A three digit number is equal to 17 times the sum of its digits. If 198 is added to the number, the digits are interchanged. The addition of first and third digit is 1 less than middle digit. Find the number.
Concept: Algebraic Methods of Solving a Pair of Linear Equations > Substitution Method
Solve the following quadratic equation for x: `4x^2 + 4bx – (a^2 – b^2) = 0`
Concept: Solutions of Quadratic Equations by Completing the Square
A milk centre sold milk to 50 customers. The table below gives the number of customers and the milk they purchased. Find the mean of the milk sold by direct method.
| Milk Sold (Litre) | 1 - 2 | 2 - 3 | 3 - 4 | 4 - 5 | 5 - 6 |
| No. of Customers | 17 | 13 | 10 | 7 | 3 |
Concept: Tabulation of Data
If 12x +13y =29 and 13x +12y=21, find x + y.
Concept: Linear Equation in Two Variables
Write the quadratic equation whose roots are ‒2 and ‒3.
Concept: Quadratic Equations
The divisor and quotient of the number 6123 are same and the remainder is half the divisor. Find the divisor.
Concept: Application of Quadratic Equation
If α + β = 5 and α3 +β3 = 35, find the quadratic equation whose roots are α and β.
Concept: Quadratic Equations
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
Write the first two terms of the sequence whose nth term is tn = 3n ‒ 4.
Concept: Arithmetic Progression
The 11th term and the 21st term of an A.P. are 16 and 29 respectively, then find:
(a) The first term and common difference
(b) The 34th term
(c) ‘n’ such that tn = 55
Concept: Arithmetic Progression
How many three digit natural numbers are divisible by 5?
Concept: Introduction to Sequence
Write the sample space for selecting a day randomly of the week.
Concept: Sample Space
In a certain race, there are three boys A, B, C. The winning probability of A is twice than B and the winning probability of B is twice than C. If P(A) + P(B) + P(C) = 1, then find the probability of win for each boy.
Concept: Basic Ideas of Probability
In a certain race, there are three boys A, B, C. The winning probability of A is twice than B and the winning probability of B is twice than C. If P(A) + P(B) + P(C) = 1, then find the probability of win for each boy.
Concept: Basic Ideas of Probability
Find the class mark of the classes 20-30 and 30-40.
Concept: Basic Ideas of Probability
Find the class mark of the classes 20-30 and 30-40.
Concept: Basic Ideas of Probability
Choose the correct alternative answer for the following question.
If n(A) = 2, P(A) =`1/5`, then n(S) = ?
Concept: Basic Ideas of Probability
Choose the correct alternative answer for the following question.
If n(A) = 2, P(A) =`1/5`, then n(S) = ?
Concept: Basic Ideas of Probability
For a certain frequency distribution, the value of Mean is 101 and Median is 100. Find the value of Mode.
Concept: Median of Grouped Data
Find the mode from the following information:
L = 10, h = 2, f0 = 58, f1 = 70, f2 = 42.
Concept: Mode of Grouped Data
