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 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.

### 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

Now drawing the graph of both equations

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 10 maths

CBSE Class 10-Question paper of maths 2021 with solutions

CBSE Class 10-Half yearly question paper of maths 2020 with solutions

CBSE Class 10 -Question paper of maths 2020 with solutions

CBSE Class 10-Question paper of maths 2019 with solutions

### NCERT Solutions for class 11 maths

 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 Chapter 16- Probability

CBSE Class 11-Question paper of maths 2015

CBSE Class 11 – Second unit test of maths 2021 with solutions

### NCERT solutions for class 12 maths

 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 Chapter 6- Application of Derivation CBSE Class 12- Question paper of maths 2021 with solutions Chapter 7- Integrals Chapter 8-Application of Integrals

Class 12 Solutions of Maths Latest Sample Paper Published by CBSE for 2021-22 Term 2

Class 12 Maths Important Questions-Application of Integrals

Class 12 Maths Important questions on Chapter 7 Integral with Solutions for term 2 CBSE Board 2021-22

Solutions of Class 12 Maths Question Paper of Preboard -2 Exam Term-2 CBSE Board 2021-22

Solutions of class 12  maths question paper 2021 preboard exam CBSE Solution

Scroll to Top
Optimized by Seraphinite Accelerator
Turns on site high speed to be attractive for people and search engines.