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

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 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: Quadratic Equations Examples and Solutions

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

If 12x +13y =29 and 13x +12y=21, find x + y.

Concept: Linear Equations in Two Variables Applications

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: Probability Examples and Solutions

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

Concept: Probability Examples and Solutions

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 sum of all numbers from 50 to 350 which are divisible by 6. Hence find the 15^{th} term of that A.P.

Concept: Sum of First n Terms of an AP

Find the term t15 of an A.P. : 4, 9, 14, …………..

Concept: General Term of an Arithmetic Progression

Babubhai borrows Rs. 4,000 and agrees to repay with a total interest of Rs. 500 in 10 instlments, each instalment being less than the preceding instalment by Rs. 10. What should be the first and the last instalments?

Concept: Arithmetic Progression

State whether the following sequence is an Arithmetic Progression or not:

3, 6, 12, 24,......

Concept: Arithmetic Progression

Find n if the nth term of the following A.P. is 68

5, 8, 11, 14, ..........

Concept: Arithmetic Progression

The first term of an A. P. is 5 and the common difference is 4. Complete the following activity and find the sum of the first 12 terms of the A. P.

a = 5, d = 4, s12 = ?

`s_n = n/2 [ square ]`

`s_12 = 12/2 [10 +square]`

`= 6 × square `

` =square`

Concept: Sum of First n Terms of an AP

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