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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

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

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 α^{3} +β^{3} = 35, find the quadratic equation whose roots are α and β.

Concept: Quadratic Equations

If the quadratic equation px^{2} − 2√5px + 15 = 0 has two equal roots then find the value of p.

Concept: Nature of Roots of a Quadratic Equation

**Choose the correct answer for the following question.**Out of the following equations which one is not a quadratic equation?

Concept: Application of Quadratic Equation

Write the first two terms of the sequence whose nth term is t_{n} = 3n ‒ 4.

Concept: Arithmetic Progression

The 11^{th} term and the 21^{st} term of an A.P. are 16 and 29 respectively, then find:

(a) The first term and common difference

(b) The 34^{th} term

(c) ‘n’ such that t_{n} = 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

Find the class mark of the classes 20-30 and 30-40.

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, f_{0} = 58, f_{1} = 70, f_{2} = 42.

Concept: Mode of Grouped Data

Solve the following simultaneous equations: `7/(2X+1)+13/(Y+2)=27,13/(2X+1)+7/(Y+2)=33`

Concept: Equations Reducible to a Pair of Linear Equations in Two Variables

If the point A(3, 2) lies on the graph of the equation 5x + ay = 19, then find a.

Concept: Algebraic Methods of Solving a Pair of Linear Equations > Substitution Method