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The Minimum Value Of Sin X Cos X Is

1) √2 2) -√2 3) 1 / √2 4) -1 / √2 5) 1 Solution: (2) - √2 y = sin x + cos x = √2 [(1 / √2) sinx + cosx (1 / √2)] = √2 [cos... View Article

1) 1/4 2) - (1/4) 3) 4 4) -4 5) 0 Solution: (2) - (1 / 4) y = x2 - (1 / x2) Slope of tangent my = dy / dx mt = d [x2 - (1 /... View Article

1) -15/2 2) -9/2 3) 15 4) 15/2 5) 9/2 Solution: (3) 15 y2 exy = 9e-3 x2 y2 exy [x (dy / dx) + y] = 9e-3 2x + exy 2y (dy /... View Article

1) -1 2) 3 3) 1 4) 0 Solution: (2) 3 f (x) = 3 + |x| |x| ≥ 0 {|x| = x, x ≥ 0 and |x| = -x, x < 0} 3 + |x| ≥ 3 + 0 f (x) ≥ 3... View Article

1) a - b 2) |a + b| 3) 2a + b 4) None of these Solution: (2) |a + b| Let x = r cos ɸ and y = r sin ɸ a2 / r2 cos2 ɸ] + b2 / [r2... View Article

1) [x / a] + [y / b] = 2 2) [x / a] + [y / b] = 1 / 2 3) [x / a] - [y / b] = 2 4) ax + by = 2 Solution: (1) [x / a] + [y / b] = 2... View Article

1) -1 2) 3 3) -3 4) 1 Solution: (3) -3 y = f (x) = x2 + bx - b m = dy / dx = 2x + b = (2 + b) The equation of the tangent at (1,... View Article

The number of points, where f (x) attains its minimum value, is 1) 1 2) 2 3) 3 4) infinitely many Solution: (1) 1 -1 < sin (1... View Article

1) x + y = 1 2) x - y = 1 3) x + y = - 1 4) x - y = - 1 Solution: 1) x + y = 1 y = 1y + 0 y = 1, slope of normal = -1 / (dy /... View Article

1) e 2) 1/e 3) e2 4) e3 Solution: (1) e f (x) = x / log x f’ (x) = [log x - 1] / [log x]2 For maxima and minima put f’ (x) =... View Article

1) π2 / 4 and 0 2) π2 / 4 and - π / 2 3) 5π2 / 4 and π2 / 8 4) π4 / 4 and -π2 / 4 Solution: (3) 5π2 / 4 and π2 / 8 (sin-1 x)2 +... View Article

1) α = -6, β = 1 / 2 2) α = -6, β = - 1 / 2 3) α = 2, β = -1 / 2 4) α = 2, β = 1 / 2 Solution: (3) α = 2, β = -1 / 2 f (x) = α log... View Article

1) 1/r2 2) 1/r 3) r2 4) r Solution: (4) r S = 4πr2 ds / dt = 8πr * (dr /dt) (ds / dt) = 8πr * 2 ds / dt = 16πr It is... View Article

1) 24500 2) 12500 3) 12250 4) 25400 Solution: (3) 12250 m h = 490t - 4.9t2 dh / dt = 0 (for maximum height) 490 [dt / dt] -... View Article

1) 0.24 π sq cm/s 2) 60 π sq cm/s 3) 24 π sq cm/s 4) 1.2 π sq cm/s Solution: (3) 24 π sq cm/s dr / dt = 0.01cm / s r = 12cm r =... View Article

1) 2h = r 2) h = 4r 3) h = 2r 4) h = r Solution: (4) h = r Volume of the cylinder = V = πr2h Surface area = S = 2πrh + πr2 ---... View Article

1) 4√3 m 2) 5√3 m 3) 5√2 m 4) 8 m 5) 6 m Solution: (5) 6m x2 + y2 = 102 x2 + y2 = 100 dx / dt = 3 cm/sec dy / dt = 4... View Article

1) 5/6π cm/min 2) 1/54π cm/min 3) 1/18π cm/min 4) 1/36π cm/min Solution: (3) 1/18π cm/min R = (10 + x) V = (4 / 3) πr3 V = (4... View Article

1) 7 sq cm/min 2) 10 sq cm/min 3) 17.5 sq cm/min 4) 28 sq cm/min Solution: (3) 10 sq cm / min V = (4 / 3) πr3 (dV / dt) = (4 /... View Article

1) (velocity)3 2) velocity 3) (velocity)2 4) (velocity)3/2 Solution: 1) (velocity)3 s = √t = t1/2 V = ds / dt = (1 / 2) t-½... View Article