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[latex]\underset{x\to 0}{\mathop{\lim }}\,\frac{\sin^{2} x}{\sqrt{2}-\sqrt{1+\cos x}}=[/latex]

A) √2B) 2C) 4D) 4√2Solution:Rationalise the denominator = (4/2) √2+√(1+1)= 4√2Answer: D... View Article

Shortest distance between the curves y² = x-2 and y = x is

A) greater than 4B) less than 2C) greater than 3D) greater than 2Solution:y2 = x-2Differentiating we get,2y (dy/dx) = 1(dy/dx) = 1/2ySlope of the... View Article

[latex]A=\left[ \begin{matrix} \cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \\ \end{matrix} \right][/latex]and [latex]{{A}^{32}}=\left[ \begin{matrix} 0 & -1 \\ 1 & 0 \\ \end{matrix} \right][/latex]. then α may be

A) 0B) π/32C) π/64D) π/16Solution:A = cos 32α = 0 and sin 32α = 1 32α = π/2α = π/64Answer: C... View Article

“If you are born in India then you are citizen of India” contrapositive of this statement is

A) If you are born in India then you are not citizen of IndiaB) If you are not citizen of India then you are not born in IndiaC) If you are... View Article

The area bounded by the curve y ≤ x²+3x, 0 ≤ y ≤ 4, 0 ≤ x ≤3 is

A) 59/6B) 57/4C) 59/3D) 57/6Solution: y = x2+3xy = 4 x2+3x= 4 = 0 x2+3x-4 = 0x = 1 or x = -4Area = = (1/3)+(3/2)+8= 59/6Answer: A... View Article

[latex]\int{\frac{\sin \frac{5x}{2}}{\sin \frac{x}{2}}}.\,dx=[/latex]

A) x+2sin x+sin 2x+cB) x+2cos x+sin 2x+cC) x-2sin x+sin 2x+cD) x+2sin x-sin 2x+cSolution: = x+2 sinx+sin 2x +cAnswer: A... View Article

The line x+y = n, n∈N, makes intercepts with x²+y² = 16. Then the sum of squares of all possible intercepts

A) 105/4B) 105C) 210D) 105/2Solution:x2+y2 = 16Centre = (0,0)OA = PRadius = 4P = n/√2 To make the intercepts n/√2 < 4 n<... View Article

Let sin(α-β) = 5/13 and cos (α+β) = 3/5 where α, β ∈ (0, π/4) then tan 2α

A) 63/16B) 61/16C) 65/16D) 32/9Solution:sin(α-β) = 5/13cos (α-β) = 12/13cos(α+β) = 3/5sin(α+β) =... View Article

The sum of coefficients of even powers of x in (x+√(x³-1)⁶ + x-√(x³-1)⁶)

A) 23B) 24C) 18D) 21Solution:(x+√(x3-1)6 + x-√(x3-1)6) = 2[6C0x6 +6C2x4(x3-1)+6C4x2(x3-1)2 +6C6(x3-1)3]= 2[x6+15x4(x3-1)+15x2(x6-2x3+1)+(x3-1)3]=... View Article