61. If the angle between the radii of a circle is 110°, then the angle between the tangents at the ends of the radii is
Answer: 70°
62. A point A is 5 cm away from the center of a circle and the length of the tangent from A is 4 cm. The radius of the circle is
Answer: 3 cm
63. AB is the chord of a circle and AOC is its diameter such that ∠ACB = 50°. If AT is the tangent at point A, then ∠BAT is
Answer: 60°
64. For two concentric circles, the radius of the outer circle is 5 cm and the length of the chord AC of 8 cm is the tangent to the inner circle. The radius of the inner circle will be
Answer: 2 cm
65. For two concentric circles, the radii are 5 cm and 3 cm. The length of the tangent from the larger circle that touches the smaller circle is
Answer: 12 cm
66. ∠A, ∠B, and ∠C are the three angles of a triangle, and ∠A/4 + ∠B/4 + ∠C/5 = 41°. What is the value of ∠A + ∠B?
Answer: 100°
67. A person sells a table for ₹2700 and incurs a 10% loss. What price (in ₹) should the table be sold for to gain a 33% profit?
Answer: ₹3600
68. A trader sells two items for ₹14784 each. If he makes a 12% profit on one item and a 12% loss on the other, what is the amount of loss (in ₹)?
Answer: ₹368
69. If the radius of a circle is increased by 25%, by what percentage will its area increase?
Answer: 56.25%
70. If a 27% discount is given on an electricity bill, ₹1825 is still left to be paid. What was the original bill amount?
Answer: ₹2500
71. Two numbers are 50% and 80% less than a third number. By what percentage should the second number be increased to make it equal to the first number?
Answer: 37.5%
72. The daily ticket price for a local train is ₹50, and the monthly pass costs ₹1125. If I buy the monthly pass and travel for 30 days in a month, what will my savings be?
Answer: 14%
73. A discount of 36% is given on the price of an item. By what percentage should the current price be increased to bring it back to the original price?
Answer: 56.25%
74. A can complete a task in 18 days. He worked for 12 days, and the remaining task was completed by B in 8 days. How many days will it take for B to complete the whole task alone?
Answer: 24 days
75. A completes 2/5 of a task in 9 days. Then B joins, and together they finish the remaining task in 6 days. How many days will it take for B to complete the entire task alone?
Answer: 12/13 days
76. If cos²A – sin²A = x, what is the value of x?
Answer: 2cos²A – 1
77. A car moving at an average speed of 72 km/h takes 9 minutes to cover a certain distance. By how much should the speed be increased (in km/h) to cover the same distance in 8 minutes?
Answer: 8
78. Two cars travel from city A to city B at speeds of 60 km/h and 108 km/h respectively. If one car takes 2 hours less than the other to cover the journey, what is the distance between city A and city B?
Answer: 270 km
79. A solid sphere with a diameter of 7 cm is cut into two equal parts. What is the increase in total surface area (in square cm)?
Answer: 77
80. What is the area (in square cm) of a rectangle with a perimeter of 90 cm and a width of 20 cm?
Answer: 400