CMAT Algebra Practice Questions With Solutions

What value comes in place of question mark (?) in the following statements and arrange them in descending order.
$A. \frac{5}{9}\times(225.40-45.4)=(?)^{2}$
$B. \sqrt{1024} \times 40 + (20)^{2}+0.5\% Of 9600+469=(?)^{3}$
$C. 8^{12} \div 16^{2} of 32^{3}\times\sqrt{256}=(2)^{?}$
$D. 18{\frac{1}{3}} + 9 {\frac{2}{3}} - 10 {\frac{1}{3}}=1 {\frac{2}{3}}+?$
Choose the correct answer from the options given below :

Given below are two statements:

Statement II : If the circumference and the area of a circle are numerical equal, then
the diameter is equal to 4.

Three vessels 'P', 'Q' and 'R' of same capacity are all full. Vessels 'P' and 'Q' contain mixture of milk and water in the ratios 4 : 1 and 7 : 3 respectively while vessel 'R' contains
only pure milk. The contents of these vessels are poured into a larger vessel 'S'. After drawing 30 litres of mixture from vessel 'S', the final quantity of water left in vessel 'S' is 40 litres, then the capacity of each vessel is :

Arrange the following in descending order :
A: $\sqrt{401} -\sqrt{399}$
B: $\sqrt{301} -\sqrt{299}$
C: $\sqrt{101} -\sqrt{99}$
D: $\sqrt{201} -\sqrt{199}$

The value of$\left(\frac{x^a}{x^b}\right)^{(a^2 + ab + b^2)} \left(\frac{x^b}{x^c}\right)^{(b^2 + bc + c^2)} \left(\frac{x^c}{x^a}\right)^{(c^2 + ca + a^2)}$ is:

Ramesh purchased two mobile phones from a shop. He sold first mobile phone at the price of ₹ 18750 and the second mobile phone at the price of ₹ 14250. If the profit percent on first mobile phone is five times of the loss percent on the second mobile phone, then find out the overall profit made by Ramesh after selling both the mobile phones, given that he purchased both at same cost.

Arrange the following in descending order
(A) $3^{3^{3^{3}}}$
(B) $3^{(33)^{3}}$
(C) $(3^3)^{33}$
(D) $3^{333}$
Choose the correct answer from the options given below :

In a circus there were a leopard and a tiger walking in the two different rings having same radii. It was observed that when leopard moved 3 steps, tiger moved 5 steps in the same time, but the distance traversed by leopard in 5 steps is equal to the distance traversed by tiger in 4 steps. How many rounds that a leopard made t ill when tiger completed 100 rounds?

There are three bottles of mixture of syrup and water in the ratios 2 : 3, 3 : 4 and 7 : 5. 10 litres of first and 21 litres of second bottles are taken. How much quantity of mixtures from third bottle is to be taken so that the final syrup and water ratio of mixture from three bottles will be 1 : 1 if the final mixture from all the three bottles is added and mixed in a big container?

If $x^2 = y + z , y^2 = z + x$ and $z^2 = x + y$ then the value of $\frac{1}{x + 1} + \frac{1}{y + 1} + \frac{1}{z + 1}$ is