Page 1 : 2 : Q1-Q.5 carry one mark each 01. The volume of a sphere of diameter 1 unit is _____ than the volume of a cube of side 1 unit. (A) least (B) less (C) lesser (D) low 01. Ans: (C) Sol: â€˜Lesser thanâ€™ is apt because the sentence should be in comparative degree. 02. The unruly crowd demanded that the accused be ____ without trial. (A) hanged (B) hanging (C) hankering (D) hung 02. Ans: (A) Sol: â€˜hangedâ€™ means death by hanging â€˜hungâ€™ is used only with things and not with people. 03. Choose the statement(s) where the underlined word is used correctly: (i) A prone is a dried plum. (ii) He was lying prone on the floor. (iii) People who eat a lot of fat are Prone to heart disease. (A) (i) and (iii) only (B) (iii) only (C) (i) and (ii) only (D) (ii) and (iii) only 03. Ans: (D) Sol: â€˜lying proneâ€™ means lie down flat. â€˜Prone toâ€™ means vulnerable to. Page 2 : 2 : Q1-Q.5 carry one mark each 01. The volume of a sphere of diameter 1 unit is _____ than the volume of a cube of side 1 unit. (A) least (B) less (C) lesser (D) low 01. Ans: (C) Sol: â€˜Lesser thanâ€™ is apt because the sentence should be in comparative degree. 02. The unruly crowd demanded that the accused be ____ without trial. (A) hanged (B) hanging (C) hankering (D) hung 02. Ans: (A) Sol: â€˜hangedâ€™ means death by hanging â€˜hungâ€™ is used only with things and not with people. 03. Choose the statement(s) where the underlined word is used correctly: (i) A prone is a dried plum. (ii) He was lying prone on the floor. (iii) People who eat a lot of fat are Prone to heart disease. (A) (i) and (iii) only (B) (iii) only (C) (i) and (ii) only (D) (ii) and (iii) only 03. Ans: (D) Sol: â€˜lying proneâ€™ means lie down flat. â€˜Prone toâ€™ means vulnerable to. : 4 : 04. Fact: If it rains, then the field is wet. Read the following statements: (i) It rains (ii) The field is not wet (iii) The field is wet (iv) It did not rain Which one of the options given below is NOT logically possible, based on the given fact? (A)If (iii), then (iv) (B) If (i), then (iii) (C) If (i), then (ii) (D) If (ii), then (iv) 04. Ans: (C) Sol: Statements i and ii are not logically possible based on the given fact. 05. A window is made up of a square portion and an equilateral triangle portion above it. The base of the triangular portion coincides with the upper side of the square. If the perimeter of the window is 6m, the area of the window in m 2 is ___ (A) 1.43 (B) 2.06 (C) 2.68 (D) 2.88 05. Ans: (B) Sol: From the given data, the following window is possible The perimeter of the window = 5x = 6 m 20 . 1 5 6 x ? ? m Area of the window = Area of square + Area of ? l e 2 ) 2 . 1 ( 4 3 2 . 1 2 . 1 ? ? ? ? = 1.44 + 0.623 = 2.06 m 2 x x x x x Page 3 : 2 : Q1-Q.5 carry one mark each 01. The volume of a sphere of diameter 1 unit is _____ than the volume of a cube of side 1 unit. (A) least (B) less (C) lesser (D) low 01. Ans: (C) Sol: â€˜Lesser thanâ€™ is apt because the sentence should be in comparative degree. 02. The unruly crowd demanded that the accused be ____ without trial. (A) hanged (B) hanging (C) hankering (D) hung 02. Ans: (A) Sol: â€˜hangedâ€™ means death by hanging â€˜hungâ€™ is used only with things and not with people. 03. Choose the statement(s) where the underlined word is used correctly: (i) A prone is a dried plum. (ii) He was lying prone on the floor. (iii) People who eat a lot of fat are Prone to heart disease. (A) (i) and (iii) only (B) (iii) only (C) (i) and (ii) only (D) (ii) and (iii) only 03. Ans: (D) Sol: â€˜lying proneâ€™ means lie down flat. â€˜Prone toâ€™ means vulnerable to. : 4 : 04. Fact: If it rains, then the field is wet. Read the following statements: (i) It rains (ii) The field is not wet (iii) The field is wet (iv) It did not rain Which one of the options given below is NOT logically possible, based on the given fact? (A)If (iii), then (iv) (B) If (i), then (iii) (C) If (i), then (ii) (D) If (ii), then (iv) 04. Ans: (C) Sol: Statements i and ii are not logically possible based on the given fact. 05. A window is made up of a square portion and an equilateral triangle portion above it. The base of the triangular portion coincides with the upper side of the square. If the perimeter of the window is 6m, the area of the window in m 2 is ___ (A) 1.43 (B) 2.06 (C) 2.68 (D) 2.88 05. Ans: (B) Sol: From the given data, the following window is possible The perimeter of the window = 5x = 6 m 20 . 1 5 6 x ? ? m Area of the window = Area of square + Area of ? l e 2 ) 2 . 1 ( 4 3 2 . 1 2 . 