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MATHEMATICS MCQ

Mid - point Theorem and Intercept Theorem · ICSE STD 9 (ICSE - English Medium). 28 questions.

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28 questions · timed · auto-graded

MCQ 11 Mark
In the figure, R is the mid-point of AB, P is the mid-point of AR and L is the mid-point of AP. If RS, PQ and LM are parallel to each other, then the length of BC is:
Image
  • A
    3 LM
  • B
    4 LM
  • C
    6 LM
  • ✓
    8 LM
Answer
Correct option: D.
8 LM
D
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MCQ 21 Mark
In which of the following cases you will get $2 XY = QR$ for the given figure?
(i) When $PX = QX$ and $PY = RY$
(ii) When $PX = QX$ and $a+b=180$.
Image
  • A
    Only in case (i)
  • B
    Only in case (ii)
  • ✓
    In both the cases
  • D
    None of these
Answer
Correct option: C.
In both the cases
C
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MCQ 31 Mark
D and E are the mid-points of the sides AB and AC respectively of ABC. DE is produced to F. To show that CF is equal and parallel to DA, we need an additional information, which is:
  • ✓
    $DE = EF$
  • B
    $AE = EF$
  • C
    $\angle DAE =\angle EFC$
  • D
    $\angle ADE =\angle ECF$
Answer
Correct option: A.
$DE = EF$
A
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MCQ 41 Mark
The figure formed by joining the mid-points of the sides of a quadrilateral ABCD, taken in order is a square only, if:
  • A
    ABCD is a rhombus
  • B
    diagonals of ABCD are equal
  • ✓
    diagonals of ABCD are equal and perpendicular
  • D
    diagonals of ABCD are perpendicular
Answer
Correct option: C.
diagonals of ABCD are equal and perpendicular
C
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MCQ 51 Mark
Assertion (A) : The mid-points of the sides of a quadrilateral ABCD are joined in order to get quadrilateral PQRS. PQRS is a rhombus.
Reason (R) : Adjacent sides of a rhombus are equal and perpendicular to each other.
Image
  • A
    A is true, R is false
  • B
    A is false, R is true
  • C
    Both A and R are true
  • ✓
    Both A and R are false.
Answer
Correct option: D.
Both A and R are false.
D
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MCQ 61 Mark
Assertion (A) : In the figure, if $AD = DC =4 cm$, $EC =10 cm$ and $DE \| AB$, then $CE =5 cm$.
Reason (R) : The straight line drawn through the mid-point of one side of a triangle parallel to other, bisects the third side.
Image
  • A
    A is true, R is false
  • B
    A is false, R is true
  • ✓
    Both A and R are true
  • D
    Both A and R are false.
Answer
Correct option: C.
Both A and R are true
C
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MCQ 81 Mark
In $\triangle ABC , E$ is the mid-point of the median $AD . BE$ is joined and produced to meet AC at F . Then, $AF =$ $\qquad$ AC.
  • A
    3
  • B
    2
  • ✓
    $\frac{1}{3}$
  • D
    $\frac{1}{2}$
Answer
Correct option: C.
$\frac{1}{3}$
C
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MCQ 91 Mark
In the figure, BP and CQ are two medians of the $\triangle ABC$. If $BC =12 cm$, the length of $QP =$.
Image
  • A
    4 cm
  • ✓
    6 cm
  • C
    8 cm
  • D
    10 cm
Answer
Correct option: B.
6 cm
B
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MCQ 101 Mark
In the adjoining figure, $AD = BD$ and $DE \| BC$. If $AC =6 cm$ and $DE =4 cm$, then the length of BC is :
Image
  • A
    4 cm
  • B
    5 cm
  • C
    6 cm
  • ✓
    8 cm
Answer
Correct option: D.
8 cm
D
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MCQ 111 Mark
$D , E$ and F are respectively the mid-points of the sides $BC , CA$ and AB of a ABC . If $BC =12 cm, CA =15 cm$ and $AB =18 cm$, then the perimeter of the quadrilateral DEAF is :
  • A
    45 cm
  • B
    27 cm
  • C
    30 cm
  • ✓
    33 cm .
Answer
Correct option: D.
33 cm .
D
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MCQ 121 Mark
$D , E$ and F are respectively the mid-points of the sides $BC , CA$ and AB of a ABC . If $BC =10 cm, CA =12 cm$ and $AB =17 cm$, then the perimeter of the DEF is :
  • A
    13 cm
  • ✓
    19.5 cm
  • C
    39 cm
  • D
    none of these
Answer
Correct option: B.
19.5 cm
B
