ims questions
Q1. A bag contains ‘a’ white and ’b’ black balls. Two players A and B alternately draw a ball from the bag, replacing the ball each time after the draw. A begins the game. If the probability of A winning (That is drawing a white ball) is twice the probability of B winning, then the ratio a:b is equal to
a) 1 : 2
b) 2 : 1
c) 1:1
d) None of these
Q2. How many natural numbers less than 1000 can be expressed as the difference of two perfect squares in at least one way?
a. 750
b. 811
c. 810
d. 749
Q3. If a,b,c are different positive real numbers such that b+c-a, c+a-b and
a+b-c are positive, then (b+c-a) (c+a-b) (a+b-c) – abc is
a)non Positive
b)negative
c)both
d)none
Q4. If the sum to infinity of the series 2 + (2-d)2/3 + (2+d)4/9 + (2+3d)8/27 + . . .is 5/2, what is the value of d ?
a. 7/12
b. -5/12
c. -7/12
d. 5/12
Q5. Which of the following divides (13^3 + 15^3 + 20^3 + 18^3) ?
i. 21 ii. 11 iii. 7 iv. 14
a. Only iii
b. Iii and iv
c. Ii and iii
d. I and iii
e. I, ii, iii and iv
Q1) a:b is 1:1
Q2 ) I was only able to find that 500 and 499 are the highest closest number whose square difference is Maximum allowed i.e. 99 (number just less than 100).
Q3) none (c)
Q4) -7/12
Q5) all 21, 7, 11, 14 so e.
How many natural numbers less than 1000 can be expressed as the difference of two perfect squares in at least one way?
a. 750
b. 811
c. 810
d. 749
nos of the form
n^2 - (n-1)^2, n>=2, will be 1,3,5,7........999. ie 500 nos
now m^2 -n^2 = k
(m+n)(m-n) = k
K can be definitely expressed as k*1
so 2m = k+1
so for all odd k, we will get integral m and n, and these are already considered
For even k, if k=2*odd no, then 2m= odd....so not possible
Hence only for even values of k such that k = 2(even), it is possible....
{4, 8, 12, 16,.......996} = 249
so total = 749 nos
n/a
If the sum to infinity of the series 2 + (2-d)2/3 + (2+d)4/9 + (2+3d)8/27 + . . .is 5/2, what is the value of d ?
a. 7/12
b. -5/12
c. -7/12
d. 5/12
I am getting -7/12
S = 2 + (2-d)2/3 + (2+d)4/9 + (2+3d)8/27 + . . = 5/2
(2/3)S = 4/3 + (2-d)4/9 + (2+d)8/27 + (2+3d)16/81 + . .
S - (2/3)S = 2 - 4/3 +(2-d)2/3 + { 4/9 (2d ) + 8/27(2d) + 16/81(2d) + . .....}
1/3S = 2 - 4/3 + 2d (4/9)/(1-2/3)
(since gp with a = 4/9 and r = 2/3)
5/6 = 2 - 4/3 + (2-d)2/3 + 8d/3
5/6 = 2 + 2d
solving, d = -7/12
n/a
Q1. A bag contains ‘a’ white and ’b’ black balls. Two players A and B alternately draw a ball from the bag, replacing the ball each time after the draw. A begins the game. If the probability of A winning (That is drawing a white ball) is twice the probability of B winning, then the ratio a:b is equal to
a) 1 : 2
b) 2 : 1
c) 1:1
d) None of these
n/a
Hi Sir,
Can you explain this question? As per my understanding without doing calculation 7 and 14 are right answer. How you can judge other two? is there any short method?
Q5. Which of the following divides (13^3 + 15^3 + 20^3 + 18^3) ?
i. 21 ii. 11 iii. 7 iv. 14
a. Only iii
b. Iii and iv
c. Ii and iii
d. I and iii
e. I, ii, iii and iv
here equation divided by all number so option (e)
Little Star
n/a
n/a