Please select a subject first
Advertisements
Advertisements
If the quadratic equation ax2 + bx + c = 0 has two real and equal roots, then 'c' is equal to ______.
Concept: Nature of Roots of a Quadratic Equation
Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.
Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.
Concept: Nature of Roots of a Quadratic Equation
Find the value of ‘p’ for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.
Concept: Nature of Roots of a Quadratic Equation
Assertion (A): If one root of the quadratic equation 4x2 – 10x + (k – 4) = 0 is reciprocal of the other, then value of k is 8.
Reason (R): Roots of the quadratic equation x2 – x + 1 = 0 are real.
Concept: Nature of Roots of a Quadratic Equation
Find the discriminant of the quadratic equation `3x^2 - 2x + 1/3` = 0 and hence find the nature of its roots.
Concept: Nature of Roots of a Quadratic Equation
Find the value of k for which the roots of the quadratic equation 5x2 – 10x + k = 0 are real and equal.
Concept: Nature of Roots of a Quadratic Equation
If one root of the quadratic equation 3x2 – 8x – (2k + 1) = 0 is seven times the other, then find the value of k.
Concept: Nature of Roots of a Quadratic Equation
In an A.P., if S5 + S7 = 167 and S10=235, then find the A.P., where Sn denotes the sum of its first n terms.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Find the 9th term from the end (towards the first term) of the A.P. 5, 9, 13, ...., 185
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Ramkali required Rs 2,500 after 12 weeks to send her daughter to school. She saved Rs 100 in the first week and increased her weekly saving by Rs 20 every week. Find whether she will be able to send her daughter to school after 12 weeks.
What value is generated in the above situation?
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Find the sum of first 15 multiples of 8.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Find how many integers between 200 and 500 are divisible by 8.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
If the ratio of the sum of the first n terms of two A.Ps is (7n + 1) : (4n + 27), then find the ratio of their 9th terms.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Find the sum of first 8 multiples of 3.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Find a and b so that the numbers a, 7, b, 23 are in A.P.
Concept: General Term (nth) of an Arithmetic Progression
Find the sum of first 20 terms of an A.P. whose nth term is given as an = 5 – 2n.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Assertion (A): a, b, c are in A.P. if and only if 2b = a + c.
Reason (R): The sum of first n odd natural numbers is n2.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, –5) and R(–3, 6), find the coordinates of P.
Concept: Distance Formula
If A(5, 2), B(2, −2) and C(−2, t) are the vertices of a right angled triangle with ∠B = 90°, then find the value of t.
Concept: Distance Formula
If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find p. Also, find the length of AB.
Concept: Distance Formula
