SarkariRojgar.org have analyse CBSE Class 10 exam very deeply. On the basis of analyse SarkariRojgar brings NCERT Class 10th Mathematics Mock test. All Mock test are available in free. There is no Negative Marking in NCERT Class 10th Online Practice Set.

Weightage of Chapter | Marks |

Chapter-1 Real Numbers | 4 Marks |

Chapter (2, 3, 4) Polynomials, Pair of Linear Equation in two Variables, Quadratic Equation | 18 Marks |

Chapter-5 Arithmetic Progressions | 06 Marks |

Chapter-(6, 10, 11) Triangles, Circles Constructions | 16 Marks |

Chapter-7 Coordinate Geometry | 06 |

Chapter-8, 9 Introduction of Trigonometry, Some Application of Trigonometry | 10 |

Chapter-12, 13 Area Related to Circles, Surface area and Volumes | 10 |

Chapter-14, 15 Statistics, Probability | 10 |

Total Marks | 80 |

Difficult | 10% |

Average | 50% |

Easy | 40% |

Forms of Questions | No. Of Questions | Marks Allotted | Time |

Essay Type | 5 | 5(25) | 50 |

Short Answer | 6 | 4(24) | 42 |

Very Short Answer | 5 | 3(15) | 24 |

Objective | 16 | 1(16) | 80 |

Total | 32 | 80 | 140+10 |

The extra 10 minutes are for revision and some other works to fill important column.

NCERT Practice Set for class 10th Mathematics all chapter all exercise in detail solution and important questions for UP Board, Haryana Board, CBSE, and all other state board. A detailed solution in PDF Is also uploaded in NCERT CLass 10 Mathematics Practice set series. You can use practice for free and dowload detail PDF. All State Board( HBSE, CBSE, UP Board) are using NCERT Books. So NCERT Books plays an important role in all State Board exam.

**Euclid’s Division Lemma:**

*Given positive integer a and b, there exist a unique integer q and r satisfying a =bq + r , where r is greater than equal to zero and less than .*

An algorithm is a series of well defined steps which gives a procedure for solving a type of problem. A lemma is a proven statement used for proving another statement. In Euclid’s division method when r becomes zero, and we cannot proceed any further.

*To obtain HCF of two positive integer say c and d, with c > d given steps will be taken*

Apply Eucild’s Lemma division to c and d So we found a whole number q and r such that c = dq + r

**Q-1 Use Eucild’s division algorithm to find HCF of 240 and 6552**

Solution-1)Using Eucild algorithm

6552 = 240×27 + 72

240 = 72×3 +24

72 = 24×3 + 0

So the Right answer is 24

**Q-2 If the L.C.M and H.C.F of two numbers are 180 and 6 then find the other number if one number is 30.**

Solution-2) LCM = 180 & HCF 6

First number = 30 then Second Number = LCM×HCF/First Number

180×6/30 = 36 Ans

**Polynomials**

**Let we have a Quadratic Polynomial**

*ax ^{2} + bx + c = 0*

whose Zeroes are α and β

and Sum of Zeroes α + β = *-Coefficient of x/Coefficient of x ^{2}*

*Product of zeroes *αβ = *Constant Term/Coefficient of x ^{2}*

In General, if α and β are zeroes of the quadratic polynomial *p(x) = ax^{2} + bx + c where a does not equal to zero, then x – *α and

** ax^{2} + bx + c = k(x-** α) (

*k[x ^{2}-(* α+ β

After Comparing the coefficient of *x*^{2} and *x* and constant term on both side we get

** **

**Q-1 Find the zeroes of the quadratic polynomials and verify the relationship between the zeroes and the coefficients.**

**x ^{2} + 7x **+ 12

Solution-1) p(x) = **x ^{2} + 7x **+ 12

x^{2} + 4x +3x + 12 = x(x+4) +3 (x +4)

(x+4) (x + 3) then x = -4, -3

Sum of Zeroes = -4 +(-3) = -7

Product of Zeroes (-4)×(-3) = 12

**Pair of Linear Equation in two Variables**

**Substitution Method**

We will discuss Substitution Method. It’s play a very big role NCERT Class 10 CBSE, HBSE UP Board and all other state board. Every year one question is asked from this chapter. To understand the substitution method let us consider it step wise :

Find the value of one variable say y in terms of the other variable, x from the either equation, whichever is convenient. Substitute the value of y in other equation and reduce it to an equation in one variable. If the statement is true, you can conclude that the pair of linear equations has infinitely solutions. If the statement is false. Then the pair of linear equation is inconsistent.