List of top Questions asked in CAT

The radii of three concentric circles are in the ratio 2: 3: 4. What is the ratio of sum of areas of two inner circles to the area of the region between outermost circle and innermost circle?
A circle is inscribed in a square of side 10 cm. Find the area of the region between the square and the circle.
Raj invested a certain sum of money in two schemes. The first scheme offers a simple interest of 10% per annum, and the second scheme offers a simple interest of 12% per annum. If the total interest earned from both schemes after 3 years is Rs. 1980, and the ratio of the amounts invested in the two schemes is 5:4, what is the amount invested in the second scheme?
∆ABC is inscribed inside a circle and there is a point D on the arc BC opposite to A such that BD = CD. If ∠BAC = 70° and ∠ABD = 85°, then find the measure of ∠BCA.
By which of the following numbers, \(N = 0.abccbaabccba……\) must be multiplied so that the product is an integer?
A sum of money is divided among A, B, and C in the ratio 3:5:7 respectively. If B gets Rs. 300 more than A, then the total amount of money is:
Vrushali invested Rs. (X+3000) on compound interest of r% p.a. compounded annually for 2 years and Tarushi invested Rs. (X – 2000) on simple interest of (r-2)% p.a. for 3 years. The total interest received by both of them is together Rs. 12360. If Anant invested Rs. (X + 8000) on simple interest for 3 years on 15% and received an interest of Rs. 13500, find the value of ‘r’.
A bag contains some red, some green and 9 blue balls. Ratio of number of red to green ball in the bag is 5:4. If the probability of drawing a red ball is \(\frac{1}{6}\) more than that of drawing a blue ball then find the probability of getting three different coloured ball when three balls are drawn from the bag one after another and without replacement.
If the LCM of three natural numbers 2412, 1816 and a is 3618, then how many values of a are possible?
A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1 : 3, then the ratio of lemon juice and sugar syrup in the new mixture is
Vrushali invested Rs. (X + 3000) on compound interest of r% p.a. compounded annually for 2 years and Tarushi invested Rs. (X - 2000) on simple interest of (r - 2)% p.a. for 3 years. The total interest received by both of them is together Rs. 12360. If Anant invested Rs. (X + 8000) on simple interest for 3 years on 15% and received an interest of Rs. 13500, find the value of ‘r’.
Four persons ‘P’, ‘Q’, ‘R’ and ‘S’ has different amounts with them. ‘S’ has thrice the amount as that with ‘P’. ‘Q’ has 25% more amount than ‘S’. The amount ‘R’ has is equal to the average amount all four persons have. If the sum of the amounts ‘P’ and ‘R’ have is Rs. 4300, then find the amount ‘R’ have.
A chemist has two solutions, A and B. Solution A is 30% acid and the rest water, while solution B is 60% acid and the rest water. If equal amounts of solutions A and B are mixed to form a new solution C, what is the percentage of acid in solution C?
Find the minimum numbers starting from 74 that are multiplied to get 50 zeros at the end ?
Aman bought '3x' shares for Rs. 420 per share, '4x' shares for Rs. 450 per share and '3x' shares for Rs. 430 per share. He sold 40% of the shares at Rs. 480 per share and the rest at Rs. 'y' per share. If he made a total profit of 20% on the whole transaction, find the value of 'y'.
A school has less than 5000 students and if the students are divided equally into teams of either 9 or 10 or 12 or 25 each, exactly 4 are always left out. However, if they are divided into teams of 11 each, no one is left out. The maximum number of teams of 12 each that can be formed out of the students in the school is
In a ∆PQR, internal angle bisectors of ∠Q and ∠R meet at I while external angle bisectors of ∠Q and ∠R meet at X. If ∠P = 54°, then find the measures of ∠QIR and ∠QXR, respectively.
A group of friends decided to share the cost of a gift equally. If each person contributed Rs. 50, the amount would have been short by Rs. 20. However, if each person contributed Rs. 60, they would have Rs. 30 more than the required amount. What is the price of the gift?
How many female dancers are interested in attending a 2-day event?
Which of the following two groups of people had identical sources?
In a library, the ratio of fiction books to non-fiction books is 7:5. The ratio of English fiction books to Hindi fiction books is 2:3. If there are 420 English fiction books, find the total number of non-fiction books in the library.
In a group of 100 people, 70 like coffee, 60 like tea, and 45 like both coffee and tea. How many people like neither coffee nor tea?
P and Q start a business with initial investment Rs.5000 and Rs.4000 respectively. After ’t’ years Q adds 25% of what he invested initially and another person R joins the business with them with initial investment Rs.7000 and after 5years from the start of the business P adds Rs.1000 more to his capital. If at the end of 8 years total profit from the business is Rs.11900 while share of Q is Rs.3750, what is the share of R in the profit.
Let a,b,c be non-zero real numbers such that b2<4ac, and f(x)=ax2+bx+c. If the set S consists of all integers m such that f(m)<0, then the set S must necessarily be
Let f(x) = ax² + bx + c, where a, b, and c are real numbers with a ≠ 0. If the graph of f(x) intersects the x-axis at two distinct points with x-coordinates p and q (p < q), then the equation ax² + bx + c + 1 = 0 has: