# Class 10 Maths(Basic) Preboard Exam (First) 2021-22 CBSE with Solutions

10 Maths(Basic) Preboard Exam (First) 2021-22 CBSE with Solutions is created for the class 10 Maths students who has chosen Maths -Basic, question paper of maths basic consists of 50 multiple questions. The students have to solve 40 questions. Each question carries 1 mark. The basic maths question paper with solutions is helpful for the students in their Term -1 exam CBSE Board 2021.The importance of studying these solutions of basic maths question paper preboard exam is to get the idea about the type of the questions in Term 1 CBSE Board exam 2021.

**Class 10 Maths Sample Paper (Basic) with Solutions for Term 1 CBSE Board Exam 2021-22**

**MCQ’s on Real Numbers for Term 1 CBSE with Solutions**

**MCQ’s on Class 10 Maths Co-ordinate Geometry for Term 1 CBSE**

**Class 10 Maths MCQโs on Trigonometry for Term 1 CBSE with Solutions**

**Class 10 MCQ’s questions with solutions-Polynomial**

## Class 10 Maths(Basic) Preboard Exam (First) 2021-22 CBSE with Solutions

**Click for online shopping**

**Future Study Point.Deal: Cloths, Laptops, Computers, Mobiles, Shoes etc**

**Q1. After how many places of decimal will the decimal expansion of the number 27/(2ยฒร5ยณ) terminate ?**

**(a) 3ย ย ย ย ย ย (b) 4ย ย ย ย ย ย (c) 4ย ย ย ย ย ย (d) 1**

Ans. (a) 3

(27)/(2ยฒร5ยณ)

Multiplying the denominator and numerator by 2

54/(2ร5)ยณ= 0.054

**Q2. A die is thrown once. The probability of getting an even number is :**

**(a) 1/3ย ย ย ย ย ย (b) 1/6ย ย ย (c) 1/4ย ย ย ย ย ย (d) 1/2**

Ans.(d) 1/2

When a die is thrown once,the total possible outcomes are = 6(1,2,3,4,5,6)

Favourable outcomes = 2,4 and 6

P(E) = favourable outcomes/total possible outcomes

P(even number) = 3/6 = 1/2

**Q3. Sum of two numbers is 35 and their difference is 13,then the numbers areย **

(a) 24,13ย ย ย ย (b) 24,11ย ย ย ย ย (c) 12,11ย ย ย ย ย ย (d) 12,23

Ansย (b) 24,11

(Let the numbers are x and y

x + y = 35…….(i)ย and x – y = 13……(ii)

Adding both equation

2x = 48 โx = 24

Putting the value in equation (i)

24 + y = 35

y = 11

**Q4. The value of sin 60ยฐ/cos 30ยฐ is**

**(a) โ3/2ย ย ย ย ย ย (b) 1/2ย ย ย ย ย ย (c) 1ย ย ย ย ย ย (d) 2**

Ans. (c) 1

**Q5. If a bag contains 3 red and 7 black balls, then what will be the probability of getting a black ball ?**

**(a) 3/10ย ย ย ย ย (b) 4/10ย ย ย ย ย (c) 7/10ย ย ย ย ย (d) 5/10**

Ans. (c) 7/10

Total number of balls are = 3 red balls + 7 black ball = 10 balls

The number of black balls = 7

P(black ball) = 7/10

**Q6.The HCF of 5 ^{13} and 2^{6ย ย }will be**

**(a) 0ย ย ย ย (b) 1ย ย ย ย ย (c) 13ย ย ย ย (d) 26**

Ans.(b) 1

The numbers givenย 5^{13} and 2^{6}are co-prime numbers(1 is a common factor between them)

- Q7. Equationsย a
_{1}x + b_{1}y + c_{1}= 0 andย a_{2}x + b_{2}y + c_{2}= 0 has infinite many solutions if :

(a)ย a_{1}/ a_{2}โ b_{1}/ b_{2ย ย ย }(b) a_{1}/ a_{2}=b_{1}/ b_{2ย ย ย }(c) a_{1}/ a_{2}= b_{1}/ b_{2}=c_{1}/ c_{2ย ย ย }(d) a_{1}/ a_{2}= b_{1}/ b_{2}โ c_{1}/ c_{2}

