QA

Five men and 7 women are standing in a line in a random order. Probability that every man stands next to at least one woman is m/n, where m and n are coprime to each other. Find m + n.

A fly and an ant are on one corner of a unit cube. They wish to head to the opposite corner of the cube. The fly can fly through the interior of the cube, while the ant has to walk across the faces of the cube. How much shorter is the fly's path if both insects take the shortest path possible

What is the least perimeter of an obtuse-angled triangle
with integer sides, whose one acute angle is twice the
other

How many of the following numbers is a prime?
101!, 101!-1, 101!-2, 101!-3.........101!-101

Given 2^50 is a 16-digit number starting with 11. How many digits are there in 2^100

Suppose that 2 − √99 is a root of x^2 + ax + b where b is a negative real number and a is an integer. The largest possible value of a is

There are 100 tokens numbered from 1 to 100. In how many ways can two tokens be drawn simultaneously so that their sum is more than 100?

A sequence {a(i)} is defi?ned as follows:
a(i+1) = 1/{1 − a(i)} for i >=? 1:
If a3 = a1, then the value of {a(9)}^9 is

P and Q are two cities on a highway 155 km apart. R, S and T are three cities on the same highway, between P and Q, with R being between P and S, and T being between S and Q, such that 3PR = TQ and RS = 2ST. One day, an accident occurred on the highway at T. The medical facilities at Q, R, S and T were poor. Hence, the victim's friend called up a hospital at P for an ambulance. The ambulance started from P at 12:00 noon and reached R at 12:10 p.m. It then doubled its speed for the remaining part of the trip and returned to P at 2:10 p.m. Find the initial speed of the ambulance.

Let A be a set of distinct positive integers. If the arithmetic mean (average) of the elements of A is 21, what is the maximum possible value of an element in A?

There are fifty successive percentage discounts given in a series
2%,4%,6%,... and so on. What is the net discount

Let P and Q be real numbers such that the fourth-degree polynomial 5x^4 + 4x^3 + 3x^2 + Px +Q divided by the quadratic polynomial x^2 + 1 has a remainder of 0. What is the value of P − Q?

f(x,y) = x-y; when x or y<0
f(x,y) = f(x-1,y) + f(x,y-1); otherwise
What is the value of f(3,2)?

1, 3, 6, 10 15 , ......... 5151... find the average of these 101 numbers.

280 people have come to participate in a musical fest. Each of them plays atleast one instrument from the piano, drums or guitar.
1) P, Q and R people respectively play the piano, drums and guitar.
2) A, B and C people respectively play only piano, only drums and only guitar.
3) Z people play only piano and drums, Y people play only piano and guitar and X people play only drums and guitar.
4) No person can play more than two instruments.
5) Z is the square of X, P > Q > R, X + Y + Z = 160, A = B = C

There are 10 points in a plane, of which 4 are collinear. How many quadrilaterals can be formedusing any 4 of these points as vertices?

The polynomial R(x) is the remainder on dividing x^2007 by x^2 − 5x + 6. R(0) can be expressed as ab(a^c − b^c). Find a + c − b.

In triangle ABC, AB = 52, BC = 56, CA = 60. Let D be the foot of the altitude from A and E be the intersection of the internal angle bisector of angle BAC with BC. Find DE.

Aman and eight of his friends took a test of 100 marks. Each of them got a different integer score and the average of their scores was 86. The score of Aman was 90 and it was more than that of exactly three of his friends. What could have been the maximum possible absolute difference between the scores of two of his friends

How many real non-zero values of b are there such that bx^2 - bx - b = 0 has b as a solution ?

If x is prime then which of the following is the highest number that will definitely divide the number (x – 1) × (77777777)x

Note:- (77777777)x means 77777777 in bas

Three A's, three B's and three C's are randomly placed in a 3 x 3 grid. find number of ways that no row or column has two of the same letter

Ronnie, Ben and Jevon are in the same math class. There are 24 students in the class, and the teacher has announced that she will be dividing the class into groups of 3. What is the probability that Ronnie, Ben and Jevon will be in the same group

The average of three consecutive multiples of 3 is a.
The average of four consecutive multiples of 4 is a + 27.
The average of the smallest and largest of these seven integers is 42.
Determine the value of a.

A is the number of different n-letter codes that can be formed using a, b, c, d. B is the number of different n-letter codes that can be formed using letters a, b, c, .....y (note that z is not to be used, i.e, we have choose from 25 letters).
If a function f(x) is defined as the number of digits of x, then f(A) + f(B) is

Bisector of angle A in triangle ABC meets BC at U. If UX is drawn parallel to AC meeting AB at X, and UY drawn parallel to AB meets AC at Y. Find BX : CY if AB = 10 and AC = 20

If E = 3 + 8 + 15 + 24 + … + 195, then what is the sum of the prime factors of E?

The number of polynomials p with integral coefficients such that p(9) = 13 and p(13) = 20 is

Three sides of the a triangle are a, b, c such that a ≤ 1, b ≤ 2 and c ≤ 3, then what will the largest possible area of the triangle

There's an instrument that is calibrated from 1 to 99999.It hasn't been working properly lately.The prob is that skips digit 5,i.e. it skips directly from 4 to 6.if it shows reading 3016,what is the correct reading

Suppose r is a root of the polynomial x^4 - x^3 + x^2 - x + 1. What is the value of r^20 - r^15 + r^10 - r^5 + 1

How many three-digit numbers are there whose product of all the digits is a perfect cube

Ram had a wooden plank that was in the shape of a right-angled triangle. Ram cut out a square piece out of it, such that he was left with exactly two smaller pieces, both of which were triangular in shape.
If the longest side of one of the smaller triangles is 85 cm and that of the other smaller triangle is 51 cm, then find the area of the original plank.

A man while rowing down a river in a boat, drops his hat in the river. He realizes this only 10 minutes after he actually dropped. So he immediately turns back.
a) After how much time will he reach back to his hat?
b) What will be the answer if originally he was rowing up the river