List of top Questions asked in CAT

There are 938 players played cricket in the world and some of them are played different-different leagues APL, BPL, and CPL in the world. There are 56 \(\frac{8}{7}\) % of players who do not play in any league.BPL has 4 more players as compare to CPL and APL have 22 players less than the CPL. The ratio between the players who play in only APL & CPL together to the players who play only BPL & CPL together is 3 : 2. The total number of players who play only in APL and BPL is equal to the sum of the players who play in only APL & CPL together and BPL & CPL together. The total number of players who play in all three leagues is 99 less than to the players who play in BPL. 40% of the players who play in all three leagues are playing in APL and CPL together. Answers the given questions based on the above information.

Answer the questions based on the information given below.
The table given below shows the total number of towels sold by a shopkeeper from Monday to Friday. Some data are given while some are missing in the table.
Note : Total number of towels sold = Number of small sized, medium sized and large sized towels sold on the particular day.

Days	Total number of towels sold	Ratio of large to small sized towels sold	Percentage of Medium sized towels	Difference between the number of large sized and small sized towels sold
Monday	950	3 : 1	20%	-
Tuesday	900	3 : 2	-	90
Wednesday	-	5 : 4	25%	70
Thursday	750	-	20%	40
Friday	-	4 : 3	40%	90

A company manufactured cups of four different types. The table given below shows the number of cups of four different types manufactured by the company in four different weeks of a month.

Types	Week I	Week II	Week III	Week IV	Total
Type A	2650	1640	-	-	8820
Type B	-	1520	1650	1730	-
Type C	3240	-	-	2550	8750
Type D	2960	1220	-	-	8270
Total	10730	-	7530	-	-

The number of cups of type D manufactured in week IV is 480 less than the number of cups of type A manufactured in week I. The number of cups of type C manufactured in week II is 1/6 of the total number of the cups of type B manufactured. The number of cups of type A manufactured in week III is 220 more than the number of cups of type B manufactured in week I.

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?

What is the number of factors of the number formed by the last three digits of 1005¹⁰⁰¹?

If the LCM of three natural numbers 24¹², 18¹⁶ and a is 36¹⁸, then how many values of a are possible?

∆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.

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.

In a school of more than 500 students, when the students were standing in a row of 7, 5 students were left out. When these students were standing in a row of 10, again 5 students were left out and when they were standing in a row of 15, 5 students were left out again. If each time, at least one row was formed and the number of students in the school is the least possible, then find the average of the number of rows formed in the above three cases.

In a trinary base system, how many numbers from 0 to 100 end with digit 1?

Find the HCF of (81²⁵-1) and (2⁷⁴-1).

If 4^(4b-3a) = 2^(2b+c) = 8^(c-a) and a + b + c = 11, then find the value of \(4(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca})\)

If a² + 32 + b² + 8(a + b) = 0, then find the value of (a3 + b3).

If (Ax + By - Cz)² = 4x²+ 3y²+ 2z²+ \(4\sqrt{3xy} \)-\( 2\sqrt{6yz}\) - 4√2xz, then find the value of A2+ B2C2.

Find the value of \(36(\frac{a}{2}+\frac{b}{6}+\frac{c}{3})^2\)

If 25^(3a-2b) = 5^(b-a) = 5² and , then find the value of ab - c.

The volume of hemisphere is equal to the volume of cylinder. Calculate the ratio of total surface area of hemisphere and total surface area of cylinder. The radius of hemisphere and cylinder is equal.

After five years, A's age will be 10.5 years less than 2.5 times of C's age. Three years ago, the ratio of age of A and C is 3: 1. If B is three times the age of C, then what is the present age of B?

Komal and Harish etered into a partnership with investment of Rs.70000 and Rs.55000 respectively after certain number of months Girish joined them with investment of Rs.60000. At the end of one year they earned a profit of Rs.297000. If share of Girish in the profit is Rs.72000. Period of investment of Harish is what percent more than the period of investment of Girish?

Pipes A, B, and C alone can fill a tank in 25 minutes, 75 minutes, and 50 minutes, respectively while a tap alone can empty the tank in 150 minutes. If pipe A and the tap opened together and after 15 minutes pipe A is closed and B and C together is opened, then in how many minutes will the tank filled completely?

A 480 L mixture of milk and water in the ratio 5: 3 If 'X' L of the mixture is replaced by water and again '(X - 24)' L of the mixture is replaced by water. If the amount of water in the final mixture is 300 L, then find the value of 'X + 15'.

Present age of P is 15 years, and he invested Rs.4500 at 20% annual Compound Interest while Q invested Rs.5824 at 25% annual Compound Interest. When they both turn 18 years, interest amount received by both of them is same, then how old are Q at present?

The average marks of the three students L, M and N is 80. Another man P enters the group of these three and makes the average 75. Now, a man Q whose marks 6 more than P, replaces M and average of the L, N, P and Q becomes 70. What is the marks of M?

In the given figure, AB is the chord of the circle with centre ‘O’. A tangent AT is drawn at point ‘A’ so that angle BAT = 48°, then measure of angle ADB is :

In triangle PQR, PM is perpendicular to QR. If ‘T’ is a point in between ‘Q’ and ‘M’ such that PT = \(5\sqrt3\) cm, PM = \(\sqrt{39}\) cm then find the value of PQ such that QM : TM = 5 : 2.