NTSE Mathematics Geometry MCQs

Question: In the adjoining figure, it is given that D and E the mid points of AB and AC respectively.

If   

• a) 1200
• b) 1600            
• c) 700           
• d) 1150

Answer: 1200

Question: In the given figureIn the given figure 

If BF = 4 cm, FD = 6 cm and BE = 8 cm, then BC =______

• a) 12 cm
• b) 15 cm
• c) 25 cm
• d) None of these

Answer: 25 cm

Question: In the given figure

   and  

If AP = 5.4 cm, OC = 7.2 cm and BO = 6 cm, then the length of DO is :

• a) 4.5 cm
• b) 4 cm
• c) 5 cm
• d) 6.5 cm

Answer: 4.5 cm

Question: ABCD is a quadrilateral piece of land in which DC = 30 m. The land has been divided into three parts as shown in the figure. If

GH = 8 m and HB = 12 m then the length of DE =

• a) 3 m
• b) 4 m
• c) 5 m
• d) 6 m

Answer: 6 m

Question: The number of triangles with any three of the lengths 1, 4, 6 and 8 cms consider is

• a) 1
• b) 2
• c) 3
• d) 4

Answer: 1

Question: In a right triangle ABC, AD = AE, and CF = CE and shown in fig. If

= x then the value of x equals.

• a) 30°
• b) 45°      
• c) 60°          
• d) 75°

Answer: 45°         

Question: In the figure given sum of all the angles is equal to

• a) 10 right angles
• b) 12 right angles
• c) 14 right angles
• d) 16 right angles

Answer: 16 right angles

Question: If three lengths are given a = 537 cms, b = 139 cms and c = 181 cms, then with these sides

• a) One triangle can be constructed
• b) No triangle can be constructed
• c) Two triangles can be constructed
• d) None of these

Answer: No triangle can be constructed

Question: Two circles touch each other externally, the number of common tangents to the circles is

• a) 1
• b) 2
• c) 3
• d) 4

Answer: 3

Question: If two circles touch each other internally then the distance between their centers is equal to

• a) Sum of their radii
• b) Difference of their radii
• c) Product of their radii
• d) Larger of the two radii

Answer: Difference of their radii

More Questions........................

Question: PQRS is a cyclic quadrilateral and RS is a diameter. If

   is equal to

• a) 300         
• b) 500          
• c) 600   
• d) 800

Answer: 500          

Question: In the given figure, AB and AC are produced to P and Q respectively. The bisectors of  and  intersect at O.  equal to

• a) 100          
• b) 300 
• c) 500   
• d) 600

Answer: 500           

Question: ABCD is cyclic quadrilateral. AB is the diameter of the circle through points A, B, C and D. If ,the  is equal to

• a) 750           
• b) 1100 
• c) 1250        
• d) 1350

Answer: 1250        

Question:  In the figure given below

 arc AC = arc BC, then  is equal to

• a) 600        
• b) 700         
• c) 800        
• d) 900

Answer:  700         

Question: ABCD is cyclic quadrilateral inscribed in a circle with the centre O. Then  is equal to

• a) 300        
• b) 400         
• c) 500       
• d) 600

Answer: 600

Question: ABCD is a parallelogram inscribed is a circle, then it is a

• a) Rhombus
• b) Square
• c) Rectangle
• d) Trapezium

Answer: Rectangle

Question: Two concentric circle of radius 3 cm and 4 cm, intersect in

• a) One paints
• b) Two points
• c) Three points
• d) None of these

Answer: None of these

Question: AB and CD are diameters of a circle, the  is equal to

• a) 400 
• b) 500 
• c) 700
• d) 800

Answer: 800

Question: A square, whose side is 2cm, has its corners cut away so as to form an octagon with all sides equal. Then the length of each side of the octagon, in meters, is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: In the Fig. AMN, APQ, QRM and PRN are all straight lines.

The value of  α + β is .

