**Solutions of the Most Important Maths Questions of 3 and 4 marks for Class 10 CBSE-Part 3**

This article brings the CBSE Class 10 Mathematics: Most Important questions of 3 Marks and 4 marks Questions to get ready for board exams 2021-22.Each question is explained by a step by step method that offers you an idea to display how to solve maths questions in the most ideal manner in the exam.

Mathematics required skillย that can be developed by practicing it. Examining the solutions to a variety of questions is the only way to be perfect in mathematics. We at Future Study Point, furnish students of class 10ย a series ofย important 3 and 4 marks questionsย with solutionsย for helping class 10 students . The students who are planning forย achievingย excellent marks inย maths in CBSE Class 10 Board Exam are encouraged to practice the questions given below.

In this article Future Study Point is delivering the CBSE Class 10 Mathematics mostย Important 3 and 4 Marks Questions for the preparation of CBSE board exam 2021-22. Every one of these questions is totally solved in a systematic and ordered way.

In CBSE Class 10 Mathematics Board Exam 2021-22, Section C and D will involve 10 and 8 questions of 3 and 4 marks each consecutively. In the maths question paper pretty much 65 percent of toatal marksย in class 10 maths paper can be accomplished by trying the 3 and 4 marks questions successfully. Along these lines, if one wishes to surpass desires in the appraisal, an incredible everyday practice with respect to 3 and 4 marks questions are fundamental since the prepration of these questions also accomodate 1 and 2 marks questions.

Here, CBSE class 10 maths most important questions and answers for 2021-22 CBSE board exam – III published by Future Study Point are presented for the students of 10 class who are going to appear in 2021-22 board exam of CBSE.

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All the questions in CBSE class 10 maths most important questions and answers for 2021-22 board-III are designed by the expert of the maths subject and their answers are readily explained in an ordered way.

Theseย CBSE class 10 maths most important questions and answers for 2021-21 board-III are designed as per the updated syllabus of CBSE, so you need not to have any kinds of doubt in the selections of the questions. Don’t forget to make a comment and to subscribe us.

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**Solutions of the Most Important Maths Questions of 3 and 4 marks for Class 10 CBSE-Part 3**

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**Q1.Two taps running together can fill a tank in 3 and 1/13 hr. If one tap takes 3 hours more than the other to fill the tank, then how much time will each tap take to fill the tank?**

Solution: Let the time is taken by one of the taps to fill the tank = x hr

โด In 1 hour it will fill the part of tank = 1/xย part

Time taken by another tap to fill the tank = (x +3) hr

โด In 1 hour it will fill the part of tank = 1/(x+3)ย part

Both of tank will fill the tank in one hour** = **(1/x) + 1/(x+3)

The part of tank filled by one of the tap to fill the tank in 1 hr + The part of tank filled by another tap to fill the tank in 1 hr = The part of tank filled by both the taps to fill the tank in 1 hr

โด(1/x) + 1/(x+3) = 13/40

(x +x +3)/x(x+3) = 13/40

80x + 120 = 13xยฒ + 39x

13xยฒ โ 41xย โ 120 = 0

Neglecting minus sign because value of time can not be negative

x = 5

Therefore the time taken by one of the tap is 5 hours and by another tap is (5+3) = 8 hours.

**Q2. Ifย ฮฑ and ฮฒ are zeroes of the polynomial P(x) = 3xยฒ +2x + 1, find**

Solution: The polynomial given to us = 3xยฒ +2x + 1 with its zeroes ฮฑ and ฮฒ

The relationship between zeroes and their coefficients is as follows:

The polynomial corresponding to given zeroes in the question can be driven from the following formula:

xยฒ โ (sum of the zeroes)x + product of the zeroes

The sum of zeroes

From (i) and (ii) we have

** **

The product of zeroes

From equation(i) and (ii)

Therefore the sum of the zeroesย and product of the zeroes of the polynomialย = 2 and 3 respectively

So, required polynomial will be = xยฒ โ 2x + 3

**Q3.If the polynomialย X4 โ6×3+ 16×2โ 25x + 10 ย is divided by another polynomialย xยฒย โ 2x + k, the remainders comes out to be x + a,, find k and a.**

See the Solution.

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**Q4. Prove that the chords of a circle that are equidistant from the center are equal in length.**

Solution:

GIVEN. A circle with center O, in which there are two chords such that OP โฅAB and OQโฅCD and OP =OQ

TO PROVE. AB = CD

PROOF. Joining A and C to O, we get two ฮ’s AOP and QOC, so considering both of these ฮ’s

AO = CO (radii of the same circle)

OQ = OP (given)

OQย โฅ CD, OP โฅ AB ( OQ and OP are distances of the chords CD and AB from the center O)

โด โ OQC = โ APO= 90ยฐ

ฮ AOP โ ฮQOC ( RHS rule)

CQ = AP ( By CPCT)

2CQ = 2AP( OQ and OP are perpendiculars on both the chords)

โด CD = AB, Hence proved

**Solutions of the Most Important Maths Questions of 3 and 4 marks for Class 10 CBSE-lll**

**Q5.If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio. Prove it.**

Solution.

GIVEN: ฮABC, In which BCโฅDE

TO PROVE:

CONSTRUCTION: Drawing PE โฅAB and DQโฅAC, Joiningย C to D and B to E

PROOF.ย

From (i) and (ii)

Area of ฮADE in terms of other dimensions

From (iv) and (v)ย

arBDE = arDCE (area of ฮ’s are equal with a common base and between the same parallel lines)

โดfrom (vi) we haveย

Comparing (iii) and (vii) we have

HENCE PROVED

**Q6.Prove thatย **

Solutions.

LHS

Changing LHS into sin and cos

=RHS

**Q7. Prove that**

Solutions.

Taking LHS

Sinceย xยณ – yยณ = (x -y)( xยฒ + yยฒ +xy)

cosยฒฮธ + sinยฒฮธ +sinฮธ.cosฮธ

= 1 + sinฮธ.cosฮธ = RHS, Hence Proved

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Chapter 1-Sets | Chapter 9-Sequences and Series |

Chapter 2- Relations and functions | Chapter 10- Straight Lines |

Chapter 3- Trigonometry | Chapter 11-Conic Sections |

Chapter 4-Principle of mathematical induction | Chapter 12-Introduction to three Dimensional Geometry |

Chapter 5-Complex numbers | Chapter 13- Limits and Derivatives |

Chapter 6- Linear Inequalities | Chapter 14-Mathematical Reasoning |

Chapter 7- Permutations and Combinations | Chapter 15- Statistics |

Chapter 8- Binomial Theorem | ย Chapter 16- Probability |

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Chapter 1-Relations and Functions | Chapter 9-Differential Equations |

Chapter 2-Inverse Trigonometric Functions | Chapter 10-Vector Algebra |

Chapter 3-Matrices | Chapter 11 – Three Dimensional Geometry |

Chapter 4-Determinants | Chapter 12-Linear Programming |

Chapter 5- Continuity and Differentiability | Chapter 13-Probability |

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Chapter 7- Integrals | |

Chapter 8-Application of Integrals |

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