21.

If there is an error of K % is measuring the edge of a cube, then the per cent error in estimating its volume is

• k

• 3k

• $\frac{\mathrm{k}}{3}$

• None of these

The equation of the tangent to the curve y = be^{- x/a} at the point where it crosses the Y-axis, is

• $\frac{\mathrm{x}}{\mathrm{a}} + \frac{\mathrm{y}}{\mathrm{b}} = 1$

• $\frac{\mathrm{x}}{\mathrm{a}} - \frac{\mathrm{y}}{\mathrm{b}} = 1$

• ax + by = 1

• ax - by = 1

Which of the following function is not differentiable at x = 1 ?

• f(x) = $\tan \left(\left|\mathrm{x} - 1\right|\right) + \left|\mathrm{x} - 1\right|$

• f(x) = $\sin \left(\left|\mathrm{x} - 1\right|\right) - \left|\mathrm{x} - 1\right|$

• f(x) = $\left|\left({\mathrm{x}}^2 - 1\right)\left(\mathrm{x} - 1\right)\left(\mathrm{x} - 2\right)\right|$

• None of the above

If the direction cosines of two lines are connected by the equations l + m + n = 0, l² + m² - n² = 0, then the angle between the lines is

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{3}$

The equation of the plane which contains the origin and the line of intersection of the planes r · a = d₁ and r · b = d₂, is

• r . (d₁a + d₂b) = 0

• r . (d₂a - d₁b) = 0

• r . (d₂a + d₁b) = 0

• r . (d₁a - d₂b) = 0

If from a point P(a, b, c) perpendiculars PA and PB are drawn to YZ and ZX - planes, then the equation of the plane OAB is

• bcx + cay + abz = 0

• bcx + cay - abz = 0

• - bcx + cay + abz = 0

• bcx - cay + abz = 0

The order of the differential equation whose general solution is given by

y = (C₁ + C₂)sin(x + C₃) - C₄e^{x + C₅}, is

• 2

• 3

• 4

• 5

If d = a x b + b x c + c x a is a non-zero vector and $\left|(\mathrm{d} · \mathrm{c}) (\mathrm{a} \mathrm{x} \mathrm{b}) + (\mathrm{d} · \mathrm{a}) (\mathrm{b} \mathrm{x} \mathrm{c}) + (\mathrm{d} . \mathrm{b}) (\mathrm{c} \mathrm{x} \mathrm{a})\right|$ = 0, then

• $\left|\mathrm{a}\right| + \left|\mathrm{b}\right| + \left|\mathrm{c}\right| = \left|\mathrm{d}\right|$

• $\left|\mathrm{a}\right| = \left|\mathrm{b}\right| = \left|\mathrm{c}\right|$

• a, b and c are coplanar

• None of the above

Let u, v and w be such that $\left|\mathrm{u}\right|$ = 1, $\left|\mathrm{v}\right|$ = 2 and $\left|\mathrm{w}\right|$ = 3. If the projection of v along u is equal to that of w along u and vectors v and w are perpendicular to each other, then $\left|\mathrm{u} - \mathrm{v} + \mathrm{w}\right|$ equals

• 2

• $\sqrt{7}$

• $\sqrt{14}$

• 14

If a and b are two vectors, such that a . b < 0 and $\left|\mathrm{a} . \mathrm{b}\right| = \left|\mathrm{a} \times \mathrm{b}\right|$ then the angle between vectors a and b is

• $\frac{3\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{4}$

• $\mathrm{\pi }$

• $\frac{7\mathrm{\pi }}{4}$