SSC (Marathi Semi-English) 10th Standard Board Exam [इयत्ता १० वी] - Maharashtra State Board Question Bank Solutions for Algebra Mathematics 1

Choose the correct alternative answer for the following sub questions and write the correct alphabet.

If the root of the given quadratic equation are real and equal, then find the value of ‘k’ X² + 2X + k = 0

Choose the correct alternative answer for the following sub questions and write the correct alphabet.

What is the value of discriminant for the quadratic equation X² – 2X – 3 = 0?

If a = 1, b = 4, c = – 5, then find the value of b² – 4ac

If b² – 4ac > 0 and b² – 4ac < 0, then write the nature of roots of the quadratic equation for each given case

Complete the following activity to find the value of discriminant for quadratic equation 4x² – 5x + 3 = 0.

Activity: 4x² – 5x + 3 = 0

a = 4 , b = ______ , c = 3

b² – 4ac = (– 5)² – (______) × 4 × 3

= ( ______ ) – 48

b² – 4ac = ______

If roots of a quadratic equation 3y² + ky + 12 = 0 are real and equal, then find the value of ‘k’

If the roots of the given quadratic equation are real and equal, then find the value of ‘m’.

(m – 12)x² + 2(m – 12)x + 2 = 0

Compare the quadratic equation `x^2 + 9sqrt(3)x + 24 = 0` to ax² + bx + c = 0 and find the value of discriminant and hence write the nature of the roots.

Complete the following activity to determine the nature of the roots of the quadratic equation x² + 2x – 9 = 0 :

Solution :

Compare x² + 2x – 9 = 0 with ax² + bx + c = 0

a = 1, b = 2, c = `square`

∴ b² – 4ac = (2)² – 4 × `square` × `square`

Δ = 4 + `square` = 40

∴ b² – 4ac > 0

∴ The roots of the equation are real and unequal.

The marks scored by students in Mathematics in a certain Examination are given below:

Draw histogram for the above data.

Draw the frequency polygon for the following frequency distribution

Given below is the frequency distribution of driving speeds (in km/hour) of the vehicles of 400 college students:

Draw Histogram and hence the frequency polygon for the above data.

Represent the following data by Histogram:

The following is the frequency distribution of waiting time at ATM centre; draw histogram to represent the data:

Draw histogram and frequency polygon on the same graph paper for the following frequency distribution

Draw a histogram of the following data.

The table below shows the yield of jowar per acre. Show the data by histogram.

In the following table, the investment made by 210 families is shown. Present it in the form of a histogram.

Time alloted for the preparation of an examination by some students is shown in the table. Draw a histogram to show the information.

Observe the following frequency polygon and write the answers of the questions below it.

1. Which class has the maximum number of students?
2. Write the classes having zero frequency.
3. What is the class-mark of the class, having frequency of 50 students?
4. Write the lower and upper class limits of the class whose class mark is 85.
5. How many students are in the class 80-90?