## NCERT Class 10th Mathematics Online Practice Set

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.

#### NCERT Class 10th CBSE Exam Pattern

 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
##### NCERT Class 10th Mathematics Difficulty Level
 Difficult 10% Average 50% Easy 40%

#### NCERT Class 10th Mathematics Weightage of Content

 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 Class 10 Mathematics Chapter wise Important Questions

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.

##### Real Numbers

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

ax2 + bx + c = 0

whose Zeroes are α and β

and Sum of Zeroes α + β = -Coefficient of x/Coefficient of x2

Product of zeroes αβ = Constant Term/Coefficient of x2

In General, if α and β are zeroes of the quadratic polynomial p(x) = ax2 + bx + c where a does not equal to zero, then x – α and  x – β are the factor of p(x). Therefore,

ax2 + bx + c = k(x- α) (x – β), where k is a constat

k[x2-( α+ β)x + αβ]  = kx2-k(α+ β)x + k αβ

After Comparing the coefficient of x2 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.

x2 + 7x + 12

Solution-1)  p(x) = x2 + 7x + 12

x2 + 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.