Advertisements
Advertisements
If the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
If 4 times the 4th term of an A.P. is equal to 18 times its 18th term, then find its 22nd term.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Prove that `(sin "A" - 2sin^3 "A")/(2cos^3 "A" - cos "A") = tan "A"`
Concept: Trigonometric Ratios
A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in given figure. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.
[Use `pi = 22/7`]
Concept: Surface Area of a Combination of Solids
If α and β are the zeroes of the polynomial x2 – 1, then the value of (α + β) is ______.
Concept: Geometrical Meaning of the Zeroes of a Polynomial
Find the value of p, for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the other.
Concept: Nature of Roots of a Quadratic Equation
Assertion (A): The point (0, 4) lies on y-axis.
Reason (R): The x-coordinate of a point on y-axis is zero.
Concept: Co-ordinate Geometry
If sin θ + cos θ = `sqrt(3)`, then prove that tan θ + cot θ = 1.
Concept: Trigonometric Identities (Square Relations)
Prove that `tan θ/(1 - cot θ) + cot θ/(1 - tanθ)` = 1 + sec θ cosec θ
Concept: Trigonometric Ratios
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?
-
- 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
