# Find the probability of a point randomly chosen in the interior of square with side length of 1 meter is within 1 meter of all the four vertices of the square

1.  1/2

2.  Π

3.  Π/2

4.  Π-2/2

5.  none of these

5

Π-2/2

Explanation :
No Explanation available for this question

# A, B, C and D are four towns, any three of which are non -collinear. The number ofways to construct three roads each joining a pair of towns so that the roads do notform a triangle is:

1.  7

2.  8

3.  9

4.  more than 9

4

more than 9

Explanation :
No Explanation available for this question

# For the product n(n + 1) (2n + 1), n N, which one of the following is necessarilyfalse?

1.  It is always even

2.  Divisible by 3.

3.  Always divisible by the sum of the square of first n natural numbers

4.  Never divisible by 237.

4

Never divisible by 237.

Explanation :
No Explanation available for this question

# Ram purchased a flat at Rs. 1 lakh and Prem purchased a plot of land worth Rs. 1.1lakh. The respective annual rates at which the prices of the flat and the plot increasedwere 10% and 5%. After two years they exchanged their belongings and one paid theother the difference. Then:

1.  Ram paid Rs. 275 to Prem

2.  Ram paid Rs. 475 to Prem

3.  Ram paid Rs. 2750 to Prem

4.  Prem paid Rs. 475 to Ram

4

Ram paid Rs. 2750 to Prem

Explanation :
No Explanation available for this question

# The remainder obtained when a prime number greater than 6 is divided by 6 is:

1.  1 or 3

2.  1 or 5

3.  3 or 5

4.  4 or 5

4

1 or 3

Explanation :
No Explanation available for this question

# For which integer n is28 + 211 + 2n a perfect square

1.  11

2.  12

3.  13

4.  14

5.  none of these

5

12

Explanation :
No Explanation available for this question

# Let x and y be consecutive integers. Suppose m be the number of solutions of x3 − y3 = 3k2 and n be the number of solutions of x3 − y3 = 2t2,where k, t are integers. Then m + n equals:

1.  31

2.  13

3.  5

4.  6

5.  none of these

5

none of these

Explanation :
No Explanation available for this question

# Ali leaves at noon and drives at constant speed back and forth from town A to town B. Bobby also leaves at noon and driving at 40 KPH back and forth from town B to town A on the same highway as Ali. Ali arrives at town B twenty minutes after first passing Bobby whereas Bobby arrives at town A 45 minutes after first passing Ali. Let X(n) be the time when they meet for the n-th time

1.  X(2)=1:30 p.m

2.   X(3)= 2:30 p.m

3.  X(4) 3:30 p.m

4.  All of these

5.  None of these

5

All of these

Explanation :
No Explanation available for this question

# Two mathematicians meet at a bar. After getting drunk A tells B, ”a, b, c are the sides of a triangle, c being the longest. If R is the circumradius of the triangle, a2 + b2 = 2Rc”. B replies ” Angle C is 900”. Then:

1.  If A is right then B is right

2.  If B is right then A is right

3.  at least one is right

4.  both of them are right

5.  none of these

5

both of them are right

Explanation :
No Explanation available for this question

# Find the number of solutions in positive integers (k; a1, a2, . . . , ak; b1, b2, . . . , bk) to the equation a1(b1) + a2(b1 + b2) + · · · + ak(b1 + b2 + . . . + bk) = 7

1.  14

2.  30

3.  35

4.  17

5.  none of these

5