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.
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Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.
How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?
Find the sum of all numbers between 200 and 400 which are divisible by 7.
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
If f is a function satisfying f(x +y) = f(x) f(y) for all x,y N such that f(1) = 3
and , find the value of n.
Find the derivative of x at x = 1.
The 5th, 8th and 11th terms of a G.P. are p, q and s, respectively. Show that q2 = ps.
If the sum of n terms of an A.P. is 3n2 + 5n and its mth term is 164, find the value of m.
If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.
Given a G.P. with a = 729 and 7th term 64, determine S7.
Suppose 3 bulbs are selected at random from a lot. Each bulb is tested and classified as defective (D) or non-defective (N). Write the sample space of this experiment?
Find the sum to n terms of the series 3 × 8 + 6 × 11 + 9 × 14 +…
Find the sum of all numbers between 200 and 400 which are divisible by 7.