Algebra

Modulus Equations PYQ | JEE Main 2025 | Sign Condition Trick

❓ Question If ∣ x + y ∣ + ∣ x − y ∣ = 2 ∣ x ∣ |x+y|+|x-y|=2|x| and ∣ x + 1 ∣ + ∣ 5 − x ∣ = 6 , |x+1|+|5-x|=6, then find the possible values of x…

❓ Question If u + log ⁡ 4 3 u + log ⁡ 2 3 = u + log ⁡ 8 3 u + log ⁡ 4 3 = V , \frac{u+\log_{4}3}{u+\log_{2}3} = \frac{u+\log_{8}3}{u+\log_{4}3} =…

❓ Question Given that x > 13 , x>13, solve log ⁡ x − 1 1 ⋅ log ⁡ x − 2 ( x − 1 ) ⋅ log ⁡ x − 3 ( x − 2 ) ⋯ log ⁡ x − 12 ( x − 11 ) = 2. \l…

❓ Question Evaluate 81 1 log ⁡ 3 5 + 27 log ⁡ 36 log ⁡ 9 + 3 4 log ⁡ 7 9 . 81^{\frac{1}{\log_3 5}} + 27^{\frac{\log 36}{\log 9}} + 3^{\frac{4}{\l…

❓ Question If log ⁡ ( x + 3 ) ( x 2 − x ) < 1 \log_{(x+3)}(x^2-x)<1 is satisfied for x ∈ ( a , b ) , x\in(a,b), then find the value of a …

❓ Question Let m = log ⁡ 245 175 , n = log ⁡ 1215 875. m=\log_{245}175,\qquad n=\log_{1215}875. Find the value of m − n 1 − m n . \frac{m-n}{1-m…

❓ Question Find the unique value of x x satisfying 4 x − 3 x + 1 2 = 3 x + 1 2 − 2 2 x − 1 . 4^x-3^{x+\frac12}=3^{x+\frac12}-2^{\,2x-1}. ✍️ S…