MCQ Two cyclists P and Q start simultaneously from towns A and B respectively and ride towards each other on a straight road at constant speeds. They first meet at a point 7.5 km from A. After meeting, each continues to the other town, turns back immediately o

TITA A vessel contains 80 litres of pure milk. In each operation, exactly x litres of the liquid in the vessel is removed and replaced by x litres of water, where x is the same positive integer in every operation. After exactly 4 operations, the volume of milk

MCQ A and B together can finish a project in 20 days. B alone takes 45 days to finish the project. They start the project together, but A leaves after some days; B alone then takes a further 21.6 days to complete the remaining work. The number of days A alone

TITA A trader marks his goods 40% above cost price and offers a discount of d% on the marked price. He also uses a faulty balance that displays 1000 g but actually delivers only 800 g of the goods. If his overall profit is exactly 40% of the actual cost pri

MCQ In a class, the average mark of the boys is 68 and that of the girls is 80. The overall class average is 74. A new group of students, consisting only of boys with average mark 62, joins the class, and after they join, the overall class average becomes 71.

TITA Let f:RR satisfy f(x)+2,f(1-x)=x^2+3x for every real x. Find the value of 3,f(5).

MCQ The number of real values of x satisfying [ _2(x^2-3x+2);+;_2(x^2-7x+12);=;3;+;_2!((x-1)(x-4)2) ] is:

MCQ Let a, b, c be positive real numbers satisfying a+b+c=12 and abc=64. The maximum possible value of a is:

MCQ Let p and q be the roots of the equation x^2-(k+3),x+(2k+1)=0. If (p-q)^2=12, then the sum of all possible values of k equals: %--------------------------- NUMBER SYSTEM --------------------------- Number System

TITA Let N be the smallest positive integer such that N leaves remainder 3 when divided by 7, remainder 5 when divided by 11, and is divisible by 13. If M is the next positive integer (after N) satisfying all three conditions, find the value of M-N.

MCQ The number of positive integers n 600 such that n is divisible by exactly two of the three numbers 4, 6, and 9 is:

TITA A three-digit positive integer abc (with a 0) satisfies all of the following simultaneously: Find the sum of all three-digit numbers abc satisfying these conditions. %--------------------------- GEOMETRY --------------------------- Geometry / Mensuration

MCQ In triangle ABC, point D lies on side BC such that BD:DC=2:3. Point E lies on segment AD such that AE:ED=3:2. The line through B and E, when extended, meets side AC at point F. The ratio AF:FC equals:

TITA Two circles of radii 5 and 3 are externally tangent to each other. A line tangent externally to both circles touches the larger circle at P and the smaller circle at Q. Find the length of PQ (in the form ab, enter the value of a b; for example, if PQ=215,

MCQ In the coordinate plane, A=(0,0) and B=(10,0). A point P=(x,y) with y>0 is chosen such that the area of triangle APB is exactly 20 square units. Over all such points P, the quantity PA+PB attains its minimum value at a unique point P^*. The value of PA PB

[Arithmetic -- Profit & Loss, Medium-Hard, MCQ]\ A retailer marks every item in his store at 60% above its cost price. As part of a promotion, on every third item that is sold he gives a discount of d% on the marked price, while the remaining items are sold

[Arithmetic -- Time & Work / Pipes, Hard, TITA]\ Pipes A and B can fill an empty tank in 10 hours and 15 hours respectively, while pipe C can empty a full tank in 30 hours. Starting at time 0 with an empty tank, the pipes are operated as follows: in the 1st h

[Arithmetic -- Time, Speed & Distance, Hard, MCQ]\ Two cars X and Y travel between cities P and Q along the same straight road of length D km. Car X leaves P at 9:00a.m. heading towards Q at 50 km/h. Car Y leaves Q at 9:45a.m. heading towards P at 40 km/h.