may touch the parabola y² = 4ax (a > 0) is:
a) c = a/m
b) c² = 4am
c) c² = 4a/m
d) c² = 4am²
Final Answer: a) c = a/m
Explanation: Substituting the line into the parabola and setting discriminant zero gives the condition for tangency as c=amc = \frac{a}{m}c=ma.
Q88. The function f(x) = |x − 1|²n in the interval [0, 2] does not satisfy Rolle’s Theorem because:
a) It is not continuous
b) It is not differentiable
c) f(0) ≠ f(2)
d) It is a polynomial
Answer: b) It is not differentiable
Explanation: The function is not differentiable at x = 1.
Q89. The equation x³ − 3x² − 4 = 0 has:
a) One real root
b) No real root
c) No repeated roots
d) Two equal roots
Answer: c) No repeated roots
Explanation: Discriminant shows distinct roots.
Q90. The length of tangent drawn from point (2, 0, −3) to the sphere 3(x² + y + z) + 4x − 5y − 6z + 1 = 0 is:
a) √22
b) √11
c) √10
d) √14
Answer: a) √22
Explanation: Use distance formula from point to sphere center and radius.
Q91. Three concurrent edges OA, OB and OC of a parallelepiped are respectively 2i + j − k, i + 2j + 3k and −3i − j + k. Then its volume will be:
a) 0
b) 5
c) −5
d) 6
Answer: c) −5
Explanation: Volume is scalar triple product of vectors OA·(OB×OC).
Q92. If x = u² + v² and y = 2uv, then the Jacobian ∂(x, y)/∂(u, v) is:
a) 0
b) −1
c) 1
d) 2
Answer: b) −1
Explanation: Compute partial derivatives and form Jacobian matrix.
Q93. The value of limₙ→∞ (n² + n)/(n² + 1) is:
a) 1
b) 0
c) ∞
d) 2
Answer: a) 1
Explanation: Divide numerator and denominator by n².
Q94. The series ∑ 1/(2n − 1) is:
a) Convergent
b) Divergent
c) Alternating
d) Finite
Answer: b) Divergent
Explanation: It is a harmonic series over odd terms and diverges.
Q95. The marks obtained by 12 students out of 50 are: 25, 20, 23, 32, 40, 27, 30, 25, 20, 10, 15, 41. Their median will be:
a) 25
b) 26
c) 27
d) 28
Answer: a) 25
Explanation: Middle two values are 25 and 25 in sorted data.
Q96. Among ordinary water, boiled water, sea water and distilled water, which one is the best conductor of electricity?
a) Ordinary water
b) Sea water
c) Distilled water
d) Boiled water
Answer: b) Sea water
Explanation: Sea water contains most ions, enhancing conductivity.
Q97. Green vitriol is:
a) FeSO₄·7H₂O
b) CuSO₄
c) Fe₂(SO₄)₃
d) FeCl₃
Answer: a) FeSO₄·7H₂O
Explanation: Green vitriol is hydrated ferrous sulfate.
Q98. In which type of rocks are metals like gold and copper mostly found?
a) Sedimentary rocks
b) Old igneous rocks
c) Metamorphic rocks
d) Fossil rocks
Answer: b) Old igneous rocks
Explanation: These rocks often contain metallic ores.
Q99. “No two electrons in an atom can have the same set of all four quantum numbers.” This statement is known as:
a) Hund’s rule
b) Aufbau principle
c) Pauli’s exclusion principle
d) Heisenberg uncertainty principle
Answer: c) Pauli’s exclusion principle
Explanation: It explains electron arrangement in atoms.
Q100. In the species He₂ and H₂⁺:
a) He₂ has higher bond order
b) H₂⁺ is more stable
c) Both have identical bond orders
d) H₂⁺ has zero bond order
Answer: c) Both have identical bond orders
Explanation: Bond order of both species is 0.5.
Q101. Atomic mass of an element is always equal to its:
a) Atomic number
b) Number of protons
c) Number of protons and neutrons
d) Number of electrons
Answer: c) Number of protons and neutrons
Explanation: Atomic mass is the sum of protons and neutrons in an atom.
Q102. Among H₂O, HF, NH₃, intermolecular hydrogen bond exists in:
a) H₂O only
b) HF only
c) NH₃ only
d) All the above
Answer: d) All the above
Explanation: All three form hydrogen bonds due to high electronegativity.
Q103. Among BaO₂, MnO₂, PbO, and NO, which oxide is a peroxide?
a) BaO₂
b) MnO₂
c) PbO
d) NO
Answer: a) BaO₂
Explanation: BaO₂ contains the peroxide ion (O₂²⁻).
Q104. A double covalent bond of ethylene (CH₂=CH₂) consists of:
a) Two sigma bonds
b) Two pi bonds
c) One sigma and one pi bond
d) One sigma and two pi bonds
Answer: c) One sigma and one pi bond
Explanation: A double bond is one sigma and one pi bond.
Q105. The chlorination of methane to give CCl₄ is an example of:
a) Elimination reaction
b) Substitution reaction
c) Addition reaction
d) Redox reaction
Answer: b) Substitution reaction
Explanation: Hydrogen atoms are replaced by chlorine atoms.
Q106. Primary, secondary, and tertiary alcohols may be distinguished from one another by:
a) Grignard reagent
b) Victor Meyer’s method
c) Lucas test
d) Tollen’s test
Answer: b) Victor Meyer’s method
Explanation: This method helps distinguish different alcohol types.
Q107. Which is used as a catalyst for preparing Grignard reagent?
a) Zinc dust
b) Mercury
c) Iodine powder
d) Sulphur
Answer: c) Iodine powder
Explanation: Iodine activates magnesium to form Grignard reagent.
Q108. All the C and H atoms in benzene molecule are:
a) In different planes
b) In straight line
c) In the same plane
d) Tetrahedral
Answer: c) In the same plane
Explanation: Benzene is a planar molecule due to sp² hybridization.
Q109. Phenol may be obtained from phenyl bromide on treatment with:
a) Sodium hydroxide (aq)
b) Ammonia
c) Zinc dust
d) Hydrochloric acid
Answer: a) Sodium hydroxide (aq)
Explanation: Nucleophilic substitution of bromine by OH⁻ forms phenol.
Q110. An aqueous solution of a substance gave a violet colour with CuSO₄ and NaOH. It is a/an:
a) Starch
b) Sugar
c) Protein
d) Fat
Answer: c) Protein
Explanation: Biuret test (CuSO₄ + NaOH) confirms protein presence.
Q111. For monoatomic gases, Cp and Cv are related as:
a) Cp = Cv
b) Cp = 1.33Cv
c) Cp = 1.67Cv
d) Cp = 2Cv
Answer: c) Cp = 1.67Cv
Explanation: Ratio Cp/Cv = γ = 5/3 = 1.67 for monoatomic gases.
Q112. If ΔG of a reaction is positive, then:
a) Reaction is at equilibrium
b) Reaction is spontaneous
c) Reaction is not spontaneous
d) Reaction is exothermic
Answer: c) Reaction is not spontaneous
Explanation: Positive ΔG indicates non-spontaneity.
Q113. Landsberger’s method is associated with the determination of:
a) Molecular weight
b) Surface tension
c) Boiling point
d) Elevation of boiling point
Answer: d) Elevation of boiling point
Explanation: It’s used for determining molecular weight via boiling point elevation.
Q114. The pH of 0.1 M solution of a salt of a weak base (Kb = 10⁻⁵) and strong acid is:
a) 1
b) 3
c) 5
d) 7
Answer: b) 3
Explanation: Weak base + strong acid → acidic salt, pH < 7.
Q115. Fraction of radiocarbon left in a sample of wood decaying by a first order process after 1000 years (k = 0.0002303 per year) is:
a) 0.25
b) 0.50
c) 0.1
d) 0.1
Answer: d) 0.1
Explanation: Use first-order decay formula: N = N₀e^(−kt).
Q116. Which electrolyte is used in silver plating?
a) Silver nitrate
b) Potassium argento cyanide
c) Sodium chloride
d) Copper sulphate
Answer: b) Potassium argento cyanide
Explanation: It provides Ag⁺ ions in electroplating.
Q117. Which metals make the most efficient catalysts?
a) Alkali metals
b) Alkaline earth metals
c) Transition metals
d) Noble metals
Answer: c) Transition metals
Explanation: Their variable oxidation states help in catalysis.
