**Class 10 Maths MCQ’S with Answers -Coordinate Geometry for CBSE Board 2021 Term 1**

**Class 10 Maths MCQ’S with Answers -Coordinate Geometry for CBSE Board 2021 Term 1** are created here in view of helping the students in the preparation of the **Term-1 CBSE** **Board exam 2021** ,in which questions are based on **MCQ’s** .**MCQ’s** are going to be asked are simple but students has to do 40 questions in 90 minutes so students are required to practice the additional **MCQ-based questions** within time slots. Here we have created and collected a few **MCQs** with their solutions to boost the preparations of the exam **Term-1 CBSE Board 2021** for **class 10** students.

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

**Class 10 Maths Trigonometry MCQโs With Solutions for Term-1 CBSE Board Exam 2021**

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

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

**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**

**Class 10 Maths MCQ’S with Answers -Coordinate Geometry for CBSE Board 2021 Term 1**

**Q1. The distance of the point (-3,5) from the x -axis**

**(a) 2ย ย ย (b) 3ย ย ย (c) 1ย ย ย (d) 5**

Ans. (d) 5

The given point is (-3,5)

First number,3 in the point (-3,5) is known as abscissa i.e distance from y-axis and second number, 5ย is ordinate i.e distance from x -axis

**Q2. The points (2,1), (-3,2),(k,4) are collinear if the value of k is**

Ans. Area of triangle formed by joining the given points must be zero because points given to us are collinear

Area of triangle =1/2[x_{1}(y_{2}-y_{3}) +x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2}) ]

x_{1}=2,y_{1}=1,x_{2}=-3,y_{2}=2,y_{3}=4,x_{3}=k,

1/2[x_{1}(y_{2}-y_{3}) +x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2}) ] = 0

x_{1}(y_{2}-y_{3}) +x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2}) = 0

2(2-4) -3(4-1) + k(1-2) = 0

2ร-2 -3ร3 + kร-1 =0

-4 -9 -k =0

-13 -k = 0

k = -13

**Q3. The distance of the point (ฮฑ, ฮฒ) from the origin is**

**(a) ฮฑ + ฮฒย (b) ฮฑยฒ + ฮฒยฒย ย (c) โ(ฮฑยฒ +ฮฒยฒ)**

Ans. The coordinates of origin are (0,0)

The distance between (0,0) and (ฮฑ, ฮฒ) = โ[(ฮฑ -0)ยฒ+(ฮฒ -0)ยฒ] =โ(ฮฑยฒ+ฮฒยฒ)

**Q4.The area of the triangle whose vertices are P(1,2), Q(-2,3) and R(-3,-4) is**

**(a) 22ย ย ย (b) 33ย ย ย (c) 41ย ย (d) 11**

Ans.(d) 11

Area of triangle =1/2[x_{1}(y_{2}-y_{3}) +x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2}) ]

x_{1}=1,y_{1}=2,x_{2}=-2,y_{2}=3,y_{3}=-4,x_{3}=-3

Area of triangle =1/2[1(3+4) -2(-4-2) -3(2-3) ]

= 1/2(1ร7 -2ร-6-3ร-1) = 1/2(7 +12 +3) = 1/2(22) = 11 sq.unit

**Q5. The distance between the points (p +q,p-q) and (p-q,-p-q) is**

Ans. 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] = โ[(p-q-p-q)ยฒ+ (-p-q-p+q)ยฒ] =โ[(-2q)ยฒ +(-2p)ยฒ] =โ(4qยฒ +4pยฒ) =2โ(pยฒ+qยฒ)

**Q6.Ifย (k/4,5) is the mid point of the line segment joining the points (-3,10) and (-9,6),then value of k is**

Ans. The mid point of the line segment joining the points ย (x_{1},y_{1}) and (x_{2},y_{2}) is given as

[(x_{1}+x_{2})/2,(y_{1}+y_{2})/2] = [(-3-9)/2,(10+6)/2] = (-12/2, 16/2) = (-6,8)