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MCQ 131 Mark
AD and BE are two medians of a ABC . F is a point on AC such that $DF \| BE$. If $AC =12 cm$, then $FC =$
  • A
    6 cm
  • B
    4 cm
  • ✓
    3 cm
  • D
    none of these
Answer
Correct option: C.
3 cm
C
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MCQ 141 Mark
On the sides AB and AC of a $\triangle ABC , D$ and E are two points such that $AD : AB = AE : AC =1: 2$. If $BC =7 cm$, then $DE =$
  • ✓
    3.5 cm
  • B
    7 cm
  • C
    14 cm
  • D
    15 cm
Answer
Correct option: A.
3.5 cm
A
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MCQ 151 Mark
ABC is a right-angled isosceles triangle in which $\angle A =90$. If D and E are the midpoints of AB and AC respectively, then $\angle ADE =$
  • A
    30
  • ✓
    45
  • C
    60
  • D
    90
Answer
Correct option: B.
45
B
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MCQ 161 Mark
BP and CQ are two medians of a $\triangle ABC$. If $QP =4 cm$, then $BC =$
  • A
    2 cm
  • B
    6 cm
  • ✓
    8 cm
  • D
    9 cm
Answer
Correct option: C.
8 cm
C
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MCQ 191 Mark
In the trapezium $A B C D, A B \| D C$ and $A B>D C$. $P$ and $Q$ are the mid-points of the diagonals $A C$ and BD . Then, $PQ \| AB$ and $PQ =$ $\qquad$ ( $AB - DC$ ).
Image
  • A
    2
  • B
    3
  • ✓
    $\frac{1}{2}$
  • D
    $\frac{1}{3}$
Answer
Correct option: C.
$\frac{1}{2}$
C
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MCQ 201 Mark
In $\triangle ABC , E$ is the mid-point of the median $AD . BE$ is joined and produced to meet AC at F . Then, $AF =$ ______ AC.
  • A
    3
  • B
    2
  • ✓
    $\frac{1}{3}$
  • D
    $\frac{1}{2}$
Answer
Correct option: C.
$\frac{1}{3}$
C
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MCQ 211 Mark
In the figure, BP and CQ are two medians of the $\triangle ABC$. If $BC =12 cm$, the length of $QP =$
Image
  • A
    4 cm
  • ✓
    6 cm
  • C
    8 cm
  • D
    10 cm
Answer
Correct option: B.
6 cm
B
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MCQ 221 Mark
In the adjoining figure, $AD = BD$ and $DE \| BC$. If $AC =6 cm$ and $DE =4 cm$, then the length of BC is :
Image
  • A
    4 cm
  • B
    5 cm
  • C
    6 cm
  • ✓
    8 cm
Answer
Correct option: D.
8 cm
D
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MCQ 231 Mark
$D , E$ and F are respectively the mid-points of the sides $BC , CA$ and AB of a $\triangle ABC$. If $BC =12 cm, CA =15 cm$ and $AB =18 cm$, then the perimeter of the quadrilateral DEAF is :
  • A
    45 cm
  • B
    27 cm
  • C
    30 cm
  • ✓
    33 cm .
Answer
Correct option: D.
33 cm .
D
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MCQ 241 Mark
$D, E$ and $F$ are respectively the mid-points of the sides $B C, C A$ and $A B$ of a $\triangle A B C$. If $BC =10 cm, CA =12 cm$ and $AB =17 cm$, then the perimeter of the $\triangle DEF$ is :
  • A
    13 cm
  • ✓
    19.5 cm
  • C
    39 cm
  • D
    none of these
Answer
Correct option: B.
19.5 cm
B
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MCQ 251 Mark
AD and BE are two medians of a $\triangle ABC$. F is a point on AC such that $DF \| BE$. If $AC =12 cm$, then $FC =$
  • A
    6 cm
  • B
    4 cm
  • ✓
    3 cm
  • D
    none of these
Answer
Correct option: C.
3 cm
C
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MCQ 261 Mark
On the sides $A B$ and $A C$ of a $\triangle A B C, D$ and $E$ are two points such that $AD : AB = AE : AC =1: 2$. If $BC =7 cm$, then $DE =$
  • ✓
    3.5 cm
  • B
    7 cm
  • C
    14 cm
  • D
    15 cm
Answer
Correct option: A.
3.5 cm
A
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MCQ 271 Mark
ABC is a right-angled isosceles triangle in which $\angle A =90^{\circ}$. If D and E are the midpoints of AB and AC respectively, then $\angle ADE =$
  • A
    $30^{\circ}$
  • ✓
    $45^{\circ}$
  • C
    $60^{\circ}$
  • D
    $90^{\circ}$
Answer
Correct option: B.
$45^{\circ}$
B
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MCQ 281 Mark
BP and CQ are two medians of a $\triangle ABC$. If $QP =4 cm$, then $BC =$
  • A
    2 cm
  • B
    6 cm
  • ✓
    8 cm
  • D
    9 cm
Answer
Correct option: C.
8 cm
C
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