_{Ans.ย ย }(c) a_{1}/ a_{2}= b_{1}/ b_{2}=c_{1}/ c_{2ย ย }

Class 10 Maths(Basic) Preboard Exam (First) 2021-22 CBSE with Solutions

**Q8. sin 2A = 2 sin A is true when A is equal to**

**(a) 0ยฐย ย ย ย ย (b) 30ยฐย ย ย ย ย (c) 45ยฐย ย ย ย ย (d) 60ยฐ**

Ans. (a) 0ยฐ

The value of LHS sin (2ร0ยฐ) =sin 0ยฐ = 0

The value of RHS 2 sin A = 2ร sin 0ยฐ = 2ร0 = 0

Hence,at A = 0,sin 2A = 2sin A

**Q9. If the ratio of areas of two circle are 4 : 9, then the ratio of their radii will be:**

**(a) 4 : 9ย ย ย ย ย (b) 2 : 3ย ย ย ย ย (c) 8 : 27ย ย ย ย ย (d) 3 : 2**

Ans. (b) 2 : 3

Area of the circle is = ฯrยฒ

Let the radii of two circles are r_{1 }and r_{2}

ฯr_{1}ยฒ/ฯr_{2}ยฒ = 4/9

r_{1}ยฒ/r_{2}ยฒ = 4/9

r_{1}/r_{2}ย = 2/3

**Q10. Distance between the points (-1,3) and (2,-1) is**

**(a) 1 unitย ย ย ย (b) 6 unitsย ย ย ย (c) 5 unitsย ย ย ย (d) 7 units**

Ans. (c) 5 units

The distance(d) between two points (x_{1},y_{1 }) and (x_{2},y_{2}) is

d= โ[(x_{2}-x_{1})ยฒ+ (y_{2}– y_{1})ยฒ]

The distance between (-1,3) and (2,-1) is

d = โ[(2+1)ยฒ+ (-1- 3)ยฒ] =โ[3ยฒ +(-4)ยฒ] =โ(9 +16) =โ25 = 5 units

**Q11. How many rational numbers are there between any two rational numbers ?**

**(a) 1ย ย ย ย ย (b) 2ย ย ย ย ย ย ย (c) 3ย ย ย ย ย ย (d) infiitely many**

Ans. (d) infinitely many

There are numberless numbers and any sets of numbers are infinite, hence between two rational numbers, there are infinite numbers.

**Q12. If coordinates of the diameter of a circle are (-6,3) and (6,9), then the coordinates of the centre is:**

**(a) (8,-8)ย ย ย ย (b) (12,6)ย ย ย ย (c) (0,6)ย ย ย ย (d) (0,3)**

Ans. (c) (0,6)

The mid point between ย two points (x_{1},y_{1 }) and (x_{2},y_{2}) is =ย (x_{1}+x_{2 })/2,ย (y_{1}+y_{2})/2

The midpoints of the diameter is the centre of the circle

The endpoints of the diameter are (-6,3) and (6,9)

The coordinates of the centre of the circle are = (-6+6)/2,( 3+9)/2 = (0,6)

Class 10 Maths(Basic) Preboard Exam (First) 2021-22 CBSE with Solutions

**Q13.If quadratic polynomial p(x) = xยฒ – x + 4 has roots ฮฑ and ฮฒ, then the value of ฮฑ + ฮฒ is :**

**(a) -1ย ย ย ย ย (b) 1ย ย ย ย ย ย (c) 4ย ย ย ย ย ย (d) 0**

Ans. (b) 1

In the standard quadratic equation axยฒ + bx + c, if the roots areย ย ฮฑ and ฮฒ

ฮฑ + ฮฒ = -b/a

The given quadratic polynomial is

p(x) = xยฒ – x + 4 ,where a = 1 and b = -1

ฮฑย + ฮฒ = -(-1)/1 = 1

**Q14. ย is a /an**

**(a) Integerย ย ย ย ย (b) Rational Numberย ย ย (c) Irrational Numberย ย (d) Natural Number**

Ans.(b) Rational Number

= 2.353535……, which is a recurrent (repeating) infinite decimal numbers,it can be written in the form of P/Q,where P and Q are co-prime numbers

x = 2.353535…..(i)

Multiplying it by 100,we get equation (ii)

