# CBSE Class 10 Maths Important Questions for Board Exam 2021 (with Solutions)

Here you will get the important questions for the CBSE Class 10 Mathematics Exam 2021. All the questions are prepared on the basis of the previous years' exam trends. You will also find appropriate solutions to all the questions.  CBSE Class 10 Maths Important Questions

When it comes to Mathematics exam, students often feel very stressed as they find it to be the most difficult subject. But to bring relief to all your stress and tensions, we have prepared a set of important questions that will help you revise the complete Mathematics syllabus in a short time and that too in the most effective way. A team of subject experts has collated these important questions for CBSE Class 10 Maths. Questions are based on all important topics involved in Class 10 Maths. Students must practice these important questions to assess their preparedness and understand the technique to decode problems asked in the exam.

The collection of important questions given here is prepared after carrying a thorough analysis of the past year exam trends and the latest syllabus. All these questions with appropriate solutions will come in handy to revise the significant part of the class 10 Maths syllabus. Moreover, the solutions given here will help students understand the technique to frame the perfect solutions in the Class 10 Maths Exam 2021. Note* Students must take care of the reduced syllabus while practicing with the important questions provided below. Ignore the questions that belong to the deleted part of the CBSE Class 10 Maths Syllabus.

Find below the important questions for CBSE Class 10 Mathematics Board Exam 2021:

Important 1 Mark Questions

Here we provide important questions that should be practiced to prepare for the 1 mark questions set to be asked in the class 10 Mathematics exam.

• In CBSE class 10 Mathematics Exam 2021, Section-A will contain 20 questions of 1 mark each. These one mark questions can be asked in different formats like MCQs, short answer type questions, case study based questions, etc.

Some sample questions from the set of Important 1 Mark Questions for CBSE Class 10 Mathematics Exam are given below:

Q. Find the length of the tangent from a point M which is at a distance of 17 cm from the centre O of the circle of radius 8 cm.

Sol.

Consider the figure:

Since, MN is the tangent of the circle,

∠MNO = 90⁰

⟹ MO2 = MN2 + ON2

⟹ 172 = MN2 + 82

⟹ 289 = MN2 + 64

⟹ 289 – 64 = MN2

⟹ MN2 = 225

⟹ MN = 15

Thus, the length of the tangent is 15 cm.

Q. If the common difference of an A.P. is 3, then find a20 – a15.

Sol.

Let the first term of the AP be a.

an = a(n − 1)d

a20 – a15 = [a + (20 – 1)d] – [a + (15 – 1)d]

= 19d – 14d

= 5d

= 5 × 3

## Check complete set of CBSE Class 10 Mathematics: Important 1 Mark Questions

Also Check:

Check Here Important MCQs for CBSE Class 10 Maths Exam 2021

CBSE Class 10 Maths Exam 2021 - Check How to Attempt Case Study Based Questions

Important 2 Marks Questions

Here you will get important 2 marks questions which might be asked in CBSE class 10 Mathematics paper.

• In CBSE class 10 Mathematics exam 2021, Section-B will contain 6 questions of 2 marks each.

Some sample questions from the set of Important 2 Marks Questions for CBSE Class 10 Mathematics Exam, are given below:

Q. Solve the following system of linear equations by substitution method:

2x – y = 2

x + 3y =15

Sol.

Here,   2x – y = 2

⟹       y = 2x – 2

⟹       x + 3y = 15

Substituting the value of y from (i) in (ii), we get

x + 6x – 6 = 15

⟹       7x = 21

⟹         x = 3

From (i), y = 2 × 3 – 2 = 4

∴             x = 3 and y = 4

Q. From a rectangular sheet of paper ABCD with AB = 40 cm and AD = 28 cm, a semi-circular portion with BC as diameter is cut off. Find the area of remining paper (use π = 22/7)

Sol.