**Q7.The points (1,1),(-2,7) and (3,-3) are**

**(a) collinearย ย (b) vertices of equilateral triangleย (c) vertices of isoscles triangle (d) None of these**

Ans.(a) collinear

The given points are (1,1),(-2,7) and (3,-3)

Area of triangle formed by joining the given points must be zero because points given to us are collinear

Area of triangle =1/2[x_{1}(y_{2}-y_{3}) +x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2}) ]

x_{1}=1,y_{1}=1,x_{2}=-2,y_{2}=7,y_{3}=-3,x_{3}=3

1/2[x_{1}(y_{2}-y_{3}) +x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2}) ] = 0

1(7+3) -2(-3-1) + 3(1-7) = 0

10 – 2ร-4 + 3ร-6 = 10 + 8 – 18 = 18 -18 =0

Therefore the given points are collinear

**Q8.The coordinates of centroid of the triangle whose vertices are (0,6),(8,12) and (8,0) is**

**(a) (4,6)ย ย (b) (16,6)ย ย ย (c) (8,6)ย ย (d) (16/3,6)**

Ans.(d) (16/3,6)

The coordinates of the centroid of a triangle with vertices (x_{1},y_{1}),(x_{2},y_{2}),(x_{3},y_{3}) are given as

[(x_{1}+x_{2}+x_{3})/3,(y_{1}+y_{2}+y_{3})/3]

Therefore centroid of the triangle with vertices (0,6),(8,12) and (8,0) is

[(0+8+8)/3, (6 + 12 + 0)/3] = (16/3,18/3) = (16/3,6)

**Q9. Two vertices of the triangle are (3,-5) and (-7,4).If its centroid is (2,-1),then the third vertex is**

**(a)(10,2)ย ย (b) (-10,2)ย ย (c) (10,-2)ย ย (d) (-10,-2)**

Ans.(c) (10,-2)

Let the third vertex of the triangle is (x,y)

The coordinates of the centroid of a triangle with vertices (x_{1},y_{1}),(x_{2},y_{2}),(x_{3},y_{3}) are given as

[(x_{1}+x_{2}+x_{3})/3,(y_{1}+y_{2}+y_{3})/3]

(3 -7 +x)/3,(-5 +4 +y)/3 = (2,-1)

(-4 +x)/3 = 2 and (-1+y)/3 = -1

-4 + x = 6 and -1 + y = -3

x = 6 + 4=10 and y = -3 +1 = -2

Therefore third vertex of the given triangle is (10,-2)

**Q10.If the pointsย A(1,2),B(0,0) and C (a,b) are collinear then**

**(a) a = -bย ย ย (b) 2a = bย ย ย (c) a = 2bย ย ย (d) a = b**

Ans.(b) 2a = b

The given points are A(1,2),B(0,0) and C(a,b)

Area of triangle formed by joining the given points must be zero because points given to us are collinear

_{1}(y_{2}-y_{3}) +x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2}) ]

x_{1}=1,y_{1}=2,x_{2}=0,y_{2}=0,y_{3}=b,x_{3}=a

1/2[1(0-b) +0(b-2) + a(2-0) ] = 0

-b +2a = 0

b = 2a

**Q11.If the distance between the points (2,-2) and (-1,x) is 5,one of the value of x is**

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

Ans.ย (b) 2

The given points are (2,-2) and (-1,x)ย and distance(d) between them is 5

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]

x_{1}=2,y_{1}=-2,x_{2}=-1,y_{2}=x

โ[(-1-2)ยฒ+ (x+2)ยฒ]ย = 5

Squaring both sides

(-3)ยฒ+ (x+2)ยฒ=25

9 + xยฒ +4 +4x = 25

xยฒ+4x + 13 -25 =0

xยฒ+4x -12 = 0

xยฒ +6x -2x -12 =0

x(x +6) -2(x +6) =0

(x +6) (x -2) =0

x = -6 and x = 2

Hence one of the zeros is 2

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**Q12. ABCD is a rectangle whose three vertices are A(0,3), B(0,0) and C(5,0), the length of its diagonal is**

**(a) 5ย ย ย ย (b) 3ย ย ย ย (c) โ34ย ย ย (d) 4**

Ans. (c) โ34

Vertices of the rectangle given to us are A(0,3), B(0,0) and C(5,0)

