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MATHEMATICS MCQ

Pythagoras Theorem · ICSE STD 9 (ICSE - English Medium). 26 questions.

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26 questions · timed · auto-graded

MCQ 11 Mark
An aeroplane leaves an airport and flies due North at 300 km/h. At the same time, another plane leaves the same airport and flies due West at 400 km/h. After 90 minutes the distance between the two planes would be:
  • A
    1000 km
  • B
    900 km
  • C
    800 km
  • ✓
    750 km
Answer
Correct option: D.
750 km
D
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MCQ 21 Mark
Hypotenuse of a right triangle is 25 cm. If out of the two legs, one is longer than the other by 5 cm, then the sum of the lengths of the legs is:
  • A
    30 cm
  • ✓
    35 cm
  • C
    40 cm
  • D
    45 cm
Answer
Correct option: B.
35 cm
B
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MCQ 31 Mark
Assertion (A): In a right angled triangle, the longest side is called hypotenuse and the other two sides are called its legs. Also sum of lengths of legs is less than the length of the hypotenuse.
Reason (R): In a right angled triangle, the side opposite to the right angle is called its hypotenuse.
  • A
    A is true, R is false
  • ✓
    A is false, R is true
  • C
    Both A and R are true
  • D
    Both A and R are false.
Answer
Correct option: B.
A is false, R is true
B
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MCQ 41 Mark
Assertion (A) : In the figure, $\triangle ABC$ is right angled at B.
Reason (R): In a right angled triangle, the square on the hypotenuse is equal to the sum of the other two sides.
Image
  • ✓
    A is true, R is false
  • B
    A is false, R is true
  • C
    Both A and R are true
  • D
    Both A and R are false.
Answer
Correct option: A.
A is true, R is false
A
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MCQ 51 Mark
There are two buildings in two sides of a road. Keeping the foot of a ladder fixed at a point on the road, when it is placed on two buildings, then its top touches the buildings respectively at a height of 48 ft and 14 ft. If the length of the ladder is 50 ft, then the width of the road is:
  • A
    56 ft
  • ✓
    62 ft
  • C
    66 ft
  • D
    70 ft
Answer
Correct option: B.
62 ft
B
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MCQ 61 Mark
ABD is a right-angled triangle, whose $\angle D$ is the right angle. C is any point on the side BD . If $AB =8 cm, BC =6 cm$ and $AC =3 cm$, then the length of CD is :
  • ✓
    $1 \frac{7}{12} cm$
  • B
    $7 \frac{1}{12} cm$
  • C
    $12 \frac{2}{7} cm$
  • D
    $12 \frac{1}{7} cm$
Answer
Correct option: A.
$1 \frac{7}{12} cm$
A
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MCQ 71 Mark
The altitude of the equilateral triangle of side a units is:
  • ✓
    $\frac{a \sqrt{3}}{2}$ units
  • B
    $\frac{\sqrt{3 a}}{2}$ units
  • C
    $\frac{\sqrt{2 a}}{3}$ units
  • D
    $\frac{3 a}{2}$ units
Answer
Correct option: A.
$\frac{a \sqrt{3}}{2}$ units
A
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MCQ 81 Mark
The lengths of the adjacent sides of the right angle of a right-angled triangle are (x 2) cm and $2 \sqrt{2} x cm$. If the length of the hypotenuse is 3 cm , then the value of $x$ is :
  • A
    1
  • B
    2
  • ✓
    3
  • D
    4
Answer
Correct option: C.
3
C
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MCQ 91 Mark
The diagonals AC and BD of a rhombus ABCD are of lengths 6 cm and 8 cm. The length of each side of the rhombus is:
  • A
    3 cm
  • ✓
    5 cm
  • C
    7 cm
  • D
    9 cm
Answer
Correct option: B.
5 cm
B
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MCQ 101 Mark
