Explore CBSE Class 10 Maths Standard Sample Paper 2021 with Full Solutions

cbse sample paper 2021 class 10 maths standard with solution provides detailed solutions and explanations to help students prepare for exams effectively.

Sure, let's create a user-friendly heading followed by a collection of 50 sample questions and answers for the CBSE Class 10 Maths Standard paper from 2021. Since we are focusing solely on mathematics, I will provide all 50 questions in a text format without using typical mathematical formulas, numbering, or bullets. Here's how it could be structured:

Sample Questions and Answers:

What is the value of the expression 2x + 3y when x = 3 and y = 5?
Answer: Substitute the values into the equation: 2(3) + 3(5) = 6 + 15 = 21.

If a triangle has sides of lengths 8 cm, 15 cm, and 17 cm, is it a right triangle?
Answer: Yes, because 8² + 15² = 17² (64 + 225 = 289).

A rectangle's length is twice its width. If the perimeter is 36 cm, what are its dimensions?
Answer: Let the width be x cm. Then, length = 2x cm and perimeter = 2(x + 2x) = 36 cm, so x = 6 cm, and the length = 12 cm.

What is the probability of drawing a red card from a standard deck of playing cards?
Answer: There are 26 red cards in 52 total cards, so the probability is 26/52 or 1/2.

Find the area of a circle with a radius of 7 cm.
Answer: Area = πr² = π(7)² = 49π cm².

Translate the following scenario into a simple equation: John has twice as many marbles as Tom, and together they have 36 marbles.
Answer: Let the number of Tom's marbles be x. Then, John's marbles = 2x. The equation is x + 2x = 36.

What is the angle sum of a polygon with 6 sides?
Answer: The sum of the interior angles of a polygon = (n-2)×180°, so for n=6, it is 720°.

Calculate the average of these numbers: 23, 29, 31, and 27.
Answer: Average = (23 + 29 + 31 + 27) / 4 = 110 / 4 = 27.5.

A train travels 360 km in 3 hours. What is its speed in kilometers per hour?
Answer: Speed = Distance / Time = 360 km / 3 h = 120 km/h.

Simplify the expression 4x - 2x + x.
Answer: 4x - 2x + x = 3x.

What is the volume of a cube with edge length 5 cm?
Answer: Volume = side³ = 5³ = 125 cm³.

How do you find the median of the data set 4, 8, 15, 16, 23?
Answer: Arrange in order, the middle value is 15.

If the price of an apple is increased from $1 to $1.20, what is the percentage increase?
Answer: Increase = $0.20, Percentage = (0.20/1) × 100% = 20%.

What does the slope of a line tell us in a graph?
Answer: The slope tells the rate of change from one point on the line to another.

Describe how to convert a fraction to a decimal.
Answer: Divide the numerator by the denominator.

A rectangular park measures 30 m by 40 m. What is its area?
Answer: Area = Length × Width = 30 m × 40 m = 1200 m².

If 5 out of 20 students in a class are absent, what percentage is present?
Answer: Absent = 25%, so present = 75%.

What is the greatest common divisor (GCD) of 36 and 60?
Answer: The GCD of 36 and 60 is 12.

How many different three-letter arrangements can be made from the word "CAT"?
Answer: The number of arrangements = 3! = 6.

Explain how to find the circumference of a circle.
Answer: Circumference = 2πr, where r is the radius.

If you buy 3 books for $15 each, what is the total cost?
Answer: Total cost = 3 books × $15/book = $45.

What is the complementary angle to 45°?
Answer: Complementary angles sum up to 90°, so it is 45°.

Define the term 'prime number'.
Answer: A prime number is a number greater than 1 that has no divisors other than 1 and itself.

A bus travels 90 km in 2 hours. At the same speed, how far will it travel in 5 hours?
Answer: Distance = Speed × Time = (90 km / 2 h) × 5 h = 225 km.

What is 15% of 200?
Answer: 15% of 200 = 0.15 × 200 = 30.

How do you find the mode of a set of data?
Answer: The mode is the number that appears most frequently in the data set.

Explain the Pythagorean Theorem without using the formula.
Answer: The theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Determine the next number in this sequence: 2, 4, 8, 16, ...
Answer: The sequence doubles each time, so the next number is 32.

What is the simple interest on $200 at 3% per year for 4 years?
Answer: Interest = Principal × Rate × Time = $200 × 0.03 × 4 = $24.

Explain what an isosceles triangle is.
Answer: An isosceles triangle has at least two sides of equal length.

What is the square root of 144?
Answer: The square root of 144 is 12.

When simplifying the fraction 20/60, what result do you get?
Answer: Simplified fraction = 20/60 = 1/3.

How many edges does a cube have?
Answer: A cube has 12 edges.

What is the name for a shape with five sides?
Answer: A five-sided shape is called a pentagon.

Explain the concept of rounding numbers to the nearest ten.
Answer: If the units digit is 5 or more, round up; if less, round down to the nearest ten.

A shopkeeper has 45 apples and sells 29. How many does he have left?
Answer: Remaining apples = 45 - 29 = 16.

How do you calculate the area of a trapezoid?
Answer: Area = 0.5 × (Base1 + Base2) × Height.

What is 7 multiplied by 8?
Answer: 7 × 8 = 56.

What term describes the number of square units needed to cover a surface?
Answer: This term is called area.

What is the difference between an acute and obtuse angle?
Answer: An acute angle is less than 90°, while an obtuse angle is more than 90° but less than 180°.

What is the decimal equivalent of 1/4?
Answer: 1/4 = 0.25.

How many liters are in 2500 milliliters?
Answer: There are 2.5 liters in 2500 milliliters.

Describe a method to find the LCM of two numbers.
Answer: List the multiples of each number until you find the lowest common multiple.

What does it mean for angles to be supplementary?
Answer: Supplementary angles add up to 180 degrees.

How do you find the percent change from 50 to 75?
Answer: Percent change = [(75 - 50) / 50] × 100% = 50%.

If a car is driving at 60 km/h, how many kilometers will it travel in 4 hours?
Answer: Distance = Speed × Time = 60 km/h × 4 h = 240 km.

Explain how to convert a percent to a fraction.
Answer: Write the percent as a fraction over 100 and simplify if possible.

If a rectangle measures 10m by 5m, what is its perimeter?
Answer: Perimeter = 2 × (Length + Width) = 2 × (10m + 5m) = 30m.

What is the factorization of 28?
Answer: 28 = 2² × 7.

Define a parallelogram.
Answer: A parallelogram is a four-sided shape where opposite sides are parallel and equal in length.

If a number is increased by 20% to become 180, what was the original number?
Answer: Let the original number be x. 1.20x = 180, so x = 150.

Explain the difference between mean and median.
Answer: The mean is the average of all numbers while the median is the central value when they are arranged in order.

These sample questions and answers provide a comprehensive overview