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If f be a polynomial, then the second derivative of f(e^x) is

(1) f’(ex) (2) f’’(ex)ex + f’(ex) (3) f’’(ex) e2x + f’’(ex) (4) f’’(ex) e2x + f’(ex) ex Solution: Let y... View Article

If e^y + xy = e, then the value of d²y/dx² for x = 0 is

(1) 1/e (2) 1/e2 (3) 1/e3 (4) none of these Solution: Given ey + xy = e When x =... View Article

If [latex]y = x \log \left ( \frac{x}{a+bx}\right )[/latex], then [latex]x^{3}\frac{d^{2}y}{dx^{2}}=[/latex]

(1) x dy/dx – y (2) (x dy/dx – y)2 (3) y dy/dx – x (4) (y dy/dx – x)2... View Article

If y = sin² α + cos² (α+β) + 2 sin α sin β cos (α+β), then d³y/dα³ is, (keeping β as constant)

(1) 1 (2) 0 (3) cos (α + 3β) (4) none of these Solution: Given y = sin2 α +... View Article

d²⁰/dx²⁰ (2 cos x cos 3x) =

(1) 220 (cos 2x – 220 cos 4x) (2) 220 (cos 2x + 220 cos 4x) (3) 220 (sin 2x... View Article

If y = a + bx²: a, b are arbitrary constants, then

(1) d2y/dx2 = 2xy (2) x d2y/dx2 = dy/dx (3) x d2y/dx2 – dy/dx + y = 0 (4) x... View Article

If y = axⁿ⁺¹+ bx^-n, then x²d²y/dx² =

(1) n(n-1)y (2) n(n+1)y (3) ny (4) n2y Solution: Given y = axn+1+ bx-n Differentiate w.r.t.x dy/dx = (n+1)axn –... View Article

If y = (x²– 1)^m, then the (2m)^th differential coefficient of y w.r.t.x is

(1) m (2) (2m)! (3) 2m (4) m! Solution: Given y = (x2 – 1)m (x2 – 1)m = mC0... View Article

If y = ae^mx+ be^-mx, then d²y/dx² – m²y =

(1) 1 (2) 0 (3) -1 (4) none of these Solution: Given y = aemx + be-mx Differentiate w.r.t.x dy/dx... View Article

If y = x² e^mx, where m is a constant, then d³y/dx³ =

(1) memx ( m2x2 + 6mx + 6) (2) 2m2 xemx (3) memx ( m2x2 + 2mx + 2) (4)... View Article

If y = cos² (3x/2) – sin² (3x/2), then d²y/dx² is

(1) 9y (2) -9y (3) 3√(1 – y2) (4) -3√(1 – y2) Solution: Given y = cos2 (3x/2) – sin2... View Article

If y = sin (log_e x), then x²d²y/dx² + x dy/dx is equal to

(1) sin loge x (2) cos loge x (3) -y (4) y2 Solution: Given y = sin (loge x) Differentiate... View Article

Is H+ an acid or base

A substance that has more number of H+ ions than OH– ions is called acid. The hydrochloric acid is more... View Article

What substance makes a better permanent magnet

Ferromagnetic substances make better permanent magnets. Few examples of ferromagnetic materials are iron, nickel and cobalt

Is HClO2 or HClO3 a stronger acid?

The acid is much stronger if the number of oxygen atoms is more. In HClO3 and HClO2, HClO3 has more... View Article

Is NaH a good base

For H-X bond to be an acid, the hydrogen should have a positive oxidation number so that it gets ionised... View Article

What are three laws of geometric optics

Geometric optics is based on the following laws The law of rectilinear propagation: Light travels in a straight line in... View Article

Is copper a ferromagnetic material?

Copper is a ferromagnetic material. Ferromagnetic substances are strong magnetic materials that exhibit strong magnetism in the direction of the... View Article

Can wood be magnetized?

Wood is a nonmagnetic material. It cannot attract a magnet or be magnetised.

Are all transistors the same

All the transistors are not the same. Based on the structure, the transistors are classified as Bipolar Junction Transistor and... View Article

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