1) π/2 2) π/2a 3) π/a 4) 1/2a Solution: (2) π/2a \(\begin{array}{l}\int_{0}^{\infty} \frac{d x}{a^{2}+x^{2}}\\=\frac{1}{a}\left[\tan ^{-1} \frac{x}{a}\right]_{0}^{\infty} \\ =\frac{1}{a}\left[\frac{\pi}{2}-0\right]\\=\frac{\pi}{2 a}\end{array} \)
1) a – 1 + (a – 1)-2 2) a + a-2 3) a – a-2 4) a2 + 1/a2... View Article
1) (2 / 3) [2 – √2] λ √λ 2) (2 / 3) [2 + √2] λ √λ 3) (1... View Article
1) 4 2) -2 3) -3 4) 3 Solution: (4) 3 \(\begin{array}{l}\int_{2}^{k}(2 x+1) d x=6 \\ {\left[2 \frac{x^{2}}{x}+x\right]_{2}^{k}=6} \\ \left(x^{2}+x\right)_{2}^{k}=6... View Article
1) 1/4 2) – (1/2) 3) 3/2 4) 1/2 Solution: (4) ½ \(\begin{array}{l}\begin{array}{l} \frac{1}{4} \int_{0}^{p} \frac{d x}{\frac{1}{4}+x^{2}}=\frac{\pi}{8} \\ \frac{1}{4} \cdot... View Article
1) π / 2 2) π 3) (π / 2) (b – a) 4) (π / 4) (b – a) Solution:... View Article
1) 1 2) 2 3) 0 4) -1 Solution: (2) 2 \(\begin{array}{l}\int_{-1}^{1} \frac{|x+2|}{x+2} d x \\ =\int_{-1}^{1} \frac{x+2}{x+2} d x\\=\int_{-1}^{1}... View Article
1) ∫01 ex dx = e 2) ∫01 2x dx = log 2 3) ∫01 √x dx = 2 /... View Article
1) [(22 / 7) – π] 2) 2 / 105 3) 0 4) [(71 / 15) – (3π / 2)]... View Article
1) f (1) – f (2) 2) ∅ (1) – ∅ (2) 3) f (2) – f (1) 4) ∅... View Article
1) 16 2) 8 3) 4 4) 1 Solution: (4) 1 \(\begin{array}{l}\int_{\frac{\pi}{6}}^{\frac{\pi}{2}}\left(\frac{1+\sin 2 x+\cos 2 x}{\sin x+\cos x}\right) d x... View Article
1) 1 2) -2 3) √2 4) 0 Solution: (3) √2 \(\begin{array}{l}\int_{0}^{\frac{\pi}{2}}\left|\cos \frac{x}{2}\right| d x \\=\int_{0}^{\frac{\pi}{2}}\left|\cos \frac{x}{2}\right| d x \\... View Article
1) π / √3 2) π / 2√3 3) 2π / 3√3 4) π / 3√3 Solution: (4) π / 3√3... View Article
1) 1/4 2) 1/2 3) 0 4) – (1/4) Solution: (4) – (1/4) \(\begin{array}{l}\begin{array}{l} \text { Given }\\ \begin{array}{l} \Delta(x)=\left|\begin{array}{ccc}... View Article
If \(\begin{array}{l}\overrightarrow{P}\times \overrightarrow{Q} = \overrightarrow{Q}\times \overrightarrow{P}\end{array} \) , the angle between \(\begin{array}{l}\overrightarrow{P}\end{array} \) and \(\begin{array}{l}\overrightarrow{Q}\end{array} \) is θ(0o<θ< 360o). The... View Article
Answer: 1 Relation b/w kinetic energy & momentum is p = √(2mKE) (∵KE = same) p1/p2 = √(m1/m2) n/2 =... View Article
Answer: 208 ∵ n = W/Qin = 1/4 ¼ = 1 – T2/T1 [for reversible heat engine] T2/T1 = 3/4... View Article
Answer: 10 Given wavelength of an X-ray beam = 10 Å ∵E = hc/λ = mc2 m = hc/λ will... View Article
A current of 6A enters one corner P of an equilateral triangle PQR having 3 wires of resistance 21Ω each... View Article
The initial velocity v1 required to project a body vertically upward from the surface of the earth to just reach... View Article
