Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

(a) *f*(*x*) is a polynomial function, therefore the function is continuous on [1, 2].

(b) *f*'(*x*) = 1.(*x* - 2)^{2} + (*x* - 1).2(*x* - 2)

= (*x* - 2)[*x* - 2 + 2*x* - 2]

= (*x* - 2)(3*x* - 4)

Thus, function is differentiable on (1, 2)

(c) *f*(1) = 0 = *f*(2).

All the three conditions of Rolle’s theorem are true

at least one point *c* (1, 2) s.t. *f*'(*c*) = 0

(*c* - 2)(3*c* - 4) = 0

*c* = 4/3 or *c* = 2

but 2 (1, 2), hence this choice is rejected and the value of *c* is 4/3.

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Let E_{1}= Student knows the answer,

E_{2}= Student guesses the answer, and

A = answer is correct

Q:

A:

Q:

A:

Q:

A:

Q:

A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening.

A:

Q:

A:

Q:

(i) Obtain the probability distribution for X.

(ii) Find mean of X.

(iii) Find variance and standard deviation of X.

A:

(i) The probability distribution for X

X | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |

P(X) | 1/36 | 2/36 | 3/36 | 4/36 | 5/36 | 6/36 | 5/36 | 4/36 | 3/36 | 2/36 | 1/36 |

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

A:

Q:

Two regression lines are represented by 2x + 3y – 20 = 0 and 4x + y – 15 = 0. Find the line of regression of y on x.

A:

Q:

Find the equation of the two lines of regression for the following observations:

(3, 6), (4, 5), (5, 4),(6, 2),(7, 3)

Find an estimate of y for x = 3.5.

A:

The constructed table is given below:

Q:

Given the total cost function for x units of a

commodity as

(i) the marginal cost function

(ii) average cost function

(iii) slope of average cost function

A:

Q:

The fixed cost of a new product is `3600 and the variable cost per unit is ` 110. If the demand function is p(x) = 800 – 30x, find the breakeven values.

A:

Let x units of the product be produced and sold.

Variable cost of producing x units = ` 110x

As the fixed cost is ` 3600,

So, total cost of producing x units,

C(x) = `(3600 + 110x)

Given demand function, p(x) = 800 – 30x

i.e., the selling price per unit = `(800 – 30x)

So, total revenue on selling x units,

R(x) = (price per unit)(number of units sold)

= `(800 – 30x)x

At breakeven values,

C(x) = R(x)

3600 + 110x = (800 – 30x)x

3600 + 110x = 800x – 30x^{2}

30x^{2} – 690x + 3600 = 0

Dividing by 30, we get

x^{2} – 23 +120 = 0

(x – 8)(x – 15) = 0

This implies that either x = 8 or x = 15

Hence, the breakeven values of x are 8 and 15.

Q:

A:

Take your CBSE board preparation to another level with AI based and rich media animation on Extramarks - The Learning App.

Features of Learning App

- Learn with studybot “Alex”
- Personalized Learning journey
- Unlimited doubt Solving
- Quiz, challenge friends
- Leaderboard Ranking
- Academic Guru