XAT Surds and Indices Practice Questions With Solutions

If $\log_4m + \log_4n = \log_2(m + n)$ where m and n are positive real numbers, then which of the following must be true?

If $\sqrt[3]{7^a\times 35^{b+1} \times 20^{c+2}}$ is a whole number then which one of the statements below is consistent with it?

Given that a and b are integers and that $5x+2\sqrt{7}$ is a root of the polynomial $x^2 - ax + b + 2\sqrt{7}$ in $x$, what is the value of b?

Let C be a circle of radius $\sqrt{20}$ cm. Let L1, L2 be the lines given by 2x − y −1 = 0 and x + 2y−18 = 0, respectively. Suppose that L1 passes through the center of C and that L2 is tangent to C at the point of intersection of L1 and L2. If (a,b) is the center of C, which of the following is a possible value of a + b?

$\frac{log (97-56\sqrt{3})}{log \sqrt{7+4\sqrt{3}}}$ equals which of the following?

It takes 2 liters to paint the surface of a solid sphere. If this solid sphere is sliced into 4 identical pieces, how many liters will be required to paint all the surfaces of these 4 pieces.

X and Y are the digits at the unit's place of the numbers (408X) and (789Y) where X ≠ Y. However, the digits at the unit's place of the numbers $(408X)^{63}$ and $(789Y)^{85}$ are the same. What will be the possible value(s) of (X + Y)?

For two positive integers a and b, if $(a + b)^{(a + b)}$ is divisible by 500, then the least possible value of a $\times$ b is:

Circle $C_{1}$ has a radius of 3 units. The line segment PQ is the only diameter of the circle which is parallel to the X axis. P and Q are points on curves given by the equations $y = a^{x} and y = 2a^{x}$ respectively, where a < 1. The value of a is:

p and q are positive numbers such that $p^q = q^p$, and $q = 9p$. The value of p is