Q118. The nature of the sigma bond in the carbonyl group of aldehydes and ketones is:
a) s–p overlap
b) sp²–p overlap
c) p–p overlap
d) s–s overlap
Answer: b) sp²–p overlap
Explanation: Carbon is sp² and oxygen p-hybridized.
Q119. Reading of a barometer going down is an indication of:
a) Clear weather
b) Rainfall
c) Snow
d) Fog
Answer: b) Rainfall
Explanation: Falling pressure often indicates bad weather.
Q120. Among Cylinder, Spark plug, and Piston, which one is used in a diesel engine?
a) Spark plug
b) Cylinder
c) Piston
d) Both b and c
Answer: d) Both b and c
Explanation: Diesel engines do not use spark plugs.
Q121. The number of degrees of freedom for the system NH₄Cl(s) ⇌ NH₃(g) + HCl(g) is:
a) 0
b) 1
c) 2
d) 3
Answer: b) 1
Explanation: One variable (e.g. pressure or temperature) defines the system.
Q122. The heart is covered by a membrane called:
a) Pleura
b) Peritoneum
c) Pericardium
d) Myocardium
Answer: c) Pericardium
Explanation: It is a protective double-walled sac around the heart.
Q123. Which plant is effective in reducing water pollution and is also useful for producing biogas?
a) Water Lily
b) Water Hyacinth
c) Lotus
d) Azolla
Answer: b) Water Hyacinth
Explanation: It absorbs pollutants and yields biogas when decomposed.
Q124. Diabetes is caused due to the malfunctioning of:
a) Liver
b) Pancreas
c) Kidney
d) Lungs
Answer: b) Pancreas
Explanation: Insufficient insulin production by pancreas causes diabetes.
Q125. Buddha died during the reign of:
a) Ashoka
b) Bimbisara
c) Ajatashatru
d) Harshavardhana
Answer: c) Ajatashatru
Explanation: Buddha passed away during Ajatashatru’s rule.
Q126. Dhanvantri, a renowned physician of ancient India, adorned the court of:
a) Ashoka
b) Vikramaditya
c) Chandragupta
d) Harsha
Answer: c) Chandragupta
Explanation: Dhanvantri served during Chandragupta’s reign.
Q127. Which Veda contains the ‘Gayatri Mantra’?
a) Yajur Veda
b) Sama Veda
c) Rig Veda
d) Atharva Veda
Answer: c) Rig Veda
Explanation: Gayatri Mantra is a hymn from the Rig Veda.
Q128. The birthplace of Swami Vivekananda is in which city?
a) Mumbai
b) Kolkata
c) Chennai
d) Lucknow
Answer: b) Kolkata
Explanation: He was born in Kolkata in 1863.
Q129. The Mughal ruler Bahadur Shah-II was exiled by the British and sent to:
a) Burma
b) Rangoon
c) Afghanistan
d) Andaman
Answer: b) Rangoon
Explanation: He was exiled to Rangoon after 1857 revolt.
Q130. The Governor of a state is removed from his office by:
a) Prime Minister
b) Chief Minister
c) President
d) Supreme Court
Answer: c) President
Explanation: The President appoints and removes state governors.
Q131. Captain Vikram Batra was awarded:
a) Ashoka Chakra
b) Param Vir Chakra
c) Maha Vir Chakra
d) Vir Chakra
Answer: b) Param Vir Chakra
Explanation: He was posthumously awarded for bravery in the Kargil War.
Q132. Himachal Pradesh got statehood on:
a) 26th January, 1950
b) 15th August, 1947
c) 25th January, 1971
d) 1st November, 1966
Answer: c) 25th January, 1971
Explanation: H.P. became the 18th state of India on this date.
Q133. The maximum strength of Lok Sabha is:
a) 500
b) 545
c) 552
d) 560
Answer: c) 552
Explanation: Article 81 of the Constitution fixes it at 552.
Q134. The area of Himachal Pradesh (in sq. km.) is:
a) 45,123
b) 55,673
c) 65,432
d) 75,000
Answer: b) 55,673
Explanation: As per official records, HP covers 55,673 sq. km.
