Solutions of Class 10 Unit Test -1(2022-23) Mathematics-G.D Lancer's Public School Delhi - Future Study Point

Solutions of Class 10 Unit Test -1(2022-23) Mathematics-G.D Lancer’s Public School Delhi

Solutions of Class 10 Unit Test -1(2022-23) Mathematics-G.D Lancer's Public School Delhi

Solutions of Class 10 Unit Test -1(2022-23) Mathematics-G.D Lancer’s Public School Delhi

Solutions of Class 10 Unit Test -1(2022-23) Mathematics-G.D Lancer’s Public School Delhi is created here for helping the class 10 students in clearing their doubts about incoming exams and tests. All students of class 10 are needed special attention in mathematics because it is the subject that helps you to increase your aggregate percentage marks in the exam. The solutions of the class 10 Unit Test will give you an idea about the technics of solving the question papers. The unit test of class 10 is presented here is taken from a reputed public school of Delhi G.D Lancer Public School. The solution to the test is created by an expert in maths in a step-by-step way so every student can understand the solution easily. The total questions in this test are 11 and divided into three sections A, B, and C. Section A contains 6 questions and each question is of one mark, section B contains 3 questions and each question is of 2 marks and section C contains 2 questions and each question is of 4 marks. The maximum mark for this maths test is 20.

Solutions of Class 10 Unit Test -1(2022-23) Mathematics-G.D Lancer’s Public School Delhi

Q1.The number √(5+3)/√(5-3) is

(a)Rational number                                   (b) Irrational number

(c)An Integer                                               (d)A natural number

Solution.(a)Rational number

The given number is

√(5+3)/√(5-3)

=√8/√2 = 2√2/√2 =2

2 is a rational number.therefore given number is rational

Q2.If a,b are both positive rational number then is (√a + √b)(√a – √b)

(a)Rational number                                    (b) Irrational number

(c)An Integer                                               (d)both rational as well as irrational

Solution.(a)Rational number

The given number is

(√a + √b)(√a – √b)

Applying the identity (x+y)(x -y) = x² -y²

√a² – √b² = a – b

Since it is given that a and c are positive rational number, according to closure property of rational number (a -b) must be a rational number,therefore the given number is a rational number.

Q3.If am ≠bl then system of equations ax +by = c,lx +my = n has

(a)Unique solution                                       (b) May or may not have solution

(c)Infinitely many the solution                         (d)no solution

Solution.(a)Unique solution

Since it is given to us

am ≠bl

a/l ≠b/m

⇒a1/a1 ≠b1/b

Comparing the coefficients of the given pair of the linear equations with the standard pair of the linear equation  a1x+b1y +c1=0 and a2x+b2y +c2=0

Q4.Form a quadratic polynomial whose zeroes are 5 +√3 and 5 -√3

Solution.The given zeroes ,α= 5 +√3 and β=5 -√3

The required polynomial is given as

x² -(α +β)x + αβ

x² -( 5 +√3 +5 -√3)x + (5 +√3 )(5 -√3)

x² -10x + (5² -√3²)

x² -10x +(25 -3)

x² -10x +22

Hence the given quadratic polynomial is x² -10x +22

Q5.What number is to be added to the polynomial x² -5x +4, so that 3 becomes the zero of the polynomial

Solution. Let k is added to the given polynomial so that  3 is the zero of the given polynomial x² -5x +4

The polynomial will become

p(x) =x² -5x +4 +k

Then it should satisfy 3 for p(x) =0

3² -5×3 +4 +k =0

9 -15 +4 +k =0

-2 +k =0

k =2

Therefore 2 is added to the given polynomial so that 3 is its zero

Q6.If sum of the zeroes of the polynomial p(x) =(k² -14)x² -2x -12 is 1,then k takes the value

(a)14                 (b)-14                  (c)2              (d)±4

Solution.  (d)±4

The sum of the zeroes is given as

α +β = -b/a, where a is the coefficient of the quadratic term and b is the coefficient of linear term

In the given quadratic equation p(x) =(k² -14)x² -2x -12

a = k² -14, b = -2 and c =-12

α +β = -(-2)/(k²-14)

Since it is given to us α +β =1

1 =2/(k²-14)

k²-14 = 2

k² = 16

k =≠4

Solutions of Class 10 Unit Test -1(2022-23) Mathematics-G.D Lancer’s Public School Delhi

Section-B

Q7.Prove that √5 is irrational.

Ans. Let √5  is a rational number

Where a and b are co-prime number ( study Number system)

b√5 = a

Squaring both sides

5 b² = a²………..(i)

5 is one of the factors of  a²

∴ 5 will also be one of the factors of a

Therefore a can be written as a multiple of 5

a = 5c ( where c is another positive integer)

Putting the value of ‘a’ in equation number (i)

5 b² = (5c)²  = 25c²

b² = 5c²…………(ii)

5 is one of the factors of b²

∴ 5 will also be one of the factors of b

It is evident from eq.(i) and (ii) that 5 is a common factor in ‘a’ and ‘b’, so  it is contrary to the fact we have supposed that √5  is a rational number

Therefore √5 is an irrational number.

