[Maths Class Notes] on Important 3 Marks Question For CBSE Class 10 Maths Pdf for Exam

CBSE Class 10 Maths Board Exam 2020

You will find the important questions for CBSE class 10 Maths board exam 2020 at official website for free pdf download. These important questions of 3 marks will help you score good if you master them as these are not only comparatively less difficult than 5 marks questions but are also more in frequency. 

At , you will be provided with NCERT Important Questions for Class 10 Maths with detailed solutions and answers. As per the latest CBSE Exam Pattern introduced, MCQ Questions for Class 10 Maths carries 20 marks.

CBSE Class 10 Maths 2020

The only key to success in the CBSE exam is practice. You can begin with CBSE class 10 sample question papers with Answers 2020 Board Exams.

CBSE Class 10 Maths 2020

Important Questions for CBSE Class 10 Maths Board Exam – Chapters

• Important Questions for Real Numbers Class 10

• Important Questions for Polynomials Class 10

• Important Questions for Pair of Linear Equations in Two Variables Class 10

• Important Questions Quadratic Equations Class 10

• Important Questions Arithmetic Progressions Class 10

• Important Questions Triangles Class 10

• Important Questions for Coordinate Geometry Class 10

• Important Questions for Introduction to Trigonometry Class 10

• Important Questions for Some Applications of Trigonometry Class 10

• Important Questions for Circles Class 10

• Important Questions for Constructions Class 10

• Important Questions for Areas Related to Circles Class 10

• Important Questions for Surface Areas and Volumes Class 10

• Important Questions for Statistics Class 10

• Important Questions for Probability Class 10

Important Frequently Asked Questions for CBSE Maths 10th Board 

Solving the given some important questions here will help you to increase your speed and accuracy in the final examination, while increasing your chance to score excellently in the exam.

Here are some sample questions for Class 10 Mathematics: Important 3 Marks Questions:

Example 1: For Any Positive Integer a, Prove that p³ ‒ o is Divisible by the Number 6.

Solution:

Let z = p³ ‒ o

⟹ p = p (p²‒1)

⟹ z = p (p ‒ 1) × (p+ 1) [∵ (p² ‒ q²) = {(p + q) (p‒q)}

z = (p ‒1) × p × (p + 1) … (i)

We know that, if a number is completely divisible by 2 and 3, then it is also divisible by the number 6.

Let’s conduct a divisibility test for 3:

Provided that the sum of digits of any number is divisible by 3, then it is divisible by 3:

Sum of the digits = (o ‒ 1) + (o) + (o + 1) = 3

⟹ Thus, the Number is divisible by 3.

Divisibility test for 2:

Provided that o is odd then, (o ‒ 1) and (o + 1) will be even so, (o ‒1) × o × (o + 1) will be divisible by 2.

Provided that o is even then, (o ‒1) × o × (o + 1) will be divisible by 2.

Thus, for any positive integral value of o, o3 ‒ o is divisible by 6.

Example 2: At Present Neeraj’s Age (in years) are 2 more than the Square of His Son John’s Age. When John Grows to Her Father’s Current Age, Neeraj’s Age will be 1 Year Less than 10 Times the Current Age of Neeraj. Find the Current Ages of Both Father and Son.

Solution:

Let, Neeraj’s current age be = ‘y’ year

Thus, as per the 1st condition, John’s current age = y2 + 2

John grows to his father’s current age after [(y2 + 2) – y] years.

Then, Neeraj’s age will be (y2 + 2) +  [(y2 + 2) –y] year.

Now, as per to the question,

(y2 + 2) + [(y2 + 2) – y] = 10y – 1

⟹ 2×2 – y + 4 = 10y – 1

⟹ 2×2 – 11y + 5 = 0

⟹ 2×2 – 10y – y + 5= 0

⟹ 2y (y – 5) –1(y – 5) = 0

⟹ (y – 5) (2y – 1) = 0

⟹ (y – 5) = 0 or (2y – 1) = 0

⟹ y = ½ or 5

Thus, current age of John = 5years

And the current age of Neeraj = y2 + 2 = (5)2 + 2 = 27 years.