Q135. Which one is an indirect tax?
a) Capital gains tax
b) Corporation tax
c) Excise duty
d) Wealth tax
Answer: c) Excise duty
Explanation: Excise duty is collected indirectly from consumers.
Q136. Maruti Car Company is established with the collaboration of:
a) Hyundai
b) Tata
c) Suzuki Company of Japan
d) Toyota
Answer: c) Suzuki Company of Japan
Explanation: Maruti Udyog was a joint venture with Suzuki.
Q137. Which of the planets is nearest to the Earth?
a) Mercury
b) Venus
c) Mars
d) Jupiter
Answer: b) Venus
Explanation: Venus is the closest planet to Earth in orbit.
Q138. Increase in carbon dioxide in atmosphere causes:
a) Acid rain
b) Global cooling
c) Rise in earth temperature
d) Ozone layer depletion
Answer: c) Rise in earth temperature
Explanation: CO₂ is a greenhouse gas contributing to global warming.
Q139. Till October 1966, Himachal Pradesh consisted of only:
a) Four districts
b) Five districts
c) Six districts
d) Eight districts
Answer: c) Six districts
Explanation: HP had six districts before merger with Punjab areas.
Q140. Dicky Dolma is distinguished in:
a) Skiing
b) Archery
c) Mountaineering
d) Athletics
Answer: c) Mountaineering
Explanation: She is the youngest woman to scale Mount Everest.
Q141. Prof. Amartya Sen has earned worldwide distinction in which area?
a) Chemistry
b) Mathematics
c) Economics
d) Literature
Answer: c) Economics
Explanation: He is a Nobel Laureate in Economics.
Q142. To form river Chenab, two streams Chandra and Bhaga meet at:
a) Keylong
b) Kullu
c) Tandi
d) Udaipur
Answer: c) Tandi
Explanation: Tandi is the confluence point of Chandra and Bhaga.
Q143. In which year was ‘All India Radio’ set up?
a) 1930
b) 1935
c) 1936
d) 1947
Answer: c) 1936
Explanation: AIR began broadcasting in 1936.
Q144. Panchayati Raj was started in Himachal Pradesh in:
a) 1952
b) 1963
c) 1971
d) 1977
Answer: b) 1963
Explanation: HP adopted Panchayati Raj in 1963.
Q145. Which pass separates Lahaul from Spiti?
a) Rohtang Pass
b) Baralacha Pass
c) Kunzum Pass
d) Shipki La
Answer: c) Kunzum Pass
Explanation: Kunzum separates Lahaul and Spiti valleys.
Q146. The script used in the earliest inscriptions of Ashoka is:
a) Sanskrit
b) Brahmi
c) Pali
d) Kharosthi
Answer: b) Brahmi
Explanation: Ashokan inscriptions were primarily written in Brahmi script.
Q147. The Treaty of Sugauli was signed between British and:
a) Burma
b) Nepal
c) Bhutan
d) Tibet
Answer: b) Nepal
Explanation: Signed in 1815–16, it defined Nepal’s boundaries with British India.
Q148. ‘Chipko Movement’ is related to:
a) Environment conservation
b) Animal protection
c) Land reforms
d) River water sharing
Answer: a) Environment conservation
Explanation: It involved hugging trees to prevent deforestation.
Q149. ‘Nobel Prize’ is awarded for the first time in which year?
a) 1900
b) 1901
c) 1910
d) 1920
Answer: b) 1901
Explanation: Nobel Prizes were first awarded in 1901.
Q150. The first war of Indian Independence started in:
a) 1757
b) 1803
c) 1857
d) 1885
Answer: c) 1857
Explanation: Also known as the Sepoy Mutiny, it began in 1857.
Q151. ‘Kinner Kailash’ is located in which district of Himachal Pradesh?
a) Chamba
b) Kullu
c) Lahaul-Spiti
d) Kinnaur
Answer: d) Kinnaur
Explanation: Kinner Kailash is a sacred peak in Kinnaur district.
Q152. The slogan ‘Jai Jawan Jai Kisan’ was given by:
a) Jawaharlal Nehru
b) Lal Bahadur Shastri
c) Indira Gandhi
d) Sardar Patel
Answer: b) Lal Bahadur Shastri
Explanation: He coined the slogan to honor soldiers and farmers.
