HP Patwari Exam 2013 – Detailed Solutions

Section 1: Arithmetic (Mathematics)

1. Which of the following fractions lies between 3/5 and 4/5?

• Question: $3/5 < x < 4/5$
• Analysis:
  • Convert the given fractions to decimals:
    • $3/5 = 0.60$
    • $4/5 = 0.80$
  • Convert the options to decimals:
    • A) $8/20 = 4/10 = 0.40$ (Too small)
    • B) $11/20 = 0.55$ (Too small)
    • C) $14/20 = 7/10 = 0.70$ (Fits between 0.60 and 0.80)
    • D) $17/20 = 0.85$ (Too large)
• Answer: (C) 14/20

2. What is the degree of the polynomial $5x^3 – 4x^2 + 7x$?

• Analysis: The degree of a polynomial is the highest power of the variable ($x$) present in the expression. In $5x^3 – 4x^2 + 7x$, the highest power is 3.
• Answer: (C) 3

3. Which of the following is NOT a solution for $x + 2y = 6$?

• Analysis: Test each option by substituting coordinates $(x, y)$ into the equation.
  • A) $(2, 2) \rightarrow 2 + 2(2) = 6$ (True)
  • B) $(3, 3) \rightarrow 3 + 2(3) = 3 + 6 = 9 \neq 6$ (False – This is not a solution)
  • C) $(4, 1) \rightarrow 4 + 2(1) = 6$ (True)
  • D) $(6, 0) \rightarrow 6 + 2(0) = 6$ (True)
• Answer: (B) (3, 3)

4. The number of lines that can pass through a single point is?

• Analysis: In geometry, an infinite number of lines can be drawn through a single specific point (like the spokes of a wheel).
• Answer: (D) Infinite (असंख्य)

5. Opposite angles of equal sides in an isosceles triangle can be?

• Analysis: In an isosceles triangle, angles opposite to equal sides are equal.
  • Let the equal angles be $x$. The sum of angles is $180^\circ$.
  • If $x=50^\circ$, sum = $50+50 = 100$. Third angle = $80^\circ$. This is valid.
  • Option A (40 and 50) are not equal.
  • Option C implies 50 and 60 (not equal).
  • Option D (70 and ?) – Needs a pair.
  • Option B ($50^\circ$) implies both are $50^\circ$, which is the only valid pair listed that satisfies the isosceles condition.
• Answer: (B) $50^\circ$ (Implying both are $50^\circ$)

6. In a parallelogram:

• Analysis:
  • Opposite sides are equal. (True)
  • Opposite angles are equal. (True)
  • Diagonals bisect each other. (True)
• Answer: (D) All of the above (उपर्युक्त सभी)

7. The average of the first five multiples of 3 is:

• Analysis:
  • Multiples: 3, 6, 9, 12, 15
  • Sum: $3+6+9+12+15 = 45$
  • Average: $45 / 5 = 9$
  • Shortcut: For an arithmetic progression with an odd number of terms, the middle term is the average. Middle of 5 terms is the 3rd term (9).
• Answer: (A) 9

8. HCF of two numbers is 7 and LCM is 210. If one number is 35, what is the other?

• Formula: $\text{Product of Numbers} = \text{HCF} \times \text{LCM}$
• Calculation:
  • $35 \times x = 7 \times 210$
  • $x = (7 \times 210) / 35$
  • $x = 1470 / 35$
  • $x = 42$
• Answer: (A) 42

9. Which of the following is NOT a quadratic equation?

• Analysis: A quadratic equation must have a degree of exactly 2.
  • A) $4x^2…$ (Degree 2, Quadratic)
  • B) $x^3 – x – 5 = 0$ (Degree 3, Cubic – Not Quadratic)
  • C) $3x^2…$ (Degree 2, Quadratic)
  • D) $x – x^2…$ (Degree 2, Quadratic)
• Answer: (B) $x^3 – x – 5 = 0$

10. Diameters of two circles are 8 cm and 10 cm. Find the ratio of their circumferences.

• Analysis:
  • Ratio of Diameters = $8 : 10 = 4 : 5$
  • Ratio of Radii = $4 : 5$
  • Ratio of Circumferences ($2\pi r$) is the same as the ratio of radii/diameters.
• Answer: (B) 4:5

11. Find the median of the heights: 155, 160, 145, 149, 150, 147, 152, 144, 148.

• Analysis:
  • First, arrange data in ascending order: 144, 145, 147, 148, 149, 150, 152, 155, 160
  • Total terms ($n$) = 9 (odd).
  • Median = $((n+1)/2)^{th}$ term = 5th term.
  • 5th term is 149.
• Answer: (C) 149 cm

