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If 'p' is a root of the quadratic equation x2 – (p + q) x + k = 0, then the value of 'k' is ______.
Concept: Method of Solving a Quadratic Equation
If one root of the quadratic equation x2 + 12x – k = 0 is thrice the other root, then find the value of k.
Concept: Nature of Roots of a Quadratic Equation
If x = 3 is one of the roots of the quadratic equation x2 – 2kx – 6 = 0, then the value of k is ______.
Concept: Nature of Roots of a Quadratic Equation
The nature of roots of the quadratic equation 9x2 – 6x – 2 = 0 is ______.
Concept: Nature of Roots of a Quadratic Equation
If the discriminant of the quadratic equation 3x2 - 2x + c = 0 is 16, then the value of c is ______.
Concept: Method of Solving a Quadratic Equation
Find the value of ‘c’ for which the quadratic equation
(c + 1) x2 - 6(c + 1) x + 3(c + 9) = 0; c ≠ - 1
has real and equal roots.
Concept: Nature of Roots of a Quadratic Equation
Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
If the ratio of the sum of first n terms of two A.P’s is (7n +1): (4n + 27), find the ratio of their mth terms.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
The houses in a row numbered consecutively from 1 to 49. Show that there exists a value of x such that sum of numbers of houses preceding the house numbered x is equal to sum of the numbers of houses following x.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
How many terms of the A.P. 18, 16, 14, .... be taken so that their sum is zero?
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
How many terms of the A.P. 27, 24, 21, .... should be taken so that their sum is zero?
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
How many terms of the A.P. 65, 60, 55, .... be taken so that their sum is zero?
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
If Sn1 denotes the sum of first n terms of an A.P., prove that S12 = 3(S8 − S4).
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
If the sum of the first n terms of an A.P. is `1/2`(3n2 +7n), then find its nth term. Hence write its 20th term.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
If Sn denotes the sum of first n terms of an A.P., prove that S30 = 3[S20 − S10]
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
The first and the last terms of an AP are 8 and 65 respectively. If the sum of all its terms is 730, find its common difference.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Find the sum of first 20 terms of the following A.P. : 1, 4, 7, 10, ........
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
The ratio of the sums of m and n terms of an A.P. is m2 : n2. Show that the ratio of the mth and nth terms is (2m – 1) : (2n – 1)
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
How many multiples of 4 lie between 10 and 250?
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
