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The ratio of LCM and HCF of the least composite and the least prime numbers is ______.
Concept: Fundamental Theorem of Arithmetic
Show the 6n cannot end with digit 0 for any natural number 'n'.
Concept: Fundamental Theorem of Arithmetic
Find the HCF and LCM of 72 and 120.
Concept: Fundamental Theorem of Arithmetic
The LCM of smallest 2-digit number and smallest composite number is ______.
Concept: Fundamental Theorem of Arithmetic
Two numbers are in the ratio 2 : 3 and their LCM is 180. What is the HCF of these numbers?
Concept: Fundamental Theorem of Arithmetic
(HCF × LCM) for the numbers 70 and 40 is ______.
Concept: Fundamental Theorem of Arithmetic
If HCF (72, 120) = 24, then LCM (72, 120) is ______.
Concept: Fundamental Theorem of Arithmetic
Find the zeroes of the quadratic polynomial `4x^2 - 4x + 1` and verify the relation between the zeroes and the coefficients.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
If one zero of the quadratic polynomial x2 + 3x + k is 2, then the value of k is ______.
Concept: Geometrical Meaning of the Zeroes of a Polynomial
The number of quadratic polynomials having zeroes –5 and –3 is ______.
Concept: Geometrical Meaning of the Zeroes of a Polynomial
The zeroes of the polynomial 3x2 + 11x – 4 are ______.
Concept: Geometrical Meaning of the Zeroes of a Polynomial
If one zero of the polynomial p(x) = 6x2 + 37x – (k – 2) is reciprocal of the other, then find the value of k.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
If α, β are the zeroes of the polynomial p(x) = 4x2 – 3x – 7, then `(1/α + 1/β)` is equal to ______.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
Find the zeroes of the quadratic polynomial x2 + 6x + 8 and verify the relationship between the zeroes and the coefficients.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
The zeroes of the quadratic polynomial 16x2 – 9 are ______.
Concept: Geometrical Meaning of the Zeroes of a Polynomial
A fraction becomes `(1)/(3)` when 2 is subtracted from the numerator and it becomes `(1)/(2)` when 1 is subtracted from the denominator. Find the fraction.
Concept: Algebraic Methods of Solving a Pair of Linear Equations >> Elimination Method
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
Solve the following quadratic equation for x : 4x2 − 4a2x + (a4 − b4) =0.
Concept: Method of Solving 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
