CBSE Class 10 Mathematics Exam 2021: Important Long Answer Type Questions with Solutions

In this article, we are providing the Important Long Answer Type questions for the CBSE Class 10 Mathematics Exam 2021. All these questions are completely solved.

In CBSE Class 10 Mathematics Board Exam 2021, Part - B will have 3 questions of 5 marks each. These questions can be attempted correctly with a lot of practice and revision only. So, if one wishes to excel in the examination, a good practice of 5 marks questions is essential.

Note - While practicing with the questions provided below, students should take care of the deleted portion of the CBSE Class 10 Maths Syllabus 2021. Ignore the questions that are from the chapters/topics that have been excluded from the syllabus. 

Given below are some sample questions for CBSE Class 10 Mathematics: Important Long Answer Type Questions:

Q. For any positive integer n, prove that n³ – n is divisible by 6.

Solution.

n³ – n = n(n2 – 1) = n(n+1)(n – 1) = (n – 1)n(n+1) = product of three consecutive positive integers.

Now, we have to show that the product of three consecutive positive integers is divisible by 6.

We know that any positive integer n is of the form 3q, 3q + 1 or 3q + 2 for some positive integer q.

Now three consecutive positive integers are n, n + 1, n + 2.  

Case I. If n = 3q.

n(n + 1) (n + 2) = 3q(3q + 1) (3q + 2)

But we know that the product of two consecutive integers is an even integer.

∴ (3q + 1) (3q + 2) is an even integer, say 2r.

⟹ n(n + 1) (n + 2) = 3q × 2r = 6qr, which is divisible by 6.

Case II. If n = 3n + 1.

∴ n(n + 1) (n + 2) = (3q + 1) (3q + 2) (3q + 3)

                             = (even number say 2r) (3) (q + 1)

                             = 6r (q + 1),

which is divisible by 6.

Case III. If n = 3q + 2.

∴ n(n + 1) (n + 2) = (3q + 2) (3q + 3) (3q + 4)

                             = multiple of 6 for every q

                             = 6r (say),

which is divisible by 6.

Hence, the product of three consecutive integers is divisible by 6.

CBSE Class 10 Mathematics Exam Pattern for Board Exam 2021

Q. The first and the last terms of an AP are 10 and 361 respectively. If its common difference is 9 then find the number of terms and their total sum?

Sol.

Given, first term, a = 10

Last term, a_l = 361

And, common difference, d = 9

a_l = a + (n −1)d

361 = 10 + (n − 1)9

361 = 10 + 9n − 9

361 = 9n + 1

9n = 360

n = 40

Therefore, total number of terms in AP = 40

Now, sum of total number of terms of an AP is given as:

S_n = n/2 [2a + (n − 1)d]

S₄₀ = 40/2 [2 x 10 + (40 − 1)9]

      = 20[20 + 39 x 9]

      =20[20 + 351]

      =20 x 371 = 7420

Thus, sum of all 40 terms of AP = 7420

To get the complete set of questions, click on the following link:

Also Check: CBSE Class 10 Maths Important Questions for Board Exam 2021

All these Class 10 Mathematics Important Questions have been prepared after carrying a thorough analysis of the trend followed in previous years’ Class 10 Maths CBSE question papers. Questions have been picked from the most important topics of Class 10 Maths. Thus practicing these questions will help to cover a significant part of the curriculum thus making an effective preparation for the CBSE Class 10 Board Exam 2021. Moreover, the solutions provided here will give an idea to present your answers in the best way to grab maximum scores.

Important: CBSE Class 10 Maths Complete Study Material & Preparation Guide for Board Exam 2021