Class 11 Mathematics - Chapter Limits And Derivatives NCERT Solutions | Find the derivative of x2 – 2

Find the derivative of 99x at x = l00.

Find the derivative of x at x = 1.

Solve 24x < 100, when
   (i)   x is a natural number.         (ii)   x is an integer.

Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.

A point is on the x-axis. What are its y-coordinates and z-coordinates?

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that

(i) repetition of the digits is allowed?

(ii) repetition of the digits is not allowed?

Find the equation of the circle with centre (0, 2) and radius 2

Describe the sample space for the indicated experiment: A coin is tossed three times.

Which of the following sentences are statements? Give reasons for your answer.

(i) There are 35 days in a month.

(ii) Mathematics is difficult.

(iii) The sum of 5 and 7 is greater than 10.

(iv) The square of a number is an even number.

(v) The sides of a quadrilateral have equal length.

(vi) Answer this question.

(vii) The product of (–1) and 8 is 8.

(viii) The sum of all interior angles of a triangle is 180°.

(ix) Today is a windy day.

(x) All real numbers are complex numbers.

If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A×B).

The base of an equilateral triangle with side 2a lies along the y-axis such that the mid-point of the base is at the origin. Find vertices of the triangle.

Find the sum to n terms of the series whose nth term is given by n (n + 1) (n + 4).

If the sum of first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms.

A die is rolled. Let E be the event “die shows 4” and F be the event “die shows even number”. Are E and F mutually exclusive?

Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

Which of the following sentences are statements? Give reasons for your answer.

(i) There are 35 days in a month.

(ii) Mathematics is difficult.

(iii) The sum of 5 and 7 is greater than 10.

(iv) The square of a number is an even number.

(v) The sides of a quadrilateral have equal length.

(vi) Answer this question.

(vii) The product of (–1) and 8 is 8.

(viii) The sum of all interior angles of a triangle is 180°.

(ix) Today is a windy day.

(x) All real numbers are complex numbers.

Find the equation of the circle with centre (0, 2) and radius 2

Describe the sample space for the indicated experiment: A coin is tossed and then a die is rolled only in case a head is shown on the coin.

Find the sum to n terms of the series whose nth terms is given by n² + 2n