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CBSE Class 10 Mathematics Exam 2018: Important questions with solutions

Mar 27, 2018 09:40 IST
    CBSE Class 10 Mathematics Important questions
    CBSE Class 10 Mathematics Important questions

    In this article we are providing important questions for CBSE class 10 Mathematics. Students must practice these important questions to assess their preparedness for the Mathematics board exam which will be held tomorrow, 28 March, 2018. 

    The collection of important questions given here has been prepared after carrying a thorough analysis of the past year exam trends and the latest syllabus. All these questions provided with appropriate solutions will come in handy to revise the significant part of class 10 Maths syllabus. Moreover, the solutions given here will help students frame a perfect solution for each question in the Class 10 Maths Exam 2018.

    Find below the important questions for CBSE Class 10 Mathematics Board Exam 2018:

    Important 1 Mark Questions

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

    • In CBSE class 10 Mathematics exam 2018, Section-A will contain 6 questions of 1 mark each.

    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

    Get here the complete set of CBSE Class 10 Mathematics: Important 1 Mark 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 2018, 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 diameteris 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 = 40cm

    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

     Get here the complete set of CBSE Class 10 Mathematics: Important 2 Marks Questions

    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 2018.

    • In CBSE class 10 Mathematics exam 2018, Section-C will contain 10 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.

    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.

    (i) What will a person have to pay for travelling a distance of 25 km?

    (ii)Which mathematical concept is used in this question?

    (iii) What is its value?

    Sol.

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

    According to the question,

    x + 10= 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)

                                                                                   = 180

    Get here the complete set of CBSE Class 10 Mathematics: Important 3 Marks Questions

    Important 4 Marks Questions

    Here you will get a set of important 4 marks questions to prepare for the CBSE Class 10 Mathematics Paper 2018.

    • In CBSE class 10 Mathematics exam 2018, Section-D will contain 8 questions of 3 marks each

    Some sample questions from the set of Important 4 Marks 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) 
    ⟹          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 [2+ (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

    Get here the complete set of CBSE Class 10 Mathematics: Important 4 Marks Questions

    Maths is one such subject which 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 and excel the efforts made to perform well in the board exams.

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