The length of the diagonal AC is evaluated by applying the distance formula

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]

x_{1}=0,y_{1}=3,x_{2}=5,y_{2}=0

d = โ[(5-0)ยฒ+ (0-3)ยฒ] =โ[5ยฒ +(-3)ยฒ] =โ(25 +9) =โ34

**Q13.A circle drawn with origin as a centre passes through the point (13/2,0), the point which doesn’t lie in the interior of the circle is**

**(a) (-3/4,1)ย ย ย (b) (2,7/3)ย ย ย (c) (5,-1/2)ย ย (d) (-6,5/2)**

Ans. (d) (-6,5/2)

Centre of the circle is the origin (0,0) and passes through the point (13/2,0)

The distance between (0,0) and (13/2,0) i.e (6.5,0) is the radius of the circle

r = โ[(6.5-0)ยฒ+(0-0)ยฒ]=โ6.5ยฒ = 6.5 unit

The distance between (-3/4,1) and (0,0) < 6.5

The distance between (2,7/3)ย and (0,0) <6.5

The distance between (5,-1/2) and (0,0) <6.5

The distance between (-6,5/2) and (0,0) > 6.5

Therefore (-6,5/2) lies in the exterior of the given circle

**Q14.The point which divides the line segment joining the points (7,-6) and (3,4) in the ratio 1 : 2 internally lies in the**

**(a) I quadrantย ย (b) II quadrantย ย ย (c) III quadrantย ย ย (d) IV quadrant**

Ans.(d) IV quadrant

The given points are (7,-6) and (3,4)

Let the point is (x,y) which divides the line segment joining the given points in the ratio of 1 : 2

If a line segment joining the given points (x_{1},y_{1}) and (x_{2},y_{2}) is divided by a point (x,y) internally in the ratio of m : n then coordinates (x,y) are determined by the section formula as following

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

x_{1}=7,y_{1}=-6,x_{2}=3,y_{2}=4, m =1 and n = 2

x = (1ร3+2ร7)/(1+2)ย and y = (1ร4+2ร-6)/(1+2)

x = (3+14)/3 and y = (4 -12)/3

x = 17/3 and y = -8/3

The required point is (17/3,-8/3) which lies in (iv) quadrant

**Q15.One of the two points of trisection of the line segment joining the points A(7,-2) and B(1,-5) which divides the line segment in the ratio 1 : 2 are**

**(a) (5,-3)ย ย ย (b) (5,3)ย ย ย (c) (-5,-3)ย ย ย (d) (13,0)**

Ans.(a) (5,-3)

The end points of the line segment AB given to us are A(7,-2) and B(1,-5), let it is trisected by the points C and D

The point C(x,y) divides the line segment AB into the ratio of 1 : 2

Applying the section formula

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

x_{1}=7,y_{1}=-2,x_{2}=1,y_{2}=-5, m =1 and n = 2

x = (1ร1+2ร7)/(1+2)ย ย and y = (1ร-5+2ร-2)/(1+2)

x = (1+14)/3 and y = (-5 -4)/3

x = 15/3 and y = -9/3

x = 5 and y = -3

**Q16.A line intersects y axis and x axis at the point P and Q,respectively .If (2,-5) is the mid point of PQ ,then coordinates of P and Q are,respectively**

**(a) (0,-5) and (2,0)ย ย ย (b) (0,10) and (-4,0)ย ย (c) (0,4) and (-10,0)ย ย (d) (0,-10) and (4,0)**

Ans.(d) (0,-10) and (4,0)

Let the line intersects x axis and y axis at P(x,0) and Q(0,y) respectively

The mid point of the line segment joining the points P(x,0)ย and Q(o,y) given to us is (2,-5)

[(x+0)/2, (0+ y)2] = [2, -5]

(x/2, y/2) = (2.-5)

x/2 = 2 and y/2 = -5

x =4 and y = -10

The coordinates of P(x,0) =(4,0) and the coordinates of Q(0,y) =(0,-10)