Given situation can be represented as the following diagram:

Length of paper, AB = l = 40cm

Width of paper, AD = b = 28cm

Area of paper = l × b = 40 × 28 = 1120 cm2

Diameter of semi-circle = 28cm

∴  Radius of semi-circle, r = 14cm

Thus, area of semi-circle = 1/2. πr2

= 1/2 × 22/7 × 14 × 14

= 308cm2

∴ Area of remaining paper = 1120 – 308 = 812 cm2

## Check complete set of CBSE Class 10 Mathematics: Important 2 Marks Questions

CBSE Class 10 Maths Sample Paper (Basic and Standard) 2021

Important 3 Marks Questions

Get here a collection of important 3 marks questions which students must practice to make an effective preparation for the CBSE Class 10 Mathematics Paper 2021.

• In CBSE class 10 Mathematics exam 2021, Section-B will contain 7 questions of 3 marks each

Some sample questions from the set of Important 3 Marks Questions for CBSE Class 10 Mathematics Exam, are given below:

Q. The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th term is 44. Find the first three terms of the AP.

Sol.

Given that sum of the 4th and 8th terms of an AP is 24.

⟹       a + 3d + a + 7d = 24

⟹       2a + 10d = 24             ...(i)

Also the sum of the 6th and 10th term is 44.

⟹       a + 5d + a + 9d = 44

⟹       2a + 14d = 44             ...(ii)

Subtracting equation (i) from equation (ii), we get:

4d = 20

⟹       d = 5

Substituting d = 5 in equation (i), we have:

2a + 10d = 24

⟹       2a + 10 (5) = 24

⟹       2a + 50 = 24

⟹       2a = −26

⟹       a = −13

Hence first term of given A.P. is −13 and common difference is 5.

CBSE Class 10 Mathematics Previous Years' Solved Question Papers (2010-2020)

Q. The taxi charges in a city comprise of a fixed charge together with the charges for the distance covered. For a journey of 10 km the charge paid is Rs. 75 and for a journey of 15 km the charge paid is Rs.  110. What will a person have to pay for travelling a distance of 25 km?

Sol.

Let the fixed charge of taxi be Rs. x per km and the running charge be Rs y per km.

According to the question,

x + 10y  = 75

x + 15y  = 110

Subtracting equation (ii)  from equation (i), we get

– 5y = – 35

⟹  y = 7

Putting y = 7 in equation (i), we get x = 5

∴Total charges for travelling a distance of 25 km = x + 25y

= (5 + 25 × 7)

= (5 + 175)

= Rs 180

 Check complete set of CBSE Class 10 Mathematics: Important 3 Marks Questions

Here you will get a set of important long answer type questions. However, CBSE Class 10 Maths Paper 2021 will not include 4 marks questions that were earlier asked in a different section of the paper. Students can practice with these questions to revise important concepts that will help them attempt the long answer type questions accurately in their Maths exam.

Some sample questions from the set of Important long answer type questions for CBSE Class 10 Mathematics Exam, are given below:

Q. A motor boat whose speed is 24 km/hr in still water takes 1 hr more to go 32km upstream than to return downstream to the same spot. Find the speed of the stream.

Sol.

Let the speed of stream be x.

Then,

Speed of boat in upstream is 24 ‒ x

In downstream, speed of boat is 24 + x

According to question,

Time taken in the upstream journey ‒ Time taken in the downstream journey = 1 hour

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, al = 361

And, common difference, d = 9

Now      al =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:

Sn = n/2 [2a + (n − 1)d]
⟹          S40 = 40/2 [2 × 10 + (40 − 1)9]
= 20[20 + 39 x 9]
=20[20 + 351]
=20 × 371 = 7420

Thus, sum of all 40 terms of AP = 7420

 Check complete set of CBSE Class 10 Mathematics: Important Long Answer Type Questions

Maths is one such subject that can be learned by intensive practice and having a good hold on basic concepts. Therefore, students are suggested to solve the class 10 Mathematics important questions given here in order to assess their preparation level and excel in the upcoming CBSE Class 10 Maths Board Exam.

Also Check: Effective Study Plan, Important Tips & Resources to Score more than  90% in CBSE Class 10 Maths Paper

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

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