12. Factorize: $12x^2 – 7x + 1$

• Analysis:
  • We need numbers that multiply to $12 \times 1 = 12$ and add to $-7$. These are $-3$ and $-4$.
  • Split the middle term: $12x^2 – 4x – 3x + 1$
  • Group: $4x(3x – 1) – 1(3x – 1)$
  • Factors: $(4x – 1)(3x – 1)$
• Answer: (D) $(4x – 1)(3x – 1)$

13. Evaluate $(102)^3$

• Analysis:
  • $(100 + 2)^3 = 100^3 + 2^3 + 3(100)(2)(100+2)$
  • $= 1,000,000 + 8 + 600(102)$
  • $= 1,000,008 + 61,200$
  • $= 1,061,208$
• Answer: (A) 1061208

14. Find quadratic polynomial with sum of zeroes = 1/4 and product = -1.

• Formula: $x^2 – (\text{sum})x + (\text{product})$
• Calculation:
  • $x^2 – (1/4)x + (-1)$
  • $x^2 – x/4 – 1$
• Answer: (D) $x^2 – 1/4x – 1$ (Note: Often multiplied by 4 to get integers $4x^2 – x – 4$, but option D matches the raw form).

15. Find K in $2x + 3y = K$ if $x=2, y=1$.

• Calculation:
  • $2(2) + 3(1) = K$
  • $4 + 3 = K$
  • $K = 7$
• Answer: (A) 7

16. Product of two consecutive positive integers is 306. Find them.

• Analysis:
  • $x(x+1) = 306 \rightarrow x^2 + x – 306 = 0$
  • $\sqrt{306}$ is roughly 17.5. So numbers are around 17 and 18.
  • $17 \times 18 = 306$.
• Answer: (A) 17, 18

17. Find roots of $2x^2 + x + 4 = 0$.

• Quadratic Formula: $x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}$
• Calculation:
  • $a=2, b=1, c=4$
  • $D = 1^2 – 4(2)(4) = 1 – 32 = -31$
  • $x = \frac{-1 \pm \sqrt{-31}}{4}$
• Answer: (C) $\frac{-1 \pm \sqrt{-31}}{4}$

18. First term and common difference of AP: 3, 1, -1, -3…

• Analysis:
  • First term ($a$) = 3
  • Common Difference ($d$) = Second term – First term = $1 – 3 = -2$
• Answer: (D) $$3, -2$$

19. Right triangle: Base 10, Hypotenuse 15. Find Altitude.

• Pythagoras Theorem: $a^2 + b^2 = c^2$
• Calculation:
  • $h^2 + 10^2 = 15^2$
  • $h^2 + 100 = 225$
  • $h^2 = 125$
  • $h = \sqrt{25 \times 5} = 5\sqrt{5}$
• Answer: (C) $5\sqrt{5}$ cm

20. Value of $\frac{\tan 26^\circ}{\cot 64^\circ}$

• Analysis:
  • $\cot 64^\circ = \tan(90 – 64)^\circ = \tan 26^\circ$
  • Expression becomes $\frac{\tan 26^\circ}{\tan 26^\circ} = 1$
• Answer: (B) 1

21. Volume of sphere with radius 7 cm.

• Formula: $\frac{4}{3} \pi r^3$
• Calculation:
  • $\frac{4}{3} \times \frac{22}{7} \times 7 \times 7 \times 7$
  • $\frac{4}{3} \times 22 \times 49$
  • $\frac{4312}{3} \approx 1437.33$
• Answer: (D) 1437.3 cm³

22. Total surface area of cuboid $15 \times 12 \times 5$.

• Formula: $2(lb + bh + hl)$
• Calculation:
  • $2(15 \times 12 + 12 \times 5 + 15 \times 5)$
  • $2(180 + 60 + 75)$
  • $2(315) = 630$
• Answer: (A) 630 cm²

23. Surface area of sphere with radius 14 cm.

• Formula: $4 \pi r^2$
• Calculation:
  • $4 \times \frac{22}{7} \times 14 \times 14$
  • $4 \times 22 \times 2 \times 14$
  • $88 \times 28 = 2464$
• Answer: (D) 2464 cm²

24. Cone: Radius 14 cm, Height 48 cm. Find Slant Height.

• Note: The English text in the image is cut off, but the logic of the numbers (Pythagorean triple 7-24-25 $\rightarrow$ 14-48-50) suggests finding the slant height.
• Formula: $l = \sqrt{r^2 + h^2}$
• Calculation:
  • $l = \sqrt{14^2 + 48^2}$
  • $l = \sqrt{196 + 2304} = \sqrt{2500} = 50$
• Answer: (C) 50 cm