1 ? ? ? ? = 1.44 + 0.623 = 2.06 m 2 x x x x x : 5 : ME Set - 02 Q.6-Q.10 carry two marks each 06. Students taking an exam are divided into two groups, P and Q such that each group has the same number of students. The performance of each of the students in a test was evaluated out of 200 marks. It was observed that the mean of group P was 105, while that of group Q was 85. The standard deviation of group P was 25, while that of group Q was 5. Assuming that the marks were distributed on a normal distribution, which of the following statements will have the highest probability of being TRUE? (A) No student in group Q scored less marks than any student in group P. (B) No student in group P scored less marks than any student in group Q. (C) Most students of group Q scored marks in a narrower range than students in group P. (D) The median of the marks of group P is 100. 06. Ans: (C) Sol: Group â€˜Pâ€™ Mean ( ?) = 105 Standard deviation ( ? 1 ) = 25 Pr (µ â€“ ? = x = µ + ?) ? ? 0.6827 ? 68% within one standard deviation µ 1 â€“ ? 1 = 105 â€“ 25 = 80 µ 1 + ? 1 = 105 + 25 = 130 ? range = 80 to 130 Distribution of P: 80 105 130 68% within one standard deviation of P Page 4 : 2 : Q1-Q.5 carry one mark each 01. The volume of a sphere of diameter 1 unit is _____ than the volume of a cube of side 1 unit. (A) least (B) less (C) lesser (D) low 01. Ans: (C) Sol: â€˜Lesser thanâ€™ is apt because the sentence should be in comparative degree. 02. The unruly crowd demanded that the accused be ____ without trial. (A) hanged (B) hanging (C) hankering (D) hung 02. Ans: (A) Sol: â€˜hangedâ€™ means death by hanging â€˜hungâ€™ is used only with things and not with people. 03. Choose the statement(s) where the underlined word is used correctly: (i) A prone is a dried plum. (ii) He was lying prone on the floor. (iii) People who eat a lot of fat are Prone to heart disease. (A) (i) and (iii) only (B) (iii) only (C) (i) and (ii) only (D) (ii) and (iii) only 03. Ans: (D) Sol: â€˜lying proneâ€™ means lie down flat. â€˜Prone toâ€™ means vulnerable to. : 4 : 04. Fact: If it rains, then the field is wet. Read the following statements: (i) It rains (ii) The field is not wet (iii) The field is wet (iv) It did not rain Which one of the options given below is NOT logically possible, based on the given fact? (A)If (iii), then (iv) (B) If (i), then (iii) (C) If (i), then (ii) (D) If (ii), then (iv) 04. Ans: (C) Sol: Statements i and ii are not logically possible based on the given fact. 05. A window is made up of a square portion and an equilateral triangle portion above it. The base of the triangular portion coincides with the upper side of the square. If the perimeter of the window is 6m, the area of the window in m 2 is ___ (A) 1.43 (B) 2.06 (C) 2.68 (D) 2.88 05. Ans: (B) Sol: From the given data, the following window is possible The perimeter of the window = 5x = 6 m 20 . 1 5 6 x ? ? m Area of the window = Area of square + Area of ? l e 2 ) 2 . 1 ( 4 3 2 . 1 2 . 1 ? ? ? ? = 1.44 + 0.623 = 2.06 m 2 x x x x x : 5 : ME Set - 02 Q.6-Q.10 carry two marks each 06. Students taking an exam are divided into two groups, P and Q such that each group has the same number of students. The performance of each of the students in a test was evaluated out of 200 marks. It was observed that the mean of group P was 105, while that of group Q was 85. The standard deviation of group P was 25, while that of group Q was 5. Assuming that the marks were distributed on a normal distribution, which of the following statements will have the highest probability of being TRUE? (A) No student in group Q scored less marks than any student in group P. (B) No student in group P scored less marks than any student in group Q. (C) Most students of group Q scored marks in a narrower range than students in group P. (D) The median of the marks of group P is 100. 06. Ans: (C) Sol: Group â€˜Pâ€™ Mean ( ?) = 105 Standard deviation ( ? 1 ) = 25 Pr (µ â€“ ? = x = µ + ?) ? ? 0.6827 ? 68% within one standard deviation µ 1 â€“ ? 1 = 105 â€“ 25 = 80 µ 1 + ? 1 = 105 + 25 = 130 ? range = 80 to 130 Distribution of P: 80 105 130 68% within one standard deviation of P : 6 : GATE_2016_Afternoon Session Group Q Mean (µ 2 ) = 85 Standard deviation ( ? 2 ) = 5 Pr (µ â€“ ? = x = µ + ?) ? 0.6827 ? 68% within one standard deviation µ 2 â€“ ? 2 = 85 â€“ 5 = 80 µ 2 + ? 2 = 85 + 5 = 90 ? Range of Q in one standard deviation is 80 to 90 Distribution of â€˜Qâ€™ 68% within one standard deviation of Q is narrower ? 68% within one standard deviation of Q means most students of group Q. ? Most students of group â€˜Qâ€™ scored marks in a narrower range than students in group â€˜Pâ€™ 68% within one standard deviation of Q 80 85 90Read More

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