Find the derivative of x2 – 2 at x = 10.
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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.
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.
Describe the sample space for the indicated experiment: A die is thrown two times.
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.
The ratio of the sums of m and n terms of an A.P. is m2: n2. Show that the ratio of mth and nth term is (2m – 1): (2n – 1).
A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.
The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7th term.
Prove the following by using the principle of mathematical induction for all n ∈ N:
n (n + 1) (n + 5) is a multiple of 3.
Which term of the following sequences:
If the first and the nth term of a G.P. are a ad b, respectively, and if P is the product of n terms, prove that P2 = (ab)n.