25. Bag has 3 red, 5 black balls. Probability of drawing a red ball?

• Analysis:
  • Total balls = $3 + 5 = 8$
  • Favorable (Red) = 3
  • Probability = $3/8$
• Answer: (A) 3/8

Section 2: English

26. Why was a family meeting held at the table?

• Answer: (D) To plan the programme for summer holiday (Directly from passage: “began to talk about the summer holiday”)

27. What was their decision regarding the summer holiday?

• Answer: (D) To go to sea-side for enjoyment (Passage: children cried, “sea-side, please!”)

28. What was an alternate programme before the family?

• Answer: (C) To go to the country (Passage: “Should they go to the sea-side, or to the country?”)

29. How was the decision taken by the family?

• Answer: (B) Programme was decided by the children and okayed by parents (Parents agreed to sit on deck chairs while children played).

30. What was the idea of deckchairs for parents?

• Answer: (D) Because it was the desire of their father (Passage: Father said, “Two deck-chairs for a fortnight…”)

31. Don’t disturb me, I ____ my homework.

• Answer: (D) am doing (Present Continuous tense for action happening now)

32. ‘Choose’ changes in past continuous as:

• Answer: (B) was choosing (Past continuous format: was/were + verb-ing)

33. Comparative degree of Good is:

• Answer: (B) Better (Good -> Better -> Best)

34. Noun of Invite is:

• Answer: (A) Invitation

35. Passive Voice: Will Ritu have sung a song?

• Answer: (B) Will a song have been sung by Ritu? (Future Perfect Passive structure)

36. Want or lack of rain:

• Answer: (B) Drought (Draught is a current of air)

37. A thing which must happen:

• Answer: (C) Inevitable

38. The news is too good ____:

• Answer: (D) to be true (Standard “too… to” construction)

39. Choose the correct spelling:

• Answer: (B) Concede

40. It has been raining ____ morning.

• Answer: (A) since (Used for a specific point in time)

41. The bus driver ____ asleep while he was driving.

• Answer: (C) fell (Past simple for an event interrupting a continuous action)

42. To carry away a person by force or fraud:

• Answer: (B) Kidnap

43. Today is ____ first day of April.

• Answer: (B) the (Definite article before ordinal numbers)

44. Honest men speak ____ truth.

• Answer: (A) the (Specific truth/abstract concept usage)

45. Synonym for PREJUDICE:

• Answer: (A) Bias

46. Synonym for STOOP:

• Answer: (C) To bow (Stoop means to bend forward)

47. What is autobiography?

• Answer: (C) A story of one’s own life

48. Passive Voice: He has finished his meal.

• Answer: (C) His meal has been finished by him.

49. The hunter aimed ____ the tiger.

• Answer: (D) at

50. Your work is ____ the average.

• Answer: (B) below

Section 3: Hindi

51. देश-प्रेम का अभिप्राय है-

• Answer: (D) देश के प्रति व्यक्ति का स्वाभाविक ममत्व

52. सच्चा देश-प्रेमी-

• Answer: (C) परीक्षा की कसौटी पर खरा उतरता है

53. संध्या समय पक्षी अपने घोंसलों में वापिस चले जाते हैं, क्योंकि-

• Answer: (D) उन्हें अपना नीड़ प्यारा होता है

54. वही देश महान् है जहां के लोग-

• Answer: (D) त्याग और उत्सर्ग से सदा आगे रहते हैं

55. देश-प्रेम का अंकुर विद्यमान है-

• Answer: (B) सभी प्राणियों में (Passage mentions humans and birds/animals)

56. आगामी का विलोम शब्द होता है-

• Answer: (C) विगत (आगामी = upcoming, विगत = past)

57. विराम चिह्न प्रश्न (सुभाष ने देश के लिए…):

• Answer: (A) अर्द्धविराम (;) और पूर्णविराम (|)

58. ‘ओछे की प्रीत बालू की भीत’ का अर्थ:

• Answer: (D) दुष्टों की मित्रता शीघ्र समाप्त (Love of mean people is like a wall of sand)

59. ‘पेट की आग’ के लिए एक शब्द:

• Answer: (A) जठरानल

60. ‘कक्षा’ कौन-सी संज्ञा है?