100 x = 235.3535….(ii)

Subtracting equation (i) from (ii)

99x = 233

x = 233/99

**Q15. If tan (3x -15ยฐ) = 1,then the value of x is:**

**Ans.**

tan (3x -15ยฐ) = 1

tan (3x -15ยฐ) = tan 45ยฐ

3x – 15ยฐ = 45ยฐ

3x = 60ยฐ

x = 20ยฐ

**Q16.From a well shuffled cards,the probability of getting a red face card is:**

**(a) 3/26ย ย ย (b) 6/13ย ย ย ย (c) 3/52ย ย ย ย (d) 1/13**

Ans. Total number of cards are = 52

The number of red face cards are = 26

P( getting a red face card) = (number of red face cards)/(total number of cards) = 26/52 =1/2

**Q17. In what ratio the point P(0,0) divides the line segment joining the points A(3,3) and B(-3,-3)?**

**(a) 1 : 2ย ย ย ย (b) 1 : 3ย ย ย ย (c) 1 : 4ย ย ย ย ย (d) 1 : 1**

Ans.ย (d) 1 : 1

Applying the section formula

x = (mx_{2}+nx_{1})(m+n), y ย = (my_{2}+ny_{1})(m+n)

We are given that the point P(0,0)ย divides the line segment A(3,3)ย and B(-3,-3)

0 = (mร-3 +nร3)/(m+n)

-3m + 3n = 0

-3m = -3n

m : n = 1 : 1

**Q18. The pair of linear equation 6x – 7y = 1 and 3x – 4y = 5 has solution:**

**(a) Two solutionsย ย ย ย (b) Infinitely many solutionsย ย (c) Unique solutionย (d) No solution**

Ans. (c) Uniques solution

From the given equation 6x -7y =1 and 3x -4y =5,we have the coefficients

are a_{1}=6,b_{1}=-7, c_{1}=-1,a_{2}=3,b_{2}=-4,c_{2}= -5

a_{1}/ a_{2}= 6/3 = 2, b_{1}/ b_{2}=(-7)/(-4) = 7/4, c_{1}/c_{2}= (-1)/(-5) = 1/5

a_{1}/ a_{2}โ b_{1}/ b_{2}

Therefore both equations has a uniques solution

Class 10 Maths(Basic) Preboard Exam (First) 2021-22 CBSE with Solutions

**Q19.If the distance between the points A (4,P) and B(1,0) is 5 units, then the value of P are :**

**(a) 4,0ย ย ย ย ย (b) -4,0ย ย ย ย (c) 4, -4ย ย ย ย ย (d) 0, 1**

Ans. (c) 4, -4

The distance(d) between two points (x_{1},y_{1 }) and (x_{2},y_{2}) is

d= [(x_{2}-x_{1})ยฒ+ โ(y_{2}– y_{1}])ยฒ

The distance between the points A (4,P) and B(1,0) is 5 units

5 = ย [(1-4)ยฒ+ โ(0- P])ยฒ

25 = (-3)ยฒ + (-P)ยฒ

Pยฒ = 25 -9 = 16

P = ยฑ 4

Q20. 225 can be expressed as :

(a) 5ยฒ ร 3ยฒย ย ย ย ย (b) 5ยฒร 3ย ย ย ย (c) 5ยฒร 3ยฒย ย ย (d) 5ยณร 3

Ans. 5ยฒร3ยฒ

225 = 3ร3ร5ร5 = 5ยฒร 3ยฒ

**Q21. In an isosceles triangle ABC, if AC = BC and ABยฒ = 2ACยฒ, then value of C is:**

**(a) 30ยฐย ย ย ย ย ย ย ย ย ย (b) 45ยฐย ย ย ย ย ย ย ย (c) 60ยฐย ย ย ย ย ย (d) 90ยฐ**

Ans.