Hence coordinates of P and Q are (4,0) ,(0,-10) respectively

**Q17.The ratio in which the point Q(3/4,5/12) divides the line segment joining the points A(1/2,3/2) and B(2,-5) is**

**(a) 1 : 5ย ย ย ย (b) 5 : 1ย ย ย (c) 3 : 1ย ย ย (d) 1 : 3**

Ans.(a) 1 : 5

Let the given ย point Q(3/4,5/12) divides the line segment joining the points A(1/2,3/2) and B(2,-5) intoย m : n

Applying the section formula

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

x_{1}=1/2,y_{1}=3/2,x_{2}=2,y_{2}=-5, x =3/4 and y = 5/12

3/4 = (mร2+nร1/2)/(m+n)ย ย and 5/12 = (mร-5+nร3/2)/(m+n)

3m + 3n = 8m +2n and 5m +5n = -60m +18n

-5mย =ย -n andย 65m = 13n

m/nย =1/5ย ย and m/n = 13/65 = 1/5

**Q18.The coordinates of a point P,where PQ is the diameter of a circle whose centre is (2,-3) and Q is (1,4) is**

**(a) (3,-10)ย ย ย (b) (-3,10)ย ย ย (c) (2,-10)ย ย ย (d) (-2,10)**

Ans.(a) (3,-10)

Let the coordinates of the point P of the given diameter PQ are (x,y)

Coordinates of Q given to us are (1,4)

The given centre of the circle is (2,-3) is the mid point of the diameter PQ

The mid point of the line segment joining the points ย (x_{1},y_{1}) and (x_{2},y_{2}) is given as

[(x_{1}+x_{2})/2,(y_{1}+y_{2})/2]

(x + 1)/2, (y + 4)/2 = (2,-3)

(x + 1)/2 = 2ย and (y + 4)/2 = -3

x + 1 = 4 and y + 4 = -6

x = 3 and y = -10

**Q19.The area of rhombus if its vertices are (3,0),(4,5),(-1,4) and (-2,-1) taken in order is**

**(a) 12 sq.unitย ย ย (b) 24 sq.unitย ย ย (c) 30 sq.unitย ย ย (d) 32 sq.unit**

Ans.(b) 24 sq.unit

The given vertices of the rhombus are (3,0),(4,5),(-1,4) and (-2,-1)

Area of the rhombus = (Product of the diagonals )/2

The length of the diagonal AD is = โ[(3+1)ยฒ+(0-4)ยฒ] =โ[4ยฒ+(-4)ยฒ] =โ(16 +16) =4โ2 unit

The length of the diagonal BC is = โ[(4+2)ยฒ+(5+1)ยฒ] =โ[6ยฒ+6ยฒ] =โ(36 +36) =6โ2 unit

Area of the rhombus = (4โ2 ร6โ2)/2 = 24 sq.unit

**Q20.If the points A(6,1),B(8,2),C(9,4) and D(p,3) are the vertices of a parallelogram,taken in order,then the value of p is**

**(a) 4ย ย ย ย (b) -6ย ย ย ย (c) 7ย ย ย ย (d) -2**

Ans. ย (c) 7

The given vertices of the parallelogram are A(6,1),B(8,2),C(9,4) and D(p,3)

Since diagonal of the parallelogram bisects each other, therefore centre O is the mid point of BD as well as of AC

The mid point of the line segment joining the points ย (x_{1},y_{1}) and (x_{2},y_{2}) is given as

[(x_{1}+x_{2})/2,(y_{1}+y_{2})/2]

(6+9)/2,(4+1)/2 =(p+ 8)/2,(3+2)/2

15/2, 5/2 = (p+8)/2, 5/2

(p + 8)/2 = 15/2

p+ 8 = 15

p = 15 -8 = 7

The importance of the MCQ questions and their solutions

The incoming CBSE board exam term-1 is totally based on MCQ’s, therefore a proper understanding of the chapter is needed to every student.The questions in the exams would be simple but the time boundation is also there, you have to do 40 MCQ’s in just 90 minutes. Therefore the practice of solvingย MCQ questions in the time slots is required for every student for achieving excellent marks.

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**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 |