MATHEMATICS
CLASS - X
Time: 3 Hours
Marks: 80
General Instructions:
1. This question paper contains two parts: Part A and Part B.
2. All questions are compulsory.
3. Read the instructions carefully and write the answers in the space provided.
4. All workings must be shown.
PART - A
Question 1:
Find the value of x for which the expression $$2x^2 - 3x + 5$$ is minimum.
Question 2:
Solve the quadratic equation $$3x^2 - 5x - 2 = 0$$ by factorization method.
Question 3:
Find the HCF of 63, 72, and 90.
Question 4:
Find the LCM of 12, 18, and 24.
Question 5:
Simplify the following expression: $$\frac{2a^2 - 3ab + b^2}{a^2 - 2ab + b^2}$$
Question 6:
Solve the equation $$2x + 3 = 5$$ for x.
Question 7:
Factorize the following expression: $$x^2 - 9$$
Question 8:
Find the area of a rectangle with length 12 cm and breadth 8 cm.
Question 9:
Find the volume of a cube with side 5 cm.
Question 10:
A train travels a distance of 240 km in 4 hours. Find its average speed in km/hr.
PART - B
Question 11:
Solve the following system of linear equations:
$$3x + 2y = 13$$
$$5x - 3y = 4$$
Question 12:
A shopkeeper sells a shirt marked at Rs 1000 at a discount of 10%. Find the selling price of the shirt.
Question 13:
Find the mean of the following numbers: 10, 15, 20, 25, 30.
Question 14:
Find the median of the following numbers: 3, 5, 7, 9, 11, 13, 15.
Question 15:
A coin is tossed twice. What is the probability of getting two heads?
Question 16:
Construct a right-angled triangle ABC with sides 4 cm, 6 cm, and 8 cm.
Question 17:
Draw a histogram for the following data:
Marks: 0-10, 10-20, 20-30, 30-40, 40-50
Frequency: 5, 10, 15, 20, 25
Question 18:
Find the equation of a line passing through points (-2, 3) and (4, -5).
Question 19:
Solve the equation $$2x - 3 = 0$$ for x.
Question 20:
Find the value of x for which the expression $$(x - 2)^2$$ is minimum.