Find the value of a, b, c in the following quadratic equation : 2x^{2} ‒ x ‒ 3 = 0

Concept: Quadratic Equations

Write the quadratic equation whose roots are ‒2 and ‒3.

Concept: Quadratic Equations

For a sequence if n `S_n=n/(n+1)` then find the value of S_{10}.

Concept: Introduction to Sequence

Verify whether 1 is the root of the quadratic equation : `x^2+3x-4=0`

Concept: Quadratic Equations

If one root of the quadratic equation kx^{2} – 7x + 12 = 0 is 3, then find the value of k.

Concept: Quadratic Equations

If α + β = 5 and α^{3} +β^{3} = 35, find the quadratic equation whose roots are α and β.

Concept: Quadratic Equations

(x + 5)(x - 2) = 0, find the roots of this quadratic equation

Concept: Quadratic Equations

The following data shows the number of students using different modes of transport:

Modes of Transport | Number of Students |

Bicycle | 140 |

Bus | 100 |

Walk | 70 |

Train | 40 |

Car | 10 |

From this table, find the central angle (θ) for the Mode of Transport ‘Bus’.

Concept: Tabulation of Data

Write the following quadratic equation in a standard form: 3x^{2} =10x + 7.

Concept: Quadratic Equations

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

Concept: Linear Equation in Two Variables

The product of four consecutive natural numbers, which are multiples of fives, is Rs. 15,000. Find those natural numbers.

Concept: Linear Equation in Two Variables

The time taken by a person to cover 150 km was 2 1/2 hours more than the time taken in the return journey. If he returned at a speed of 10 km/hour more than the speed while going, find the speed per hour in each direction.

Concept: Quadratic Equations

Find the values of a, b, c for the quadratic equation 2x_{2} = x + 3 by comparing with standard form ax^{2} + bx + c = 0.

Concept: Quadratic Equations

Find the first two terms of the sequence for which S_{n} is given below: `S_n=n^2(n+1)`

Concept: Introduction to Sequence

Find the value of discriminant (Δ) for the quadratic equation: `x^2+7x+6=0`

Concept: Quadratic Equations

Find the value of k for which the given simultaneous equations have infinitely many solutions:

kx + 4y = 10;

3x + 2y = 5.

Concept: Linear Equation in Two Variables

How many three digit natural numbers are divisible by 5?

Concept: Introduction to Sequence

Three horses A, B and C are in a race, A is twice as likely to win as B and B is twice as likely to win as C. What are their probabilities of winning?

Concept: Probability - A Theoretical Approach

State whether the given equation is quadratic or not. Give reason.

`5/4m^2 - 7 = 0`

Concept: Quadratic Equations

If S = {2, 4, 6, 8, 10, 12} and A = {4, 8, 12}, find A'

Concept: Probability - A Theoretical Approach