Monika Jagdale

Q1 Solve ecos⁡x−e−cos⁡x−6=0 Solution: et−e−t−6=0 e2t−1et=6⇒e2t−1=6et e2t−6et−1=0 (et)2−6et−1=0 Roots: et=6±36+42=6±402=6±2102=3±10 Q2 If roots of x2−2x+2=0 are α,β, find α2025+β2025. Solution: α,β=2±4−82=1±i αn+βn=2(2)ncos⁡(nπ4) cos⁡(2025π4)=cos⁡(20254π) Divide 2025 … Read more

Q1 If one real root of the quadratic equation 49×2+kx+64=0 is the square of the other root, then find k. Solution: Q2 If 3+2i is … Read more

1. Domain of function Problem: Find the domain of f(x)=log⁡5(1−log⁡3(x2−7x+12)) If domain is (α,β)∪(γ,δ), compute α+β+γ+δ. Solution: Ans: 21 2. Domain of logarithmic function Problem: … Read more

1. Range of Variable: If x+y+z=6 and xy+yz+zx=9, find the range of x. Solution: Ans: Range of x is [0,4]. 2. Polynomial Relatio: In polynomial … Read more

🔢 Questions with Solutions 1. Question: If log⁡(p+q)+log⁡(p−2r+q)=2log⁡(p−q), then find the relation among p,q,r. Solution: 2. Question: Solve log⁡(x2−4x+5)=log⁡(x−1). Solution: 3. Question: Solve ∣x−4∣(x2−6x+8)(x−3)=2. Solution: … Read more

Q.1 Which of the following are the roots of the quadratic equation x² – 9x + 20 = 0? (a) 3, 4 (b) 4, 5 (c) 5, … Read more

Q4 Find k so that the quadratic equation x2−(k+3)x+k=0 has equal and real roots. Solution: Step1 – For a quadratic ax2+bx+c=0 here a=1,  b=−(k+3),  c=k. Step 2 … Read more

Q3. If z1 and z2 are two non-zero complex numbers such that ∣z1+z2∣=∣z1∣+∣z2∣, then find arg⁡(z1)−arg⁡(z2). Step 1: For any complex numbers (or vectors), we … Read more

Q.1 Find two numbers such that each one is the square of the other. Step 1: Let the two numbers be x and y. According … Read more

Q. 1 Solve the given quadratic equation (x−1)3+8=0,     given that cube roots of unity are 1,ω,ω2. Solution: Step 1: (x−1)3+8=0 (x−1)3=−8 Step 2: −8=8⋅(−1). … Read more