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If x = 3 is one root of the quadratic equation 2x2 + px + 30 = 0, find the value of p and the other root of the quadratic equation.
Concept: Method of Solving a Quadratic Equation
The roots of the equation x2 + 3x – 10 = 0 are ______.
Concept: Method of Solving a Quadratic Equation
Determine the A.P. whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
If the ratio of sum of the first m and n terms of an AP is m2 : n2, show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1) ?
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
The next term of the A.P. \[\sqrt{7}, \sqrt{28}, \sqrt{63}\] is ______.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
The Sum of first five multiples of 3 is ______.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
If the sum of the first four terms of an AP is 40 and that of the first 14 terms is 280. Find the sum of its first n terms.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
How many multiples of 4 lie between 10 and 205?
Concept: General Term of an Arithmetic Progression
In an A.P., if Sn = 3n2 + 5n and ak = 164, find the value of k.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
The ratio of the 11th term to the 18th term of an AP is 2 : 3. Find the ratio of the 5th term to the 21st term, and also the ratio of the sum of the first five terms to the sum of the first 21 terms.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Write the next two terms of the A.P.: `sqrt(27), sqrt(48), sqrt(75)`......
Concept: General Term of an Arithmetic Progression
Find the sum of first 16 terms of the A.P. whose nth term is given by an = 5n – 3.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Find the sum of first 25 terms of the A.P. whose nth term is given by an = 5 + 6n. Also, find the ratio of 20th term to 45th term.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
If the vertices of ΔABC be A(1, -3) B(4, p) and C(-9, 7) and its area is 15 square units, find the values of p
Concept: Co-ordinate Geometry
Find the point on the y-axis which is equidistant from the points (5, −2) and (−3, 2).
Concept: Co-ordinate Geometry
The point R divides the line segment AB, where A(−4, 0) and B(0, 6) such that AR=34AB.">AR = `3/4`AB. Find the coordinates of R.
Concept: Co-ordinate Geometry
In what ratio does the point P(−4, y) divides the line segment joining the points A(−6, 10) and B(3, −8)? Hence find the value of y.
Concept: Distance Formula
The distance of the point P(–6, 8) from the origin is ______.
Concept: Distance Formula
