Quant Question Bank by VP  Set 2

Q8) How many ordered pairs (P, Q) are there such that the unit’s digits of P^P and Q^Q are the same?
P and Q are natural numbers less than 10 and are not necessarily distinct

Q9) lf the length and breadth of a rectangle are increased by 4 units each, then the area of the rectangle increases by 100%. lf the breadth is Decreased by 6 units and the length is increased by 2 units, then the area decreased by 75%. Find the ratio of the length of the diagonal of the rectangle and the length of the rectangle.

Q10) P is a group of four numbers 1, 2, 3 and 1. In every step, 1 is added to any two numbers in group P. In how many such steps is it possible to make all the four numbers in group P equal?

Q11) A triangle has its longest side as 38 cm. lf one of the other two sides is 10 cm and the area of the triangle is 152 sq cm, find the length of the third side.

Q12) A circle of radius 3 units is drawn with centre as (8,7) and another circle is drawn taking the line segment joining (12, 8) and (4, 4) as diameter. Find the number of common tangents that can be drawn to these two circles

Q13) A boat moves at a speed of 12 kmph in stillwater. lt has to travel a distance of 6O km downstream fromP to Q. The moment the boat reached a point R,between P and Q, the speed of the current suddenlydoubled. lf as a result, the boat reached itsdestination half an hour earlier than it normally would have, what is the speed of the stream ?

Q14) A natural number n is such that 120 ≤ n ≤ 240. If HCF of n and 240 is 1, how many values of n are possible?

Q15) The function f(x) is defined such that f(2x) + f(3x) + f(x + 2) + f(3  x) = x. for all real values of x. Find f(0)

Q16) In an exam there are 90 questions. There are three sections, 1,2,3. Each question in section 1 carries 2 marks, each question in section 2 carries 3 marks, and each question in section 3 carries 4 marks. All questions in section 1 together carry at least 40% of the total marks of the exam. If section 3 has atleast 36 questions, section 1 has how many questions?
a. 52 or 53 or 54
b. 50 or 51 or 52
c. 51 or 52 or 53
d. 52 or 53

Q17) Find the distance between the lines, 2x  5y  9 = 0 and 10y = 4x  93

Q18) There are three containers A, B and C filled with 60%, 75% and 80% solution of alcohol in water. The solution in the three containers are taken in a certain ratio and mixed thoroughly to form a 70% solution of alcohol in water. In this mixture, the quantity of solution taken from C is 40% less than the quantity taken from A. By what percent is the quantity taken from B less or more than the quantity taken from A?

Q19) Y = 2, 3, 4, 5 …., 103
Sm = am : a∈Y, m∈N
Find the least element in the set[Y–(S2∪S3∪S4∪….∪S89)]

Q20) Three natural numbers a, b and c are such that a^2 + b^2= c^2. If a = 20, how many ordered pairs (b, c) are possible?

Q21) If all the fourdigit numbers that can be formed using the digits 1, 2, 3, 4, 5, 6, 7 and 8 without repetition are arranged in ascending order, what will be the rank of the number 5283?

Q22) Find the ratio of the sum of first 20 terms to the sum of first 40 terms of the series S, where S = (4/5) + 4/45 + 4/117 + 4/221 + ...

Q23) How many integers “a” are there such that 9x^2 + 3ax + (a + 5) > 0 for all values of x?

Q24) xy + zy = 37 and xz + zy = 72. Find the number of ordered triplets (x, y and z) such that x, y and z are positive integers

Q25) Two people start swimming from the opposite ends of a swimming pool simultaneously. They meet at a distance of 410 m from one of the ends and continue swimming further till they reach the opposite ends. They take rest for 1 hr each and then start off the return journey. Now they meet at a distance of 230 m from the other end. Find the length of the pool.
(1) 750 m
(2) 1000 m
(3) 1100 m
(4) 840 m

Q26) Lakhjeet had 130 lts of blue paint,160 lts of red paint, and 180 lts of white paint. He painted four equallysized stripes on a wall, making a blue stripe, a red stripe, a white stripe and a pink stripe. Pink paint is a mixture of red and white paints. When lakhjeet finished, he had equal amount of blue, red, and whitepaints left. If he has to paint four more stripes of the same dimensions on another wall in exactly thesame way, then which of the following is true?
(1) lakhjeet requires 30 lts of blue paint, 0 lts of red paint and 40 lts of white paint
(2) lakhjeet requires 30 lts of blue paint, 60 lts of red paint and 60 lts of white paint
(3) lakhjeet requires 30 lts of blue paint, 60 lts of red paint and 80 lts of white paint
(4) lakhjeet requires 80 lts of blue paint, 110 lts of red paint and 130 lts of white paint

Q27) N is a natural number which gives remainders 1 and 2 when divided by 6 and 5, respectively. All such N’s are written in the ascending order, side by side from left to right. What is the 99th digit from the left?