Solved MCQ

Q. The difference between the place value and the face value of 6 in the numeral 856973 is
a) 973
b) 6973
c) 5994
d) none of these.

Q. Each side of equilateral triangle is 6 cm. Its altitude is
a) 6√3
b) 3√3
c) 2√3
d) √3

Q. The length, breadth and height of a box are respectively 14 m, 12 m, 13 m. The length of the greatest rod that can be put in it is
a) 22.31 m
b) 22.56 m
c) 20 m
d) 19.5 m

Q. From a solid wooden right circular cylinder, a right circular cone whose radius and height are same as the radius and height of the cylinder respectively, is carved out. What is the ratio of the volume of the utilized wood to that of the wasted wood?
a) 1 : 2
b) 2 : 1

Q. A solid spherical ball of radius 4cm is melted to form spheres of radius 2cm each. The number of spheres so formed is
a) 8
b) 9
c) 10
d) 16

Q. If cosA+ cos²A =1, then what is 2(sin²A + sin⁴A) equal to?
a) 4
b) 2
c) 1
d) 1/2

Q. The LCM of two numbers is 2376 while their HCF is 33. If one of the two numbers is 297, then the other number is
a) 216
b) 264
c) 642
d) 792

• Dhebar Lake (also known as Jaisamand Lake) is Asia's second-largest artificial lake.

Q. If the height of a pole is 2√3 meters and the length of its shadow is 2 meters, find the angle of elevation of the sun.

When square of a number which ends with 5 is to be derived, we can find the square by simply multiplying the digits in other places excluding the unit's place by a number one more than the digits and substituting it preceding 25.

For instance. 35²=____25 to get the number which can fill the blank we will have to multiply 5 with the number 1 less than 3 i.e 3+1=4. (3x4=12). So  the square of 35 is 1225. 

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: