#ssc cgl

0 questions

What is the area of a triangle with sides 13 cm, 14 cm and 15 cm? Answer: D. 84 cm² Answer: (D) 84 cm² s = 13 + 14 + 15/2 = 21. Area = √(21 × 8 × 7 × 6) = √7056 = 84 cm². Mensuration 1 answer
The diagonals of a rhombus are 24 cm and 10 cm. What is its perimeter? Answer: D. 52 cm Answer: (D) 52 cm The diagonals bisect each other at right angles. Side = √(12² + 5²) = 13 cm. Perimeter = 4 × 13 = 52 cm.... Mensuration 1 answer
If the radius of a circle is increased by 20%, by what percent does its area increase? Answer: B. 44% Answer: (B) 44% Area ∝ r². Shortcut: 20 + 20 + 20 × 20/100 = 44%. Mensuration 1 answer
The total surface area of a cube is 294 cm². What is its volume? Answer: B. 343 cm³ Answer: (B) 343 cm³ 6a² = 294, so a² = 49 and a = 7 cm. Volume = 7³ = 343 cm³. Mensuration 1 answer
The perimeter of a rectangle is 46 cm and its area is 120 cm². What is the length of its diagonal? Answer: C. 17 cm Answer: (C) 17 cm l + b = 23 and lb = 120, so l = 15, b = 8. Diagonal = √(15² + 8²) = √289 = 17 cm. Shortcut: d² = (l + b)²... Mensuration 1 answer
What is the volume of a right circular cone of radius 6 cm and height 8 cm? Answer: B. 96π cm³ Answer: (B) 96π cm³ V = 1/3π r² h = 1/3 × π × 36 × 8 = 96π cm³. Trap: 288π forgets the 1/3 ; 60π is the curved surface ar... Mensuration 1 answer
A metal sphere of radius 6 cm is melted and recast into small spheres of radius 2 cm each. How many small spheres are made? Answer: D. 27 Answer: (D) 27 Number = (6/2)³ = 3³ = 27 (the 4/3π cancels). Trap: 9 compares areas instead of volumes. Mensuration 1 answer
A wheel of radius 35 cm covers a distance of 1.1 km. How many revolutions does it make? Take \(\pi = \frac{22}{7}\). Answer: A. 500 Answer: (A) 500 Circumference = 2 × 22/7 × 35 = 220 cm. 1.1 km = 1,10,000 cm. Revolutions = 110000 ÷ 220 = 500. Mensuration 1 answer
A rectangular garden 40 m long and 30 m wide has a path 2 m wide all around it on the outside. What is the area of the path? Answer: C. 296 m² Answer: (C) 296 m² Outer rectangle = 44 m × 34 m = 1496 m². Path = 1496 − 1200 = 296 m². Shortcut: path outside = 2w(l + b... Mensuration 1 answer
What is the total surface area of a solid hemisphere of radius 7 cm? Take \(\pi = \frac{22}{7}\). Answer: A. 462 cm² Answer: (A) 462 cm² TSA of a solid hemisphere = curved 2πr² + base πr² = 3πr² = 3 × 22/7 × 49 = 462 cm². Trap: 308 cm² is... Mensuration 1 answer
The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. What is the ratio of their volumes? Answer: D. 20 : 27 Answer: (D) 20 : 27 V ∝ r²h. Ratio = (2² × 5) : (3² × 3) = 20 : 27. Mensuration 1 answer
Water flows at 5 km/h through a cylindrical pipe of internal radius 7 cm into a rectangular tank 20 m long and 11 m wide. In how many hours will the water level in the tank rise by 1.4 m? Take \(\pi = \frac{22}{7}\). Answer: A. 4 hours Answer: (A) 4 hours Water per hour = πr² × length = 22/7 × 0.07² × 5000 = 77 m³. Volume needed = 20 × 11 × 1.4 = 308 m³.... Mensuration 1 answer
The largest possible right circular cone is cut out of a cube of edge 14 cm. What is the volume of the cone? Take \(\pi = \frac{22}{7}\). Answer: A. 7182/3 cm³ Answer: (A) 7182/3 cm³ The largest cone has radius = 7 cm (half the edge) and height = 14 cm. V = 1/3 × 22/7 × 49 × 14... Mensuration 1 answer
The curved surface area of a cylinder is 880 cm² and its height is 10 cm. What is its volume? Take \(\pi = \frac{22}{7}\). Answer: A. 6160 cm³ Answer: (A) 6160 cm³ 2πrh = 880 → r = 880 × 7/2 × 22 × 10 = 14 cm. Volume = πr²h = 22/7 × 196 × 10 = 6160 cm³. Shortcut:... Mensuration 1 answer
What is the area of the circle inscribed in an equilateral triangle of side 12 cm? Answer: B. 12π cm² Answer: (B) 12π cm² Inradius of an equilateral triangle = a/2√(3) = 12/2√(3) = 2√(3) cm. Area = π (2√(3))² = 12π cm². Tra... Mensuration 1 answer
The length of a rectangle is 3 cm more than its breadth. If the length is increased by 2 cm and the breadth is decreased by 1 cm, the area stays the same. What is the area of the rectangle? Answer: C. 40 cm² Answer: (C) 40 cm² Let the breadth be b. Then (b + 5)(b − 1) = b(b + 3). b² + 4b − 5 = b² + 3b, so b = 5 cm and length = 8... Mensuration 1 answer
What is the average of the first ten multiples of 7? Answer: A. 38.5 Answer: (A) 38.5 Average = 7 × (average of 1 to 10) = 7 × 5.5 = 38.5. Average 1 answer
The average of 13 results is 40. The average of the first seven is 38 and the average of the last seven is 43. What is the seventh result? Answer: A. 47 Answer: (A) 47 The seventh result is counted in both groups of seven. Seventh = 7 × 38 + 7 × 43 − 13 × 40 = 266 + 301 − 520 =... Average 1 answer
A car goes from P to Q at 40 km/h and returns from Q to P at 60 km/h. What is its average speed for the whole journey? Answer: A. 48 km/h Answer: (A) 48 km/h Shortcut: for equal distances, average speed = 2xy/x+y = 2 × 40 × 60/100 = 48 km/h. Trap: 50 km/h is... Average 1 answer
The average of 50 numbers is 38. If two numbers, 45 and 55, are removed, what is the average of the remaining numbers? Answer: B. 37.5 Answer: (B) 37.5 Sum of 50 = 1900. Remaining sum = 1900 − 100 = 1800. Average = 1800 ÷ 48 = 37.5. Average 1 answer
The average marks of 40 students were found to be 60. Later it was found that one student's mark of 85 had been entered as 58. What is the correct average? Answer: B. 60.675 Answer: (B) 60.675 Shortcut: the total was short by 85 − 58 = 27, so the average rises by 27 ÷ 40 = 0.675. Correct average... Average 1 answer
A batsman scores 96 runs in his 19th innings, and this raises his average by 4. What is his average after the 19th innings? Answer: D. 24 Answer: (D) 24 Shortcut: new average = runs in this innings − (old innings × rise) = 96 − 18 × 4 = 24. Plain: let the old aver... Average 1 answer
The average of three numbers is 77. The first number is twice the second, and the second is twice the third. What is the first number? Answer: C. 132 Answer: (C) 132 Let the third be x. Then the second is 2x and the first is 4x. 7x = 3 × 77 = 231, so x = 33. First number = 4... Average 1 answer
Section A has 30 students with average marks 65, and section B has 20 students with average marks 70. What is the average of all 50 students? Answer: B. 67 Answer: (B) 67 Combined average = 30 × 65 + 20 × 70/50 = 3350/50 = 67 . Shortcut: the answer lies closer to 65 because section... Average 1 answer

← Previous

Page 18 of 20