The given triangle is isosceles triangle in which AC = BC and we are given ABยฒ = 2ACยฒ

ABยฒ = 2ACยฒ = ACยฒ + ACยฒ

Putting AC = BC

ABยฒ = BCยฒ + ACยฒ

AB =Hyptenuse ,BC and AC are perpendicular to each other

โด โ C = 90ยฐ

**Q22. In a triangle ABC ,DE parallel to BC, then the value of EC is**

**(a) 5 cmย ย ย (b) 10 cmย ย ย ย (c) 8 cmย ย ย ย (d) 10 cm**

Ans.(c) 8 cm

In ฮABC and ฮADE

DE parallel to BC and AB is the transversal

โ ADE = โ ABC (corresponding angle)

โ AED = โ ACB (corresponding angle)

โดฮABC โผฮADE (AA rule criteria)

Applying the rule of similar triangles

AD/AB = AE/AC = DE/BC

3/(3 +4) = 6/AC

3/7 = 6/AC

3AC = 42

AC = 14

EC = AC – AE = 14 – 6 = 8 cm

**Q23. The parimeter of semicircular protector whose radius โr โ is**

**(a) ฯ + rย ย ย ย ย (b) ฯrย ย ย ย ย (c) ฯ + 2rย ย ย ย (d) ฯr + 2r**

Ans. The perimeter of semicircular protector = Length of the semicircular arc + Diameter

Length of semicircular arc = (2ฯr)/2 =ฯr

Diameter = 2r

Hence perimeter of semicircular protector = ฯr + 2r

**Q24. What is the area of a sector of a circle with radius 14 cm and central angle 45ยฐ?**

**(a)76 cmยฒย (b) 77 cmยฒย ย ย (c)66 cmยฒย ย ย (d) 55 cmยฒ**

Ans. (b) 77 cmยฒ

Area of sector of a circle is given as

Where ฮธ = 45ยฐ, r = 14 cm

Class 10 Maths(Basic) Preboard Exam (First) 2021-22 CBSE with Solutions

**Q25. What will be radius of the circle whose circumference is 44 m ?**

**(a) 14 mย ย ย ย (b) 7 mย ย ย ย (c) 5 mย ย ย ย (d) 44 m**

Ans.(b) 7 m

The circumerence of the circle =2ฯr

The circumference of the given circle is = 44 m

2ฯr = 44

2 (22/7) r = 44

r = (44ร7)/(44) = 7 m

**Q26. (1 +tanยฒA)/cosecยฒA will be equal to:**

**(a) secยฒAย ย ย ย ย ย ย ย (b) cosecยฒAย ย ย ย ย (c) cotยฒAย ย ย ย ย (d) tanยฒA**

Ans. (d) tanยฒA

The given expression is

(1 +tanยฒA)/cosecยฒA

Converting tan A and cosec A into sin A and cos A

(1 + sinยฒA/cosยฒA)

**Q27. If p and q are co-prime numbers, then the HCF of pยณqยฒ and pยฒq will be:**

**(a) pยณqยฒย ย ย ย (b) pยฒqย ย ย ย ย (c) pยฒqยฒย ย ย (d) pq**

Ans. (b) pยฒq

Since p and q are co-prime numbers,therefore in p and q there is no common factor except to 1.

The HCF ofย pยณqยฒย and pยฒq is = the lower power of p in both terms ร lower power of q in both terms =pยฒq

**Q28. In equation x + 2y =9 ,if x = 5,then the value of y will be:**

**(a) 1ย ย ย ย ย (b) -2ย ย ย ย (c) 2ย ย ย ย ย ย (d) 4**

Ans. (c) 2

Putting x = 5 in given equation x + 2y =9

5 + 2y =9

2y = 9 -5 = 4

y = 4/2 = 2

**Q29. If (2K -1,K) is the solution of 10 x -9y =12, then the value of K will be:**

**(a) 1ย ย ย ย ย ย (b) 2ย ย ย ย ย ย (c) 3ย ย ย ย ย (d) 4**

Ans. (b) 2

The solution of the given equation is 10x – 9y =12 is =(2K-1,K)

