List of top Questions asked in CAT

In the questions two columns are given. You are required to solve the equations given in the "equations" column and match them with the correct statement given about the desired equation in the "conditions" column.
Equations  Conditions
(a)2x2 – 11x + 12 = 0 (d)Product of roots is negative
(b)5x2 21x – 20 = 0(e)Product of roots is completely divisible by 6
( c)x2 – 17x + 72 = 0(f)Sum of both roots is positive
Find the HCF of (8125-1) and (274-1).
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?
The average weight of ‘b’ boys in a group is 63 kg. A boy whose weight is 147 kg joins the group such that the average weight of the group becomes a prime number in between 65 and 91. Find the value of ‘b+1’.
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’.
Scheme A offers 25% interest and scheme B offers 20% interest. M invested Rs.4000 in scheme A and Rs.6000 in scheme B at compound interest. After 2 years, he invested the amount received from scheme A and B in schemes B and A respectively at simple interest for 2 more years. If another person N invested Rs.6000 in scheme A and Rs.4000 in scheme B at compound interest. After 2 years, he invested the amount received from scheme A and B in schemes B and A respectively at simple interest for 2 more years, then what is the difference between total amount received by M and N after 4 years?
If (Ax + By - Cz)2 = 4x2+ 3y2+ 2z2+ \(4\sqrt{3xy} \)-\( 2\sqrt{6yz}\) - 4√2xz, then find the value of A2+ B2C2.
A triangular garden has its corners at points A(2, 3), B(5, 7), and C(1, 6) on a coordinate plane. If a fourth point D is added to form a parallelogram ABCD, what are the coordinates of point D?
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 rectangular plot of land measures 55 meters by 25 meters. A path of uniform width surrounds the plot. If the area of the path is equal to the area of the plot, what is the width of the path in meters?
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
If 25(3a-2b) = 5(b-a) = 52 and , then find the value of ab - c.
All the vertices of a rhombus lie on a circle of radius R. If the length of one diagonal of the rhombus is D, then the area of the rhombus is:
Eight years hence from now, ratio of ages of ‘A’ and ‘B’ will be 10 : 9, respectively. Present age of ‘B’ is 60% more than age of ‘C’ 8 years ago from now. If ratio of present ages of ‘A’ and ‘C’ is 3:2, respectively then find the present age of ‘C’.
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 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'.
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.
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?