Solved MCQ

Q5.  If a + b= 2m² , b + c = 6m, a + c = 2, where m is a real number and a <= b <= c, then which one of the following is correct?

A) 0 <= m <= 1/2 
B) -1<= m <= 0 
C) 1/3 <= m <=1
D) 1 < m <= 2

Soln:     Adding all the given equations we get, 2a + 2b + 2c = 2m² + 6m + 2   >>>  a + b + c = m² + 3m + 1.

Therefore, a =  m² - 3m + 1, c = - m² + 3m + 1 and b = m² + 3m - 1.

Given, a<=b  >>>   m² - 3m + 1 <= m² + 3m - 1  >>>  2 <= 6m  >>>  m >= 1/3.  

Given, b<=c  >>>   m² + 3m - 1 <= - m² + 3m + 1  >>>  m² <= 1  >>>  m <= 1.  


So, 1/3 <= m <= 1. 


Q9.  If x:y=1:3, y:z=5:k, z:t=2:5 and t:x=3:4, then what is the value of k?

Soln:    Adding all the ratios, (x*y*z*t)/(x*y*z*t)=(1*5*3*2)/(3*k*5*4).
            >>>  1=30/(60k)  >>>  K=1/2.

Q4.  What is the least number which when divided by 42, 72 and 84 leaves the remainder 25, 55 and 67 respectively?

Soln:   To find the least number divisible by all the three we will have to find the LCM and the LCM of these three numbers is 2*2*3*6*7 = 504.

If you find any difficulty in finding LCM click here

Now the difference 42-25 = 17, 72-55 = 17 and 84-67 = 17. So the number required is 504+17 = 521.

Q2.  A person borrowed Rs. 7500 at 16% compound interest. How much does he have to pay at the end of two years to clear the loan?

Soln:

Q1.  P and Q can do job in 2 days. Q and R can do it in 4 days; and P and R in 12/5 days. What is the number of days required for P alone to do the job?

Soln: