# SSC (Marathi Semi-English) 10th Standard [इयत्ता १० वी] - Maharashtra State Board Question Bank Solutions for Algebra

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Algebra
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Find the value of a, b, c in the following quadratic equation : 2x2 ‒ x ‒ 3 = 0

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

For a sequence if n S_n=n/(n+1) then find the value of S10.

[0.03] Arithmetic Progression
Chapter: [0.03] Arithmetic Progression
Concept: Introduction to Sequence

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

If one root of the quadratic equation kx2 – 7x + 12 = 0 is 3, then find the value of k.

If α + β = 5 and α33 = 35, find the quadratic equation whose roots are α and β.

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

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’.

[0.06] Statistics
Chapter: [0.06] Statistics
Concept: Tabulation of Data

Write the following quadratic equation in a standard form: 3x2 =10x + 7.

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

[0.01] Linear equations in two variables
Chapter: [0.01] Linear equations in two variables
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.

[0.01] Linear equations in two variables
Chapter: [0.01] Linear equations in two variables
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.

Find the values of a, b, c for the quadratic equation 2x2 = x + 3 by comparing with standard form ax2 + bx + c = 0.

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

[0.03] Arithmetic Progression
Chapter: [0.03] Arithmetic Progression
Concept: Introduction to Sequence

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

Find the value of k for which the given simultaneous equations have infinitely many solutions:
kx + 4y = 10;
3x + 2y = 5.

[0.01] Linear equations in two variables
Chapter: [0.01] Linear equations in two variables
Concept: Linear Equation in Two Variables

How many three digit natural numbers are divisible by 5?

[0.03] Arithmetic Progression
Chapter: [0.03] Arithmetic Progression
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?

[0.05] Probability
Chapter: [0.05] Probability
Concept: Probability - A Theoretical Approach

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

5/4m^2 - 7 = 0

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

[0.05] Probability
Chapter: [0.05] Probability
Concept: Probability - A Theoretical Approach
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