Quant Question Bank by VP  Set 2

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?

Q28) Boxes of 2 types viz. A and B are used for packing balls of 2 different colours. Each of the type A boxescan hold a maximum of 17 blue balls or 19 green balls, and each of the type B boxes can hold amaximum of 18 blue balls or 23 green balls. When all the boxes of type A are to be completely filledwith blue balls and all the boxes of type B with green balls, the total number of balls required is 566. Butwhen the boxes of type A are to be completely filled with green balls and the boxes of type B with blueballs, the total number of balls required is 49 less. How many boxes are there? (All balls of the same colour and are identical.)

Q29) If bhavya and Karmveer work on alternate days to complete a work, then the work gets completed in
exactly 24 days. If B and K denote the number of days required by bhavya and Karmveer respectively tocomplete the work independently, then how many ordered pairs of integral values of R and K are possible?

Q30) How many fourdigit numbers, having distinct digits, using the digits 1, 2, 3, 4 and 5 can be formedsuch that the numbers formed are divisible by each of the digits used in the number ?

Q31) The product of three positive integers is 6 times their sum. One of these integers is the sum of the othertwo integers. If the product of these three numbers is denoted by P, then find the sum of all distinctpossible values of P.