List of top Questions asked in CAT

In a triangle ABC,AB=AC=8cm. A circle drawn with BC as diameter passes through A. Another circle drawn with center at A passes through B and C. Then the area,in sq.cm,of the overlapping region between the two circles is

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 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?

The four sentences (labelled 1, 2, 3, 4) below, when properly sequenced would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer:
1. Complex computational elements of the CNS are organized according to a “nested” hierarchic criterion; the organization is not permanent and can change dynamically from moment to moment as they carry out a computational task.
2. Echolocation in bats exemplifies adaptation produced by natural selection; a function not produced by natural selection for its current use is exaptation --feathers might have originally arisen in the context of selection for insulation.
3. From a structural standpoint, consistent with exaptation, the living organism is organized as a complex of “Russian Matryoshka Dolls” -- smaller structures are contained within larger ones in multiple layers.
4. The exaptation concept, and the Russian-doll organization concept of living beings deduced from studies on evolution of the various apparatuses in mammals, can be applied for the most complex human organ: the central nervous system (CNS).

For any natural number n, suppose the sum of the first n terms of an arithmetic progression is n(n+1). If the nth term of the progression is divisible by 7, then the smallest possible value of n is:

The average weight of a group of people increases by 2 kg when a person weighing 65 kg joins them. If the initial average weight of the group was 55 kg, find the ratio of the number of people initially in the group to the total number of people in the new group.

Two buses start simultaneously from the same place towards a destination which is 180 km away. The first bus travels at a speed of 40 km/h and the second bus travels at a speed of 60 km/h. The second bus reaches the destination, waits for some time and returns back. If the buses cross each other 90 km away from the starting point, then for how long did the second bus wait at the destination?

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 the given figure, ‘O’ is the centre of the semi-circle and ∠MON =48°, Find ∠MRP.

In triangle ABC, ‘D’ and ‘E’ are two points on sides AB and AC, respectively such that DE is parallel to BC. If AD=16 cm, BD=(5x-16) cm, AE=2x cm and EC=(25-2x) cm, then find the value of ‘x’.

Is\( (\sqrt{x}-\frac{1}{\sqrt{x}})=\sqrt{-5}\) and x≠ 0, then what is the value of \(\frac{3(x^2+3)-6-3x}{4x}\) ?

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.

PQRS is a rhombus such that length of its each side is 30 cm. If PR=36 cm and QS=\(4\sqrt{x}\) cm then the length of each side of the rhombus (in terms of ‘x’) is:

Find the value of: \( \frac{x^4-81}{ 2x2+13x+15 }\times\frac{2x+3}{x^3+27}\times\frac{[(x-3)^2+3x](x+5)}{(x+3)^2-6x}\)

How many factors of N=2⁶ x 3⁸ x 5¹⁰ x 7¹² are perfect squares as well as perfect cubes?

How many numbers between 90 and 600 have exactly three factors?

How many odd factors of the number 45⁶ x 56⁵ x 77⁶ are multiples of 63?

If=\(\frac{2x^2+x-6}{(x+2)^2-(x-2)^2}\), Q=\(\frac{x^2+3x+9}{(2x-3)(x^2-4)}\) and \(R=\frac{x^2-27}{x^4-4}\), then find the value of PXQ÷R

If (3x-\(\frac{1}{3x}\))=4, , then what is the value of (27x³-\(\frac{1}{27x^3}\)) ?

If \(\frac{5(4x^2+1)-3x}{4x}=8\) and x ≠ 0, then what is the value of \((√2x-\frac{1}{√2x}) \)?

If \(A=\frac{x^2-y^2}{x^2-y^2}\), \(B=\frac{x+y}{x^2+y^2+xy}\) and \(C=\frac{ 3xy^2-3x^2y}{x^2-y^2}\), then find the value of AB (A+C)

If \(N = 2^5 \times 3^4 \times 5^5 \times 11^2\), then how many factors of N are multiples of 66 but not of 72?

What is the minimum value of (a + b) such that 4a x 5b will be a multiple of 5000?

If x²-4x+3=0, then what is the value of (x³+4x²+7x+24)(x²+2x+3)^-1?

Directions: Answer the questions based on the information given below.
Sonia deposited Rs. 20 and Rs. 50 notes in her piggy bank on different days of the month and used to count total number of Rs. 20 and Rs. 50 notes deposited by her in the piggy bank at the end of the month. The bar graph given below shows the percentage by which number of Rs. 50 notes in the piggy bank was more/less than number of Rs. 20 notes at the end of the given months. (Note: +ve value shows more while –ve value shows less)

Added Information:
1. Number of Rs. 20 notes deposited in February was 42(6/7)% of total notes deposited in the same month.
2. Number of Rs. 50 notes deposited in February and March together is 35(5/13)% less than number of Rs. 20 notes deposited in February and March together.
3. Number of Rs. 20 notes deposited in April and March together is 80 more than total number of Rs. 20 notes deposited at the end of February.
4. If number of Rs. 20 notes deposited in April would have been 160 more, then number of Rs. 50 notes deposited in April would have been 26% more than number of Rs. 20 notes deposited.
5. Number of Rs. 50 notes deposited in April was 6 times more than number of Rs. 50 notes deposited in May.
6. Number of Rs. 20 notes deposited in June was 50% more than that deposited in May.