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The prime factorisation of the number 5488 is ______.
Concept: Fundamental Theorem of Arithmetic
If two positive integers a and b are written as a = x3y2 and b = xy3, where x, y are prime numbers, then the result obtained by dividing the product of the positive integers by the LCM (a, b) is ______.
Concept: Fundamental Theorem of Arithmetic
National Art convention got registrations from students from all parts of the country, of which 60 are interested in music, 84 are interested in dance and 108 students are interested in handicrafts. For optimum cultural exchange, organisers wish to keep them in minimum number of groups such that each group consists of students interested in the same artform and the number of students in each group is the same. Find the number of students in each group. Find the number of groups in each art form. How many rooms are required if each group will be allotted a room?
Concept: Fundamental Theorem of Arithmetic
Three bells toll at intervals of 9, 12 and 15 minutes respectively. If they start tolling together, after what time will they next toll together?
Concept: Fundamental Theorem of Arithmetic
The HCF of two numbers 65 and 104 is 13. If LCM of 65 and 104 is 40x, then the value of x is ______.
Concept: Fundamental Theorem of Arithmetic
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
6x2 – 3 – 7x
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
Find the zeroes of the quadratic polynomial f(x) = 4x2 – 4x – 3 and verify the relation between its zeroes and coefficients.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
Find the value of k such that the polynomial x2-(k +6)x+ 2(2k - 1) has some of its zeros equal to half of their product.
Concept: Geometrical Meaning of the Zeroes of a Polynomial
Find the value of k such that the polynomial x2 − (k + 6)x + 2(2k −1) has sum of its zeros equal to half of their product.
Concept: Geometrical Meaning of the Zeroes of a Polynomial
Check whether g(x) is a factor of p(x) by dividing polynomial p(x) by polynomial g(x),
where p(x) = x5 − 4x3 + x2 + 3x +1, g(x) = x3 − 3x + 1
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
If the zeroes of the quadratic polynomial x2 + (a + 1) x + b are 2 and –3, then ______.
Concept: Geometrical Meaning of the Zeroes of a Polynomial
Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and the coefficients.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
If α and β are the zeros of a polynomial f(x) = px2 – 2x + 3p and α + β = αβ, then p is ______.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
If the zeroes of the polynomial x2 + px + q are double in value to the zeroes of the polynomial 2x2 – 5x – 3, then find the values of p and q.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
A quadratic polynomial the sum and product of whose zeroes are – 3 and 2 respectively, is ______.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
A quadratic polynomial whose sum and product of zeroes are 2 and – 1 respectively is ______.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
If α, β are zeroes of the quadratic polynomial x2 – 5x + 6, form another quadratic polynomial whose zeroes are `1/α, 1/β`.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
The number of polynomials having zeroes – 3 and 4 is ______.
Concept: Geometrical Meaning of the Zeroes of a Polynomial
The zeroes of the polynomial p(x) = 25x2 – 49 are ______.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
The zeroes of the polynomial p(x) = 2x2 – x – 3 are ______.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