Q153. The headquarters of UNESCO is situated in:
a) New York
b) Paris
c) Geneva
d) London
Answer: b) Paris
Explanation: UNESCO’s head office is located in Paris, France.
Q154. Which of the following is not a Fundamental Right in India?
a) Right to Equality
b) Right to Property
c) Right to Freedom
d) Right to Constitutional Remedies
Answer: b) Right to Property
Explanation: It was removed from Fundamental Rights by 44th Amendment.
Q155. Who was the first Governor-General of free India?
a) Lord Mountbatten
b) C. Rajagopalachari
c) Jawaharlal Nehru
d) Dr. Rajendra Prasad
Answer: a) Lord Mountbatten
Explanation: He continued as the first Governor-General after 1947.
Q156. The headquarters of World Bank is located in:
a) New York
b) Washington D.C.
c) Geneva
d) Paris
Answer: b) Washington D.C.
Explanation: World Bank’s head office is in Washington D.C., USA.
Q157. The total number of districts in Himachal Pradesh at present is:
a) 10
b) 11
c) 12
d) 13
Answer: c) 12
Explanation: HP has 12 districts as of now.
Q158. The longest river in India is:
a) Yamuna
b) Ganga
c) Brahmaputra
d) Godavari
Answer: b) Ganga
Explanation: Ganga is the longest river flowing through India.
Q159. Who was the founder of the ‘Arya Samaj’?
a) Raja Ram Mohan Roy
b) Swami Vivekananda
c) Swami Dayanand Saraswati
d) Rabindranath Tagore
Answer: c) Swami Dayanand Saraswati
Explanation: He founded Arya Samaj in 1875 for religious reform.
Q160. ‘Kalka-Shimla Railway’ is recognized as a:
a) Industrial heritage site
b) UNESCO World Heritage site
c) National heritage monument
d) State protected monument
Answer: b) UNESCO World Heritage site
Explanation: It was declared a World Heritage site in 2008.
Q161. ‘Dharamshala’ is the headquarters of which district?
a) Kangra
b) Una
c) Hamirpur
d) Chamba
Answer: a) Kangra
Explanation: Dharamshala serves as the district HQ of Kangra.
Q162. Which instrument is used to measure atmospheric pressure?
a) Thermometer
b) Barometer
c) Hygrometer
d) Anemometer
Answer: b) Barometer
Explanation: A barometer measures atmospheric pressure.
Q163. What is the name of the gas which causes suffocation during fire?
a) Methane
b) Carbon monoxide
c) Carbon dioxide
d) Ammonia
Answer: b) Carbon monoxide
Explanation: It is a toxic gas produced during incomplete combustion.
Q164. The working principle of a washing machine is:
a) Centrifugation
b) Reverse osmosis
c) Diffusion
d) Absorption
Answer: a) Centrifugation
Explanation: It spins clothes to separate water using centrifugal force.
Q165. The atomic number of oxygen is:
a) 6
b) 8
c) 16
d) 18
Answer: b) 8
Explanation: Oxygen has 8 protons in its nucleus.
Q166. The chemical formula of washing soda is:
a) NaHCO₃
b) Na₂CO₃·10H₂O
c) CaCO₃
d) NaOH
Answer: b) Na₂CO₃·10H₂O
Explanation: Washing soda is hydrated sodium carbonate.
Q167. Which one of the following is a vector quantity?
a) Mass
b) Speed
c) Temperature
d) Velocity
Answer: d) Velocity
Explanation: Velocity has both magnitude and direction.
Q168. The speed of light in vacuum is:
a) 3 × 10⁸ m/s
b) 3 × 10⁶ m/s
c) 3 × 10⁵ km/s
d) 3 × 10⁴ m/s
Answer: a) 3 × 10⁸ m/s
Explanation: It is the standard constant for speed of light in vacuum.
Q169. Which vitamin is primarily obtained from sunlight?
a) Vitamin A
b) Vitamin B
c) Vitamin C
d) Vitamin D
Answer: d) Vitamin D
Explanation: Sunlight helps the skin synthesize Vitamin D.
Q170. The ‘Green Revolution’ in India mainly focused on the production of:
a) Fruits
b) Vegetables
c) Cereals
d) Dairy
Answer: c) Cereals
Explanation: The Green Revolution boosted wheat and rice production significantly.