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A 2-digit number is such that the product of its digits is 24. If 18 is subtracted from the number, the digits interchange their places. Find the number.
Concept: Algebraic Methods of Solving a Pair of Linear Equations >> Elimination Method
Solve for x: `sqrt(3x^2)-2sqrt(2)x-2sqrt3=0`
Concept: Nature of Roots of a Quadratic Equation
Find that non-zero value of k, for which the quadratic equation kx2 + 1 − 2(k − 1)x + x2 = 0 has equal roots. Hence find the roots of the equation.
Concept: Nature of Roots of a Quadratic Equation
For what value of k, the roots of the equation x2 + 4x + k = 0 are real?
Concept: Nature of Roots of a Quadratic Equation
Find the value of k for which the roots of the equation 3x2 – 10x + k = 0 are reciprocal of each other.
Concept: Nature of Roots of a Quadratic Equation
Which of the following equations has 2 as a root?
Concept: Nature of Roots of a Quadratic Equation
Find the value of 'p' for which the quadratic equation p(x – 4)(x – 2) + (x –1)2 = 0 has real and equal roots.
Concept: Nature of Roots of a Quadratic Equation
‘The sum of the ages of a boy and his sister (in years) is 25 and product of their ages is 150. Find their present ages.
Concept: Nature of Roots of a Quadratic Equation
Find the value of 'k' so that the quadratic equation 3x2 – 5x – 2k = 0 has real and equal roots.
Concept: Nature of Roots of 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 (nth) 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 (nth) of an Arithmetic Progression
