216 questions asked across 4 exam years, newest first
The sum of two consecutive even numbers is 174. Find the smaller number.
Answer: A
Find the value of (cosec θ - sin θ )(sec θ - cos θ )(tan θ + cot θ ).
Answer: D
Find the value of tan 72° – tan 27° – tan 72° tan 27°.
Answer: C
If secθ + tanθ = x, then find sinθ.
Answer: A
A, B and C invested money in a business such that 2 times A's share, 4 times B's share and 6 times C's share are all equal. If they earned ₹44,000, find the share of A.
Answer: C
If tanA + cotA = 2, then the value of tan²A + cot²A is:
Answer: D
If two straight lines are coinciding with each other, then the number of points of intersection is/are:
Answer: A
The value of θ, when √3 cos θ + sin θ = 1 (1 ≤ θ ≤ 90°), is:
Answer: D
Let x = r cos(t), y = r sin(t) cos(u), z = r sin(t) sin(u). Then the value of x² + y² + z² is ___.
Answer: C
For what value of t is the value of sin²(t), half of the value of tan(t)?
Answer: B
The sum of five consecutive numbers is 80. Find the largest number.
Answer: A
If the system of the following equations has the value of the variables as three consecutive integers, then the value of a is ____. x - y + z = 2a x + 4y - 2z = 3(4 - a) 2x - 3y + 4z = 6 - 2a
Answer: B
Arvind and Chetan started running simultaneously from the same point in the same direction on a circular track of length 210 m. If Arvind takes 180 seconds to complete one round, and Chetan takes 420 seconds to complete one round, after how much time will they meet for the first time at the starting point on the track?
Answer: D
At a cafe, Rama bought drinks for her 7 friends at ₹240. Some of them wanted coffee, while others wanted black tea. A regular cup of coffee cost ₹40 and a regular cup of black tea cost ₹ 30. How many cups of tea did she purchase?
Answer: D
Two different quantities of the same solution having ingredients A and B are stored in two different containers. In the first container, there are 252 litre of A and 441 litre of B. In the second container, the total quantity of the solution was 1188 litre. How much of the solution in the second container was made up of ingredient B?
Answer: A
2 biscuits and 1 chocolate cost ₹69. 2 chocolates and 3 cups of coffee cost ₹127. 3 biscuits, 4 chocolates, and 2 cups of coffee cost ₹229. Find the total cost (in ₹) of 5 biscuits, 5 chocolates, and 5 cups of coffee.
Answer: A
Study the given pie chart carefully and answer the question that follows. The given pie chart shows the number of successful start-ups in different sectors in a particular year. If the total number of successful start-ups is 2910, then find the number of start-ups in the education and agriculture sectors. (Neglect the decimal part.)
Answer: D
If 2cosec²θ + 3cot²θ = 17, then the value of 'θ' when 0° ≤ θ ≤ 90° is:
Answer: B
In ΔDEF, the bisector of ∠D intersects side EF at point N. If DE = 36 cm, DF = 40 cm and EF = 38 cm, then the length (in cm) of NF is ________.
Answer: B
If asin³ x + bcos³ x = sin x cos x and asin x = bcos x, then find the value of a² + b², provided that x is neither 0° nor 90°.
Answer: B
A rectangular courtyard is 4m 95cm long and 16m 65cm broad. It is to be paved with square tiles of the same size. Find the least number of such square tiles required to pave the rectangular courtyard.
Answer: A
The inner and outer radii of a circular track are 28 m and 25 m, respectively. The cost (in ₹) of levelling the track at ₹28 per m² is: [Use π = 22/7]
Answer: B
Atul gives Vishu a head-start of 20 seconds in a 900 m race and beats him by 135 m. While running the same race again, Atul gives a start of 189 m and beats him by 8 seconds. In how much time can Vishu complete the full race of 900 m?
Answer: B
If p sin A − cos A = 1, then p2 − (1 + p2) cos A equals:
Answer: B
If p cos A = 2q sin A and 2p cosec A − q sec A = 3, then the value of p² + 4q² is:
Answer: A
