Full fledge assessment (Please watch the above videos before attempting this assessment)

Question 1 of 20
Q1. To divide a line segment in 5:3, we have to make
  • 5 equal divisions
  • 3 equal divisions
  • 2 equal divisions
  • 8 equal divisions

Solution :

To divide a line segment in m:n, we have to make m+n equal divisions.
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Q2. Two tangents drawn from the external points to a circle are 
  • Perpendicular
  • Parallel
  • Equal
  • None of these

Solution :

Two tangents drawn from the external points to a circle are equal. 
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Q3. To divide a line segment in m:n, we have to make
  • M equal divisions
  • N equal divisions
  • m+n equal divisions
  • m-n equal divisions

Solution :

To divide a line segment in m:n, we have m+n equal divisions.
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Q4. The tangent is perpendicular to the
  • Radius
  • Diameter
  • Both radius and diameter
  • None of these

Solution :

The tangent makes an angle of measure 90o with the radius and diameter.
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Q5. In the figure below, ∠XAO = 30°. What is the measure of ∠XOA?    
  • 30°
  • 45°
  • 60°
  • 90°

Solution :

∠XAO = 30° ∠OXA = 90° So, ∠XOA = 60° … (sum of the angles of a triangle) 
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Q6. If AB is divided into 3 equal parts at P and R, then  
  • AP = 1/3 AB
  • PB = 2/3 BA
  • PR = RB
  • All of these

Solution :

A-P-R-B If PB = 2x, BA = 3x, AP = x, PR = RB = x.
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Q7. The length of the tangent from the external point P is 15 cm, and the distance of P from the centre is 17 cm. So, the radius of the circle is
  • 6 cm
  • 7 cm
  • 8 cm
  • 9 cm

Solution :

By Pythagoras' theorem, 172 = 152 + radius2 radius2 = 64 radius = 8 cm
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Q8. In the figure below, if AO = 29 cm, XO = 21 cm, then AY =?   
  • 25 cm
  • 24 cm
  • 22 cm
  • 20 cm

Solution :

Since the tangent is perpendicular to the radius, By Pythagoras' theorem, 292 = 212 + AX2 AX2 = 400 AY = AX = 20 cm 
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Q9. How many tangents can be drawn to a circle having a diameter 15 cm from a point at a distance of 7.5 cm from the centre? 
  • 0
  • 1
  • 2
  • 3

Solution :

The distance from the centre is 7.5 cm. The radius is 7.5 cm. Since the point lies on the circle, 1 tangent can be drawn to the circle.
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Q10. If the scale factor is less than one, then the new triangle is 
  • larger than the original one
  • smaller than the original one
  • equal to the original one
  • None of these
Construction of Similar Triangles

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Solution :

If the scale factor is less than one, then the new triangle is smaller than the original one.
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Q11. In the figure below, if ∠XAO = 30°, then what is the measure of ∠XAY?   
  • 30°
  • 45°
  • 60°
  • 90°

Solution :

The line joining the centre of a circle to the external point bisects the angle between two tangents and two radii.  2∠XAO = ∠XAY
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Q12. The angle drawn in a semicircle from the end points of the diameter is 
  • 30°
  • 45°
  • 60°
  • 90°

Solution :

The angle drawn in a semicircle from the end points of the diameter is 90°. 
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Q13. The number of tangents which can be drawn through a point on the circle is
  • one
  • two
  • three
  • many

Solution :

Only one tangent can be drawn through a point on the circle. 
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Q14. While constructing a similar triangle such that its corresponding sides are in the ratio 5:2, we need to construct an acute angle at any one of the bases of the given triangle and make 
  • 7 equal divisions
  • 6 equal divisions
  • 5 equal divisions
  • 2 equal divisions

Solution :

While constructing a similar triangle, we need to construct an acute angle at any one of bases of the given triangle and make 5 equal divisions (max (5 and 2)).
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Q15. If PQ is divided into 5 equal parts at A, B, C and D, then PB:BQ is 
  • 2:3
  • 3:2
  • 2:5
  • 5:2

Solution :

P-A-B-C-D-Q, PB = 2x, BQ = 3x
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Q16. While constructing ∆PQR similar to ∆ABC such that AB:PQ = 3:5, we need to make an acute angle at A and divide it 
  • 3 times
  • 5 times
  • 8 times
  • 10 times
Construction of Similar Triangles

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Solution :

While constructing a triangle similar to the given triangle, such that their sides are in the ratio m:n, we need to make an acute angle and divide it max (m,n) times. 
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Q17. A tangent cuts the circle at 
  • one point
  • two points
  • no point
  • three points

Solution :

A tangent cuts the circle at one point. 
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Q18. How many tangents can be drawn to a circle having a diameter 12 cm from a point at a distance of 10 cm from the centre? 
  • 0
  • 1
  • 2
  • 3

Solution :

The distance from the centre is 10 cm. The radius is 6 cm. Since the point lies outside the circle, 2 tangents can be drawn to the circle.
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Q19. The number of tangents which can be drawn from a point inside a circle to it is
  • 0
  • 1
  • 2
  • 3

Solution :

No tangents can be drawn from a point inside a circle.
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Q20. In the figure below, AO = 5 cm and XO = 3 cm, then AX =?   
  • 4 cm
  • 5 cm
  • 6 cm
  • 7 cm

Solution :

As the radius is perpendicular to the tangent,  By Pythagoras' theorem, 52 = 32 + AX2AX2 = 16 AX = 4
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