Therefore putting x = 2K-1 and y = k in the given equation

10(2K-1) – 9K =12

20 K -10 -9K = 12

11K = 10 + 12 = 22

K = 2

**Q30. If x = a cosฮธ and y = b sinฮธ, then the value of bยฒxยฒ +aยฒyยฒ is :**

**(a) aยฒ +bยฒย ย ย ย (b) aยฒ/bยฒย ย ย ย ย (c) aยฒbยฒย ย ย ย ย (d) 1/aยฒ + 1/bยฒ**

Ans. (c) aยฒbยฒ

Putting the value of x = a cos ฮธ and y = b sin ฮธ in the expression bยฒxยฒ + aยฒyยฒ

bยฒ aยฒ cosยฒฮธ + aยฒbยฒ sinยฒฮธ

aยฒbยฒ( cosยฒฮธ + sinยฒฮธ) = aยฒbยฒ

**Q31. Distance of the point Q(3,-4) from the origin is :**

**(a)ย 3 unitsย ย ย ย ย ย ย (b) 4 unitsย ย ย ย (c) 5 unitsย ย ย ย ย (d) 7 units**

Ans. (c) 5 units

The coordinates of the origins are (0,0) and the point given to us is Q(3, -4),distance(d) between two two points is given as

d=โ [(x_{2}-x_{1})ยฒ+ โ(y_{2}– y_{1}])ยฒ

= โ[(3 -0)ยฒ + (-4 -0)ยฒ] = โ(3ยฒ + 4ยฒ) = โ(9 + 16) = โ25 = 5 units

**Q32. If the point C(K,4) divides the line segement joining the two points A(2,6) and B(5,1) in the ratio 2 : 3, then the value of K is:**

**(a) 4/5ย ย ย ย (b) 16/5ย ย ย ย (c) 11/5ย ย ย ย ย (d) 19/5**

Ans.(b) 16/5

Applying the section formula

x = (mx_{2}+nx_{1})(m+n), y ย = (my_{2}+ny_{1})(m+n)

Putting the value , x = K , y = 4, x_{1}

=2,x_{2 }= 5,ย y_{1}= 6,y_{2}=1, m : n = 2: 3

K=(2ร5 + 3ร2)/(2+3) =(10 +6)/5 = 16 /5

**Q33. An event A is very unlikely to happen ,then its probabilty will be closest to :**

**(a) 0.0001ย ย ย ย ย (b) 0.001ย ย ย ย ย ย ย (c) 0.01ย ย ย ย (d) 0.1**

Ans.

The probabilty of an event is very likely to happen =ย ย P(A)ย = 1

The sum of probabilty of an event andย not happening of the probabiltyย is equal to 1

**Q34.In a linear equation ax +by +c = 0,a,b and c are:**

**(a) Natural numberย ย ย ย ย ย ย (b) Whole numberย ย ย ย (c) Integersย ย ย ย (d) Real Number**

Ans. (d) Real Number

As an example โ2 x + 3y -4 = 0 ,3x + 3y – 5 = 0 ,both are linear equations,no matters if a,b and c are natural numbers,whole numbers,integers ,rational or irrational numbers ,so a,b and c should be real numbers.

**Q35. If a pair of dice is thrown once,then probability of getting a sum of 8 will be :**

**(a) 1/6ย ย ย ย ย (b) 5/36ย ย ย ย (c) 1/9ย ย ย ย ย (d) 1/12**

Ans. (b) 5/36

If a pair of dice is thrown once then the total outcomes are = 6ยฒ = 36

Theย outcomes in which sum of the digits in both dice is 8 are = (2,6),(3,5),(4,4),(5,3),(6,2) [i.e 5)

P(getting the sum of 8) = 5/36

Class 10 Maths(Basic) Preboard Exam (First) 2021-22 CBSE with Solutions

**Q36.The perimeter of rectangle is 44 cm.Its length exceeds twice its breadth by 4 cm. Find the area of rectangle:**

**(a) 46 cmยฒย ย ย (b) 49 cmยฒย ย ย ย (c) 96 cmยฒย ย ย ย (d) 69 cmยฒ**

Ans. (c) 96 cmยฒ

Let the breadth of rectangle = x cmย then length = (2x + 4 ) cm

Perimeter of the rectangleย given to us = 44 cm

Perimeter of the rectangle is = 2 ( L+ B) = 2( 2x + 4+x) = 2(3x + 4)

