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What is the HCF of the smallest prime number and the smallest composite number?
Concept: Fundamental Theorem of Arithmetic
Find HCF and LCM of 404 and 96 and verify that HCF × LCM = Product of the two given numbers.
Concept: Fundamental Theorem of Arithmetic
Read the following passage:
|
Khushi wants to organize her birthday party. Being health conscious, she decided to serve only fruits in her birthday party. She bought 36 apples and 60 bananas and decided to distribute fruits equally among all. |
Based on the above information, answer the following questions:
- How many guests Khushi can invite at the most?
- How many apples and bananas will each guest get?
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- If Khushi decides to add 42 mangoes, how many guests Khushi can invite at the most?
OR - If the cost of 1 dozen of bananas is ₹ 60, the cost of 1 apple is ₹ 15 and cost of 1 mango is ₹ 20, find the total amount spent on 60 bananas, 36 apples and 42 mangoes.
- If Khushi decides to add 42 mangoes, how many guests Khushi can invite at the most?
Concept: Fundamental Theorem of Arithmetic
The prime factorisation of the number 2304 is ______.
Concept: Fundamental Theorem of Arithmetic
If n is a natural number, then 8n cannot end with digit
Concept: Fundamental Theorem of Arithmetic
The HCF of the smallest 2-digit number and the smallest composite number is ______.
Concept: Fundamental Theorem of Arithmetic
Find all zeroes of the polynomial `(2x^4 - 9x^3 + 5x^2 + 3x - 1)` if two of its zeroes are `(2 + sqrt3)` and `(2 - sqrt3)`
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
Find the sum and product of the roots of the quadratic equation 2x2 – 9x + 4 = 0.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
If p(x) = x2 + 5x + 6, then p(– 2) is ______.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
The graph of y = f(x) is shown in the figure for some polynomial f(x).
The number of zeroes of f(x) is ______.
Concept: Geometrical Meaning of the Zeroes of a Polynomial
Find a quadratic polynomial whose zeroes are 6 and – 3.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
Find the zeroes of the polynomial x2 + 4x – 12.
Concept: Relation Between Zeroes (Roots) and Coefficients of a Quadratic Equation
Read the following passage:
Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹ x per student and Cricket ₹ y per student. School 'P' decided to award a total of ₹ 9,500 for the two games to 5 and 4 Students respectively; while school 'Q' decided to award ₹ 7,370 for the two games to 4 and 3 students respectively. |
Based on the above information, answer the following questions:
- Represent the following information algebraically (in terms of x and y).
- (a) What is the prize amount for hockey?
OR
(b) Prize amount on which game is more and by how much? - What will be the total prize amount if there are 2 students each from two games?
Concept: Algebraic Methods of Solving a Pair of Linear Equations >> Elimination Method
If the quadratic equation px2 − 2√5px + 15 = 0 has two equal roots then find the value of p.
Concept: Nature of Roots of a Quadratic Equation
If `x=2/3` and x =−3 are roots of the quadratic equation ax2 + 7x + b = 0, find the values of a and b.
Concept: Nature of Roots of a Quadratic Equation
If `x = (-1)/2`, is a solution of the quadratic equation 3x2 + 2kx – 3 = 0, find the value of k.
Concept: Nature of Roots of a Quadratic Equation
Solve the quadratic equation 2x2 + ax − a2 = 0 for x.
Concept: Nature of Roots of a Quadratic Equation
Find the value of k for which the equation x2 + k(2x + k – 1) + 2 = 0 has real and equal roots.
Concept: Nature of Roots of a Quadratic Equation
Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.
Concept: Nature of Roots of a Quadratic Equation
Find the nature of the roots of the quadratic equation:
4x2 – 5x – 1 = 0
Concept: Nature of Roots of a Quadratic Equation
