May 2026

Assertion Reason Exponents 🎥 Watch Video Solution Q. Assertion–Reason Type Question Statement-1: \( \left[ \{(1/7^2)^{-2}\}^{-1/3} \right]^{1/4} = 7^{-1/3} \) Statement-2: \( ((a^m)^n)^s = a^{mns},\ a>0 \) ✏️ Solution \( \frac{1}{7^2} = 7^{-2} \) \( (7^{-2})^{-2} = 7^4 \) \( (7^4)^{-1/3} = 7^{-4/3} \) \( (7^{-4/3})^{1/4} = 7^{-4/12} = 7^{-1/3} \) So Statement-1 is TRUE Statement-2 […]

Surds MCQ 🎥 Watch Video Solution Q. If \( 0 < y < x \), which statement must be true? (a) \( \sqrt{x} – \sqrt{y} = \sqrt{x-y} \) (b) \( \sqrt{x} + \sqrt{x} = \sqrt{2x} \) (c) \( x\sqrt{y} = y\sqrt{x} \) (d) \( \sqrt{xy} = \sqrt{x}\sqrt{y} \) ✏️ Solution (a) \( \sqrt{x} – \sqrt{y}

Exponent Root Problem 🎥 Watch Video Solution Q. If \( \sqrt[x]{3} \times \sqrt[y]{5} = 10125 \), find \( 12xy \) (a) 1    (b) \( \frac{1}{3} \)    (c) 2    (d) \( \frac{1}{2} \) ✏️ Solution \( \sqrt[x]{3} = 3^{1/x},\quad \sqrt[y]{5} = 5^{1/y} \) \( 3^{1/x} \cdot 5^{1/y} = 10125 \) \( 10125 =

Compare Powers 🎥 Watch Video Solution Q. Which is greatest among \( 3^{198}, 27^{64}, 9^{100}, 81^{49} \)? (a) \( 9^{100} \)    (b) \( 81^{49} \)    (c) \( 27^{64} \)    (d) \( 3^{198} \) ✏️ Solution Convert all into base 3 \( 27^{64} = (3^3)^{64} = 3^{192} \) \( 9^{100} = (3^2)^{100} =

Exponent Equation 🎥 Watch Video Solution Q. If \( 6^{x-y} = 36 \) and \( 3^{x+y} = 729 \), find \( x^2 – y^2 \) (a) 12    (b) 4    (c) 24    (d) 8 ✏️ Solution \( 6^{x-y} = 36 = 6^2 \Rightarrow x – y = 2 \) \( 3^{x+y} = 729

Exponent Relation MCQ 🎥 Watch Video Solution Q. If \( x^y = y^z = z^x \) and \( xz = y^2 \), find correct option (a) \( z = \frac{2xy}{x+y} \) (b) \( y = \frac{x-z}{x+z} \) (c) \( x = \frac{y-z}{yz} \) (d) \( xyz = \frac{x-z+y}{x+z-y} \) ✏️ Solution \( x^y = y^z

Exponent Relation Problem 🎥 Watch Video Solution Q. If \( 2^x = 3^y = 6^z \), find \( \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \) (a) \( \frac{2}{x} \)    (b) \( \frac{2}{y} \)    (c) \( \frac{2}{z} \)    (d) 1 ✏️ Solution \( 2^x = 3^y = 6^z = k \) \( x =

Minimum Value Problem 🎥 Watch Video Solution Q. If \( a^{b^c} = 6561 \), find least value of \( abc \) (a) 24    (b) 36    (c) 162    (d) none of these ✏️ Solution \( 6561 = 3^8 \) So \( a^{b^c} = 3^8 \) Take smallest base: \( a = 3 \Rightarrow

Maximum Value Problem 🎥 Watch Video Solution Q. If \( a^{b^c} = 256 \), find maximum value of \( abc \) (a) 12    (b) 16    (c) 32    (d) 256 ✏️ Solution \( 256 = 2^8 \) Possible forms: \( a^{b^c} = 2^8 \) Take \( a = 2 \Rightarrow b^c = 8

Exponent Evaluation 🎥 Watch Video Solution Q. If \( \sqrt{5^n} = 125 \), find \( 5^{\sqrt[n]{64}} \) (a) 25    (b) \( \frac{1}{125} \)    (c) 625    (d) \( \frac{1}{5} \) ✏️ Solution \( (5^n)^{1/2} = 125 = 5^3 \) \( 5^{n/2} = 5^3 \Rightarrow n = 6 \) \( \sqrt[6]{64} = (2^6)^{1/6} =