According to question

2(3x + 4) = 44

3x + 4 = 22

3x = 22 – 4 = 18

x = 6

Therefore breadth =6 cm and the length of rectangleย = 2x + 4 = 2ร6 + 4 =16 cm

Area of the rectangle = L ร B = 16 ร6 = 96 cmยฒ

**Q37. If sin ฮธ = cos ฮธ, then the value of tan ยฒฮธ + cotยฒฮธ is:**

**(a) 2ย ย ย ย ย ย ย (b) 4ย ย ย ย ย ย (c) 1ย ย ย ย ย ย ย (d) 10/3**

Ans. We are given

sin ฮธ = cos ฮธ

sinฮธ/cos ฮธ = 1

tan ฮธ = 1 โ cot ฮธ = 1/tan ฮธ = 1

The value of

tanยฒฮธ + cotยฒฮธ = 1ยฒ + 1ยฒ = 1 + 1 = 2

Te questions 38 -40 consists of Assertion (A) and Reason (R) . Answer these questions selecting the appropriate option given below:

(a) Both A and R are true and R is the correct exolanation of A.

(b) Both A and R are true but R is not the correct exolanation of A.

(c) A is true,but R is false

(d) A is false, but R is true

**Q38.Assertion(A): The point (0,4) lies on the y-axis.**

**Reason(R): The x coordinate of the point on the y-axis is zero.**

Ans.(a) Both A and R are true and R is the correct explanation of A.

The point (0,4) lies on the y -axis because x = 0

Class 10 Maths(Basic) Preboard Exam (First) 2021-22 CBSE with Solutions

**Q39. Assertion(A): If the circumference of two circles are in the ratio 2 : 3, then the ratio of their areas is 4 : 9.**

**Reason(R): The circumference of a circle of radius is 2ฯr and its area is ฯrยฒ**

Ans.(a) Both A and R are true and R is the correct explanation of A.

Let the radii of two circles are r_{1 }and r_{2}

The ratio of their circumference is given as 2 : 3

2ฯr_{1}/2ฯr_{2}= 2/3

r_{1}/r_{2}= 2/3

Ratio between their areas

= ฯr_{1}ยฒ/ฯr_{2}ยฒ = (r_{1}/r_{2})ยฒ =(2/3)ยฒ = 4/9

**Q40. Assertion(A):ย For any two positive integers a and b, LCM (a,b) รHCF(a,b) = aร b.**

**Reason (R) : Product of two numbers is 150 and HCF is 5,then their LCM is 40**.

Ans.(a) A is true but R is false

The relationship between HCF(a,b) and LCM(a,b) and the product of numbers a and bย is given as

LCM (a,b) รHCF(a,b) = ab

LCMร5 = 150

LCM = 150/5 =30

SECTION – C

(Case Study Basedย Questions)

Section โCโ consists of 10 questions. Do any 8 questions.

Points A and B are on the opposite edges of a pond a shown in below figure. To find distance between the two points, Ramesh makes a right angled triangle using the rope. Distance between point B and C is 12 m, distance betweenย C and D is 40 m andย A and D is 30 m such that โ ADC = 90ยฐ.

**Q41. Which property of geometry is used to find the distance in the figure ?**

**(a) Similarity of trianglesย ย ย ย ย ย (b) Thales theorem**

**(c) Pythogorus theoremย ย ย ย ย ย ย ย ย ย ย ย (d) Converse of thales**

Ans.Pythogorus theorem

**Q42. What is total length of pond AB and rope BC in the figure ?**

**(a) 50 mย ย ย ย (b) 70 mย ย ย ย (c) 100 mย ย ย ย (d) 38 m**

Ans. (a) 50 m

โ ADC = 90ยฐ

ADย and DC are perpendicular to each other

ACยฒ = ADยฒ + DCยฒ

ACยฒ = 30ยฒ + 40ยฒ = 900 + 1600 = 2500

AC = โ(2500) = 50

AB = AC – BC = 50 – 12 = 38

**Q43. Length of the total rope used is:**

**(a) 82 mย ย ย ย (b) 70 mย ย ย ย (c) 120 mย ย ย ย (d) 100 m**

Ans.(a) 82 m

The lenghth of total rope = BCย +DC + AD =12 + 40 + 30 = 82 m

**Q44. Which of the following doesn’t form Pythagoras triplet ?**

**(a) (20,21,28)ย ย ย (b) (8,15,17)ย ย ย ย (c) (5,12,13)ย ย ย (d) (7,24,25)**

Ans.(a) (20,21,28)

