A) √2 B) 2 C) 4 D) 4√2 Solution: Rationalise the denominator \(\begin{array}{l}\underset{x\to 0}{\mathop{\lim }}\,\frac{{{\sin }^{2}}x\left[ \sqrt{2}+\sqrt{1+\cos x} \right]}{2-\left( 1+\cos... View Article
A) greater than 4 B) less than 2 C) greater than 3 D) greater than 2 Solution: y2 = x-2... View Article
A) 0 B) π/32 C) π/64 D) π/16 Solution: A = \(\begin{array}{l}\left[ \begin{matrix} \cos \alpha & -\sin \alpha \\ \sin... View Article
A) If you are born in India then you are not citizen of India B) If you are not citizen... View Article
A) 59/6 B) 57/4 C) 59/3 D) 57/6 Solution: y = x2+3x y = 4 x2+3x= 4 = 0 x2+3x-4... View Article
A) x+2sin x+sin 2x+c B) x+2cos x+sin 2x+c C) x-2sin x+sin 2x+c D) x+2sin x-sin 2x+c Solution: \(\begin{array}{l}\int{\frac{\sin \frac{5x}{2}}{\sin \frac{x}{2}}}.\,dx\end{array}... View Article
A) 105/4 B) 105 C) 210 D) 105/2 Solution: x2+y2 = 16 Centre = (0,0) OA = P Radius =... View Article
A) 63/16 B) 61/16 C) 65/16 D) 32/9 Solution: sin(α-β) = 5/13 cos (α-β) = 12/13 cos(α+β) = 3/5 sin(α+β)... View Article
A) 23 B) 24 C) 18 D) 21 Solution: (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] = 2[x6+15x7-15x4+15x8-30x5+15x2+x9-3x6+3(x3-1)]... View Article
1) -π 2) 0 3) π 4) 2π Solution: (4) 2π \(\begin{array}{l}I =\int_{-\pi}^{\pi}(\cos p x-\sin q x)^{2} d x \\... View Article
1) 0 2) (π2 / 4) [1 + (π / 2)] 3) 1 4) π2 / 2 Solution: (1) 0... View Article
1) 0 2) π/4 3) π 4) π/2 Solution: (1) 0 \(\begin{array}{l}\begin{array}{l} f(\theta)= \log (\sec \theta-\tan \theta) \\ f(-\theta) =\log... View Article
1) 0 2) π/4 3) π/2 4) π Solution: (1) 0 \(\begin{array}{l}\begin{array}{l} I=\int_{0}^{\frac{\pi}{2}} \frac{\sin x-\cos x}{1+\sin x \cos x} d... View Article
1) 2 – √2 2) 2 + √2 3) √2 – 1 4) √2 – 2 Solution: (3) √2 –... View Article
1) 0 2) 4 3) 8 4) 1 Solution: (2) 4 \(\begin{array}{l}\begin{array}{l} I=\int_{0}^{2 \pi}(\sin x+|\sin x|) d x \\ =\int_{0}^{\pi}(\sin... View Article
1) 12 2) 25 3) 23 4) 24 Solution: (2) 25 \(\begin{array}{l}\text \ x-[x] \ is \ a \ periodic... View Article
1) π – 4 2) (2π / 3) – 4 – 4√3 3) 4√3 – 4 4) 4√3 – 4 –... View Article
1) 2/3 2) 1/3 3) 3/2 4) ln 2 Solution: (1) ⅔ \(\begin{array}{l}\begin{array}{l} \text { Put } 1+\log x=t \\... View Article
1) 1 2) cos (log 3) 3) sin (log 3) 4) π/4 Solution: (3) sin (log 3) \(\begin{array}{l}\begin{array}{l} I=\int_{1}^{3} \frac{\cos... View Article
1) 0 2) 1 3) -1 4) 2 Solution: (2) 1 \(\begin{array}{l}\begin{array}{l} \int_{0}^{\frac{\pi}{2}} x \sin x d x \\ =\left.x(-\cos... View Article
