HSC Science (Computer Science) 11th Standard - Maharashtra State Board Question Bank Solutions

Fill in the blanks:

y = `sinx/(x^2 + 2)`

Differentiating. w.r.t.x.

`("d"y)/("d"x) = (square "d"/("d"x) (sin x) - sin x "d"/("dx) square)/(x^2 + 2)^2`

= `(square  square - sin x  square)/(x^2 + 2)^2`

= `(square - square)/(x^2 + 2)^2`

Fill in the blanks:

y = (3x² + 5) cos x

Differentiating w.r.t.x

`("d"y)/("d"x) = "d"/("d"x) [(3x^2 + 5) cos x]`

= `(3x^2 + 5) "d"/("d"x) [square] + cos x  "d"/("d"x) [square]`

= `(3x^2 + 5) [square] + cos x  [square]`

∴ `(dx)/("d"y) = (3x^2 + 5) [square] + [square] cos x`

Fill in the blank:

Differentiate tan x and sec x w.r.t.x. using the formulae for differentiation of `"u"/"v" and 1/"v"` respectively

Select the correct answer from the given alternative:

If y = `(5sin x - 2)/(4sin x + 3)`, then `("d"y)/("d"x)` =

Select the correct answer from the given alternative:

Suppose f(x) is the derivative of g(x) and g(x) is the derivative of h(x).

If h(x) = a sin x + b cos x + c then f(x) + h(x) = 

Find the value of :

`sin  pi/8`

A card is drawn from a pack of 52 cards. What is the probability that, card is either black or a face card?

Following data gives age of 100 students in a college. Calculate variance and S.D.

An insurance agent insures lives of 5 men, all of the same age and in good health. The probability that a man of this age will survive the next 30 years is known to be 2/3 . Find the probability that in the next 30 years at most 3 men will survive.

Suppose that 80% of all families own a television set. If 5 families are interviewed at  random, find the probability that
a. three families own a television set.
b. at least two families own a television set.

Find the trigonometric function of :

0°

Find the trigonometric function of:

30°

Find the trigonometric function of:

45°

Find the trigonometric function of :

60°

Find the trigonometric function of : 

150°

Find the trigonometric functions of :

180°

Find the trigonometric function of :

210°

Find the trigonometric function of :

300°

Find the trigonometric functions of :

330°

Find the trigonometric functions of :

−30°