(a) 28ยฒ = 21ยฒ +20ยฒ

784 โ 441 + 400=841

(b) 17ยฒ = 15ยฒ + 8ยฒ

289 = 225 + 64 =289

(c) 13ยฒ = 12ยฒ + 5ยฒ

169 = 144 + 25 =169

(d)ย 25ยฒ = 24ยฒ + 7ยฒ

625 = 576 +49 = 625

(a) doesn’t show Pythogoras triplet because 28ยฒ โ 21ยฒ+20ยฒ

**Q45. Length of the Pond AB is:**

**(a) 50 mย ย ย ย ย (b) 62 mย ย ย ย (c) 70 mย ย ย ย (d) 38** **m**

(d) 38 m

Case Study -II

The path moved by a group of ants has been traced on graph. Aditi is a student of class 10. She compared the ant’s path with the diagram she learned in maths class then she drew the sketch on the graph.

**Q46. The shape of the path formed by ants is:**

**(a) Spiralย ย ย ย (b) Ovalย ย ย ย (c) Parabolaย ย ย (d) Linear**

Ans. (c) Parabola

**Q47. How many zeroes are possible for this shape ?**

**(a) 2ย ย ย ย ย (b) 3ย ย ย ย (c) 4ย ย ย ย (d) 0**

Ans. (a) 2

A parabola can intersects any of the axises in two points,so maximum possible zeroes of the parabolic polynomial is 2.

**Q48. According to graph ,the zeroes of the polynomial are:**

**(a) -3,-1ย ย ย ย (b) 3,-1ย ย ย ย (c) -3, 1ย ย ย ย ย (d) 0,0**

Ans.(c) -3,1

The parabola is intersecting the x-axis at x = -3 and at x = 1,therefore its zeroes are -3,1

**Q49. What will be the expression of the polynomial shown in figure?**

**(a) xยฒ -2x +3ย ย (b) xยฒ -3x +2ย ย (c) xยฒ +3x +2ย ย ย (d) xยฒ +2x – 3**

Ans. (d) xยฒ +2x -3

The algebraic expression of a quadratic polynomial with zeroes ฮฑ and ฮฒ is given as

xยฒ – (ฮฑ +ฮฒ) x + ฮฑฮฒ

Here ฮฑ = -3 and ฮฒ = 1

xยฒ -(-3 +1)x +(-3) 1

xยฒ +2x -3

**Q50. What will be the value of the polynomial if x = -1 ?**

**(a) -5ย ย ย ย ย (b) 6ย ย ย ย ย (c) -4ย ย ย ย (d) 0**

Ans.(c) -4

The polynomial,P(x) = xยฒ +2x -3

P(-1)ย = (-1)ยฒ + 2(-1) -3 = 1 -2 -3 = 1-5 = -4

For solutions of other CBSE maths and science question papers please subscribe our website and U tube channel Future Study Point. For achieving excellent marks in mathematics and science, study our posts on Maths and Science MCQs for Term 1 CBSE Board exam 2021.

**You can compensate us by donating any amount of money for our survival**

**Our Paytm No 9891436286**

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

**NCERT Solutions of class 9 maths**

Chapter 1- Number System | Chapter 9-Areas of parallelogram and triangles |

Chapter 2-Polynomial | Chapter 10-Circles |

Chapter 3- Coordinate Geometry | Chapter 11-Construction |

Chapter 4- Linear equations in two variables | Chapter 12-Heron’s Formula |

Chapter 5- Introduction to Euclid’s Geometry | Chapter 13-Surface Areas and Volumes |

Chapter 6-Lines and Angles | Chapter 14-Statistics |

Chapter 7-Triangles | Chapter 15-Probability |

Chapter 8- Quadrilateral |

**NCERT Solutions of class 9 scienceย **

**CBSE Class 9-Question paper of science 2020 with solutions**

**CBSE Class 9-Sample paper of science**

**CBSE Class 9-Unsolved question paper of science 2019**

**NCERT Solutions of 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 of class 10 science**

**Solutions of class 10 last years Science question papers**

**CBSE Class 10 – Question paper of science 2020 with solutions**

**CBSE class 10 -Latest sample paper of science**

**NCERT solutions of 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 | ย Chapter 16- Probability |

**CBSE Class 11-Question paper of maths 2015**

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

**NCERT solutions of 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 |