How do you use Boolean logic?
Boolean logic is a form of algebra in which the variables have only two values 0 and 1. 1 is... View Article
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What is the efficiency formula?
In science, efficiency is given by the ratio of the output energy to the input energy. The energy is in... View Article
The points on the curve y3 + 3x2 = 12y where the tangent is vertical (parallel to the y-axis), is (are)
1) (± 4 / √3, -2) 2) (± √11 / 3 + 1) 3) (0, 0) 4) (± 4 /... View Article
If the normal to the curve y = f (x) at the point (3, 4) makes 3π / 4 with the postive x-axis then f’ (3) =
1) -1 2) -3 / 4 3) 4 / 3 4) 1 Solution: (4) 1 y = f (x) dy... View Article
At what points of the curve y = (2 / 3)x3 + (1 / 2)x2, tangent makes the equal anlge with the axis
1) (1 / 2, 5 / 24) and (-1, -1 / 6) 2) (1 / 2, 4 / 9) and... View Article
If y = 4x – 5 is tangent to the curve y2 = px3 + q at (2, 3), then
1) p = 2, q = –7 2) p = – 2, q = 7 3) p = –2, q... View Article
The distance travelled s (in metre) by a particle in t seconds is given by, s = t3 + 2t2 + t. The speed of the particle after 1 second will be
1) 8 cm/sec 2) 6 cm/sec` 3) 2 cm/sec 4) None of these Solution: (1) 8 cm/sec s = t3... View Article
The radius of the cylinder of maximum volume, which can be inscribed in a sphere of radius R is
1) (2 / 3) R 2) √(2 / 3) R 3) (3 / 4) R 4) √(3 / 4) R... View Article
A man height 1.8 metre is moving from a lamp post at the rate of 1.2 m/sec. If the height of the lamp post be 4.5 metre, then the rate at which the shadow of the man is lengthening is
1) 0.4 m/sec 2) 0.8 m/sec 3) 1.2 m/sec 4) None of these Solution: (2) 0.8 m/sec dy / dx... View Article
The volume of a spherical balloon is increasing at the rate of 40 cubic centimetre per minute. The rate of change of the surface of the balloon at the instant when its radius is 8 centimetre, is
1) (5 / 2) sq.cm/min 2) 5 sq. cm/min 3) 10 sq.cm/min 4) 20 sq. cm/min Solution: (3) 10 sq.cm/min... View Article
Let f : (0, + ∞) → R and F (x) = integral from 0 to x f (t) dt. If F (x2) = x2 (1 +x), then f (4) =
1) 5 / 4 2) 7 3) 4 4) 2 Solution: (3) 4 x2 (1 + x) = ∫0x^2 f... View Article
If x = sin t and y = sin pt, then the value of (1 – x2) d2y / dx2 – x (dy / dx) + p2y =
1) 0 2) 1 3) –1 4) √2 Solution: (1) 0 x = sin t and y = sin pt... View Article
If In = dn (xn log x) / dxn, then In – nIn-1 =
1) n 2) n –1 3) n! 4) (n –1)! Solution: (4) (n –1)! In = dn (xn log x)... View Article
Let f (x) and g (x) be two functions having finite non-zero 3rd order derivatives f’’’ (x) and g’’’ (x) for all, x ∈ R. If f (x) g (x) = 1 for all x ∈ R, then (f’’ / f’) – (g’’’ / g’) =
1) 3 [(f’’ / g) – (g’’ / f)] 2) 3 [(f’’ / f) – (g’’ / g)] 3) 3... View Article
If y2 = p (x) is a polynomial of degree 3, then 2 d [y3 (d2y / dx2)] / dx =
1) p’’ (x) + p’ (x) 2) p’’ (x) . p’’ (x) 3) p (x) . p’’’ (x) 4) Constant... View Article
The derivative of tan-1 [(√1 + x2 – 1) / x] with respect to tan-1 [(2x √1 – x2) / (1 – 2x2)] at x = 0 is
1) 1 / 8 2) 1 / 4 3) 1 / 2 4) 1 Solution: (2) 1 / 4 Let... View Article
If y = sec-1 (2x) / (1 + x2) + sin-1 [x – 1] / [x + 1], then dy / dx =
1) 1 2) [x – 1] / [x + 1] 3) Does not exist 4) None of these Solution: (3)... View Article
If √1 – x6 + √1 – y6 = a3 (x3 – y3), then dy / dx =
1) (x2 / y2) [(√1 – x6 / √1 – y6)] 2) (y2 / x2) [(√1 – y6 / √1... View Article
d [tan-1 (√1 + x2 + √1 – x2) / (√1 + x2 – √1 – x2)]
1) – x / √1 – x4 2) x / √1 – x4 3) – 1 / 2√1 – x4... View Article
If y = (x log x)log log x, then dy / dx =
1) {(x log x)log log x {(1 / x log x) (log x + log log x) + (log log... View Article
