Ravi Kant Kumar

Assertion Reason Infinite Roots 🎥 Watch Video Solution Q. Assertion–Reason Type Question Statement-1: \( \sqrt{6+\sqrt{6+\sqrt{6+\cdots}}} = 3 \) Statement-2: \( \sqrt{x+\sqrt{x+\sqrt{x+\cdots}}} = x,\ x>0 \) ✏️ Solution Let \( y = \sqrt{6+\sqrt{6+\sqrt{6+\cdots}}} \) Then \( y = \sqrt{6+y} \) Squaring: \( y^2 = 6 + y \) \( y^2 – y – 6 = 0 […]

Assertion Reason Infinite Roots 🎥 Watch Video Solution Q. Assertion–Reason Type Question Statement-1: \( \sqrt{5\sqrt{5\sqrt{5\cdots}}} = 5\sqrt{5} \) Statement-2: \( \sqrt{x\sqrt{x\sqrt{x\cdots}}} = x,\ x>0 \) ✏️ Solution Let \( y = \sqrt{5\sqrt{5\sqrt{5\cdots}}} \) Then \( y = \sqrt{5y} \) Squaring: \( y^2 = 5y \) \( y(y-5) = 0 \Rightarrow y = 5 \) (since

Assertion Reason Nested Roots 🎥 Watch Video Solution Q. Assertion–Reason Type Question Statement-1: \( \sqrt{7\sqrt{7\sqrt{7\sqrt{7}}}} = \sqrt[16]{7^{15}} \) Statement-2: \( \sqrt{a\sqrt{a\sqrt{a\cdots}}} \ (n\text{ terms}) = a^{\frac{2^n – 1}{2^n}} \) ✏️ Solution Number of nested roots = 4 Using formula: \( = 7^{\frac{2^4 – 1}{2^4}} = 7^{\frac{16 – 1}{16}} = 7^{15/16} \) \( = \sqrt[16]{7^{15}} \)

Assertion Reason Exponents 🎥 Watch Video Solution Q. Assertion–Reason Type Question Statement-1: If \( a^x = b^y = c^z = abc \), then \( xy + yz + zx + xyz = 1 \) Statement-2: If \( a^n = k \), then \( a = k^{1/n} \) ✏️ Solution Let \( a^x = b^y =

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