• Answer: (C) समुदायवाचक (Collective Noun)

61. जो शब्द संज्ञा/सर्वनाम की विशेषता प्रकट करें:

• Answer: (D) विशेषण (Adjective)

62. जहाँ शब्द और अर्थ दोनों में विशेषता हो:

• Answer: (A) उभयालंकार

63. ‘विद्यार्थी’ का संधि-विग्रह:

• Answer: (D) विद्या + अर्थी (Long vowel sandhi)

64. ‘बादल’ का पर्यायवाची:

• Answer: (A) जलद (Jalad gives water. Payodhi is ocean, Pankaj is lotus)

65. $$Missing Question in visual, derived from key$$

• Answer: (C) Key indicates C.

66. विराम चिह्न सुधार:

• Answer: (A) पेड़ को मत देखो, देखो केवल मछली की आँख, जो तुम्हारे लक्ष्य का केन्द्र बिन्दु है।

67. हिन्दी की लिपि:

• Answer: (D) देवनागरी

68. ‘दिनेश आम खाता है’ – क्रिया:

• Answer: (A) सकर्मक (Transitive – involves an object ‘mango’)

69. शुद्ध वाक्य:

• Answer: (D) उसने अपना नाम बताया।

70. ‘सूर्य’ का पर्यायवाची:

• Answer: (B) रवि

71. ‘जोर से बोलिए’ – क्रिया विशेषण:

• Answer: (B) No, actually ‘जोर से’ is the adverb, but key says B. Let’s re-read Q71 options. A: जोर, B: बोलिए, C: जोर से, D: से. The question asks “What is the Adverb?”. ‘Bolie’ is the verb. ‘Zor se’ describes the verb. However, the answer key provided in the PDF for 71 is B. This seems like an error in the original key or interpretation. Standard grammar dictates ‘जोर से’ is the adverb. Based on official key provided in doc: B.

72. एक शब्द का एक प्रयोग परन्तु अनेक अर्थ:

• Answer: (B) श्लेष अलंकार

73. ‘हाथ पर हाथ धरे रह जाना’:

• Answer: (B) कुछ भी प्राप्त न होना (To regret/gain nothing)

74. ‘इतिहास से पहले का’:

• Answer: (B) प्रागैतिहासिक (Prehistoric)

75. ‘जलना’ की भाववाचक संज्ञा:

• Answer: (D) जलन

Section 4: General Knowledge

76. Where is terrace farming done?

• Answer: (D) Uttarakhand (Hilly regions)

77. Author of Vande Mataram?

• Answer: (B) Bankim Chandra Chatterjee

78. What is celebrated on 5th June?

• Answer: (B) World Environment Day

79. Medicine for indigestion?

• Answer: (C) Antacid

80. Which is NOT a biomass energy source?

• Answer: (C) Nuclear Energy (Others like wood, gobar gas are biomass)

81. Sardar Sarovar Dam is on which river?

• Answer: (C) Narmada River (Note: Snippet has cut off options, but Narmada is the correct river for this dam)

82. Which is a leguminous crop?

• Answer: (A) Pulses (दालें)

83. Oldest Veda?

• Answer: (A) Rigveda

84. President nominates 2 members to Lok Sabha from?

• Answer: (D) Anglo-Indian Community (Note: This provision was removed in 2020, but was valid in 2013).

85. District with highest population density in HP?

• Answer: (D) Hamirpur

86. Currency of Bangladesh?

• Answer: (A) Taka

87. Xylem in plants is responsible for?

• Answer: (A) Transport of water

88. What are manuscripts?

• Answer: (A) Handwritten documents (हस्तलिखित लेख)

89. What is Rinderpest?

• Answer: (A) Animal disease found in Africa (Cattle plague)

90. Official language of Sri Lanka?

• Answer: (A) Sinhala

91. Indian cricketer who scored double century in ODI (context 2013)?

• Answer: (A) Rohit Sharma

92. Golf course in Shimla district?

• Answer: (C) Naldehra

93. Not a correct reason for flora/fauna depletion?

• Answer: (C) Grazing and fuel wood collection (Usually considered less damaging than major development or agriculture expansion).

94. Which Gorkha commander attacked Kangra in 1805?

• Answer: (A) Amar Singh Thapa

95. Napoleon Bonaparte was related to?

• Answer: (A) France

96. UN Headquarters?

• Answer: (A) New York

97. Kidneys in humans are part of?

• Answer: (C) Excretion system

98. Iron ore is what type of resource?

• Answer: (D) Non-renewable

99. When did Simon Commission come to India?

• Answer: (A) 1928

100. Kwashiorkor is caused by deficiency of?

• Answer: (A) Protein