The lengths of the diagonals of a rhombus are 5 cm and 12 cm. The length of each side of the rhombus is:
  • A
    13 cm
  • ✓
    6.5 cm
  • C
    6.25 cm
  • D
    5.25 cm
Answer
Correct option: B.
6.5 cm
B
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MCQ 131 Mark
In $\triangle ABC , \angle B$ is a right angle. If D is the foot of the perpendicular drawn from B on AC , then :
  • A
    $BC ^2+ CD ^2= AC ^2$
  • ✓
    $AB ^2 \quad BC ^2= AD ^2 \quad CD ^2$
  • C
    $BC ^2 \quad BD ^2= AB ^2 \quad AD ^2$
  • D
    none of these
Answer
Correct option: B.
$AB ^2 \quad BC ^2= AD ^2 \quad CD ^2$
B
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MCQ 141 Mark
The lengths of the sides of some triangles in some unit are given below. Which of them is a right-angled triangle?
  • A
    7, 9, 13
  • ✓
    10, 24, 26
  • C
    6, 8, 12
  • D
    8, 12, 16
Answer
Correct option: B.
10, 24, 26
B
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MCQ 171 Mark
There are two buildings in two sides of a road. Keeping the foot of a ladder fixed at a point on the road, when it is placed on two buildings, then its top touches the buildings respectively at a height of 48 ft and 14 ft . If the length of the ladder is 50 ft , then the width of the road is :
  • A
    56 ft
  • ✓
    62 ft
  • C
    66 ft
  • D
    70 ft
Answer
Correct option: B.
62 ft
B
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MCQ 181 Mark
ABD is a right-angled triangle, whose $\angle D$ is the right angle. C is any point on the side $B D$. If $A B=8 cm, B C=6 cm$ and $A C=3 cm$, then the length of $C D$ is :
  • ✓
    $1 \frac{7}{12} cm$
  • B
    $7 \frac{1}{12} cm$
  • C
    $12 \frac{2}{7} cm$
  • D
    $12 \frac{1}{7} cm$
Answer
Correct option: A.
$1 \frac{7}{12} cm$
A
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MCQ 191 Mark
The altitude of the equilateral triangle of side $a$ units is :
  • ✓
    $\frac{a \sqrt{3}}{2}$ units
  • B
    $\frac{\sqrt{3 a}}{2}$ units
  • C
    $\frac{\sqrt{2 a}}{3}$ units
  • D
    $\frac{3 a}{2}$ units
Answer
Correct option: A.
$\frac{a \sqrt{3}}{2}$ units
A
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MCQ 201 Mark
The lengths of the adjacent sides of the right angle of a right-angled triangle are $(x-2) cm$ and $2 \sqrt{2} x cm$. If the length of the hypotenuse is 3 cm , then the value of $x$ is :
  • A
    1
  • B
    2
  • ✓
    3
  • D
    4
Answer
Correct option: C.
3
C
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MCQ 211 Mark
The diagonals AC and BD of a rhombus ABCD are of lengths 6 cm and 8 cm . The length of each side of the rhombus is :
  • A
    3 cm
  • ✓
    5 cm
  • C
    7 cm
  • D
    9 cm
Answer
Correct option: B.
5 cm
B
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MCQ 221 Mark
The lengths of the diagonals of a rhombus are 5 cm and 12 cm . The length of each side of the rhombus is :
  • A
    13 cm
  • ✓
    6.5 cm
  • C
    6.25 cm
  • D
    5.25 cm
Answer
Correct option: B.
6.5 cm
B
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MCQ 251 Mark
In $\triangle A B C, \angle B$ is a right angle. If $D$ is the foot of the perpendicular drawn from $B$ on AC , then :
  • A
    $BC ^2+ CD ^2= AC ^2$
  • ✓
    $AB ^2- BC ^2= AD ^2- CD ^2$
  • C
    $BC ^2- BD ^2= AB ^2- AD ^2$
  • D
    none of these
Answer
Correct option: B.
$AB ^2- BC ^2= AD ^2- CD ^2$
B
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MCQ 261 Mark
The lengths of the sides of some triangles in some unit are given below. Which of them is a right-angled triangle?
  • A
    $7,9,13$
  • ✓
    $10,24,26$
  • C
    $6,8,12$
  • D
    $8,12,16$
Answer
Correct option: B.
$10,24,26$
B
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