Solutions of Class 10 Unit Test -1(2022-23) Mathematics-G.D Lancer’s Public School Delhi

Section-C

Q10.Solve the following graphically

2x -3y -4 =0

x – y -1 = 0

Shade the triangle between x-axis and given lines.

Solution. The given pair of the linear equation is

2x -3y -4 =0

x – y -1 = 0

The solutions of the equations 2x -3y -4 =0 and x – y -1 = 0 are given as

Unit test 1 class 10 maths 2022-23

Now drawing the graph of both equations

Solutions of Class 10 Unit Test -1(2022-23) Mathematics-G.D Lancer's Public School Delhi

The graph of the both equations intersect at (-1,-2),therefore the solutions of the equation is x=-1 and y=-2

Q11.Show that 15n

can not end with the digits 0,2,4,6 and 8 for any natural number

Solution.

The number given is

15n

= (3×5)n

= 3n×5n

3n ×5ncan not end at at 0,2,4,6 and 8  for any value n =1,2,3…. because 3 and 5 both are   odd numbers

As an example

If n = 1

then 31×51=15

For n =2

32×52=225

And so on

NCERT Solutions of Science and Maths for Class 9,10,11 and 12

NCERT Solutions for class 9 maths

Chapter 1- Number SystemChapter 9-Areas of parallelogram and triangles
Chapter 2-PolynomialChapter 10-Circles
Chapter 3- Coordinate GeometryChapter 11-Construction
Chapter 4- Linear equations in two variablesChapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s GeometryChapter 13-Surface Areas and Volumes
Chapter 6-Lines and AnglesChapter 14-Statistics
Chapter 7-TrianglesChapter 15-Probability
Chapter 8- Quadrilateral

NCERT Solutions for class 9 science 

Chapter 1-Matter in our surroundingsChapter 9- Force and laws of motion
Chapter 2-Is matter around us pure?Chapter 10- Gravitation
Chapter3- Atoms and MoleculesChapter 11- Work and Energy
Chapter 4-Structure of the AtomChapter 12- Sound
Chapter 5-Fundamental unit of lifeChapter 13-Why do we fall ill ?
Chapter 6- TissuesChapter 14- Natural Resources
Chapter 7- Diversity in living organismChapter 15-Improvement in food resources
Chapter 8- MotionLast years question papers & sample papers

NCERT Solutions for class 10 maths

Chapter 1-Real numberChapter 9-Some application of Trigonometry
Chapter 2-PolynomialChapter 10-Circles
Chapter 3-Linear equationsChapter 11- Construction
Chapter 4- Quadratic equationsChapter 12-Area related to circle
Chapter 5-Arithmetic ProgressionChapter 13-Surface areas and Volume
Chapter 6-TriangleChapter 14-Statistics
Chapter 7- Co-ordinate geometryChapter 15-Probability
Chapter 8-Trigonometry

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Chapter 1- Chemical reactions and equationsChapter 9- Heredity and Evolution
Chapter 2- Acid, Base and SaltChapter 10- Light reflection and refraction
Chapter 3- Metals and Non-MetalsChapter 11- Human eye and colorful world
Chapter 4- Carbon and its CompoundsChapter 12- Electricity
Chapter 5-Periodic classification of elementsChapter 13-Magnetic effect of electric current
Chapter 6- Life ProcessChapter 14-Sources of Energy
Chapter 7-Control and CoordinationChapter 15-Environment
Chapter 8- How do organisms reproduce?Chapter 16-Management of Natural Resources

NCERT Solutions for class 11 maths

Chapter 1-SetsChapter 9-Sequences and Series
Chapter 2- Relations and functionsChapter 10- Straight Lines
Chapter 3- TrigonometryChapter 11-Conic Sections
Chapter 4-Principle of mathematical inductionChapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbersChapter 13- Limits and Derivatives
Chapter 6- Linear InequalitiesChapter 14-Mathematical Reasoning
Chapter 7- Permutations and CombinationsChapter 15- Statistics
Chapter 8- Binomial Theorem Chapter 16- Probability

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NCERT solutions for class 12 maths

Chapter 1-Relations and FunctionsChapter 9-Differential Equations
Chapter 2-Inverse Trigonometric FunctionsChapter 10-Vector Algebra
Chapter 3-MatricesChapter 11 – Three Dimensional Geometry
Chapter 4-DeterminantsChapter 12-Linear Programming
Chapter 5- Continuity and DifferentiabilityChapter 13-Probability
Chapter 6- Application of DerivationCBSE Class 12- Question paper of maths 2021 with solutions
Chapter 7- Integrals
Chapter 8-Application of Integrals

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