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In the given figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region.
Concept: Areas of Sector and Segment of a Circle
A car has two wipers that do not overlap. Each wiper has a blade of length 21 cm sweeping through an angle of 120°. Find the total area cleaned at each sweep of the blades. `("Take" π =22/7)`
Concept: Areas of Sector and Segment of a Circle
Water is flowing at the rate of 2.52 km/h through a cylindrical pipe into a cylindrical tank, the radius of whose base is 40 cm. If the increase in the level of water in the tank, in half an hour is 3.15 m, find the internal diameter of the pipe.
Concept: Concept of Surface Area, Volume, and Capacity
A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears a prime number less than 23, is ______.
Concept: Basic Ideas of Probability
A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears a prime number less than 23, is ______.
Concept: Basic Ideas of Probability
Prove that is `sqrt2` irrational number.
Concept: Proofs of Irrationality
What is the HCF of the smallest prime number and the smallest composite number?
Concept: Fundamental Theorem of Arithmetic
Given that `sqrt2` is irrational prove that `(5 + 3sqrt2)` is an irrational number
Concept: Concept of Irrational Numbers
Find HCF and LCM of 404 and 96 and verify that HCF × LCM = Product of the two given numbers.
Concept: Fundamental Theorem of Arithmetic
A shopkeeper buys some books for Rs 80. If he had bought 4 more books for the same amount, each book would have cost Rs 1 less. Find the number of books he bought.
Concept: Real Numbers Examples and Solutions
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 39 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
Prove that `3 - 2sqrt(5)` is an irrational number, given that `sqrt(5)` is an irrational number.
Concept: Concept of Irrational Numbers
The HCF of the smallest 2-digit number and the smallest composite number is ______.
Concept: Fundamental Theorem of Arithmetic
If x = 3 is one root of the quadratic equation x2 – 2kx – 6 = 0, then find the value of k.
Concept: Polynomials
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: Relationship Between Zeroes and Coefficients of a Polynomial
A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km away in time, it had to increase its speed by 100 km/h from the usual speed. Find its usual speed.
Concept: Polynomials
Find the sum and product of the roots of the quadratic equation 2x2 – 9x + 4 = 0.
Concept: Relationship Between Zeroes and Coefficients of a Polynomial
If p(x) = x2 + 5x + 6, then p(– 2) is ______.
Concept: Relationship Between Zeroes and Coefficients of a Polynomial