• a) 700  
• b) 550            
• c) 900          
• d) 750

Answer: 700 

Question: The areas of three adjacent faces of a cuboids are x, yz. If the volume is V, then V2 will be equal to

• a) xy/z
• b) yz/x2    
• c) x2y2/z2   
• d) xyz

Answer: xyz

Question: If ABC is a quarter circle and a circle is inscribed in it and if AB = 1 cm, find radius of smaller circle.

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: In the diagram given below,

If AB : CD = 3 : 1, the ratio of CD  PQ is

• a) 1 : 0.69
• b) 1 : 0.75
• c) 1 : 0.72
• d) None of the above

Answer: 1 : 0.75

Question: In the right-angled triangle QPR given below, PS is the altitude to the hypotenuse. The figure is followed by three possible inferences.

I.   Triangle PQS and Triangle RPS and similar.

II.  Triangle PSQ and Triangle RSP are congruent. 

III. Triangle PSQ and Triangle RPQ are similar.

• a) I and II are correct
• b) I and III are correct
• c) Only II is correct
• d) All three are correct

Answer: I and III are correct

Question: In the adjoining figure DP is parallel to AC; then the ratio of area of triangle PCB and quadrilateral ABCD is

• a) 1 : 1
• b) 1 : 2
• c) 1 : 4
• d) 2 : 3

Answer: 1 : 1

Question: In a triangle ABC, the internal bisector of the angle A meets BC at D. If AB = 4, AC = 3 and 

• a) 2√3
• b)

  

• c)

  

• d) None of these

Answer:

Question: In the figure below, AL is perpendicular to BC and CM is perpendicular to AB. If CL = AL = 2BL, find MC/AM.

• a) 2
• b) 3
• c) 4
• d) Cannot be determined

Answer: 3

Question: In the triangle ABC shown below DE is parallel to BC such that D divides AB in the ratio 1 : 3.

In the area of triangle ADE is 5 cm2. What is the area of the triangle EFC ?

• a) 12 cm2
• b) 14.4 cm2 
• c) 15 cm2
• d) 20 cm2

Answer: 12 cm2

Question: In the figure given below, PC is tangent to the circle from the point P and B is a point of the circle such that PB = CB. Find 

• a) 1200        
• b) 1400   
• c) 1200          
• d) 1000

Answer: 1400         

Question: PQRS is a parallelogram and PA, SB, RC, QD are angle bisectors. If PQ = QD = 6 units find m  

• a) 300
• b) 600 
• c) 1200  
• d) Indeterminate

Answer: 1200  

Question: In the below diagram, ABCD is a rectangle with AE = EF = FB. What is the ratio of the areas of   and that of the rectangle ?

• a) 1/6
• b) 1/8
• c) 1/9
• d) None of these

Answer: 1/6

Question: In the below figure, ABC is a right-angled triangle. CD is the altitude. Circles are inscribed within the  and 

P and Q are the centers of the circles. The distance PQ is

• a) 5
• b) √50
• c) 7
• d) 8

Answer: √50

Question: In the adjoining figure, chord ED is parallel to the diameter AC of the circle. If  then what is the value of  

• a) 350 
• b) 550 
• c) 450 
• d) 250

Answer: 250

Question: In the adjoining figure, the chords XY and SR are produced to meet outside the circle at P. The chords XR and YS meet inside the circle at T. If x = x0 and  is equal to

• a) (x + y)0
• b) (y - x)0 
• c) 2(y - x)0
• d) (y - 2x)0

Answer: (y - 2x)0

Question: In the given figure, ABC is a right angled triangle. Also   and AG = GE = EB. If De = 12 cm, then the measure of BC is

• a) 12 cm
• b) 18 cm
• c) 24 cm
• d) 30 cm

Answer: 18 cm

Question: In the figure AE : EB = 1 : 2 and BD : DC =  5 : 3 Find EG : GC.

• a) 5 : 9
• b) 2 : 3
• c) 3 : 2
• d) Cannot be determined

Answer: 5 : 9

Question: In the above diagram O1 and O₂ are the centers of the circles 1 and 2 respectively and O₁ lies on the smaller circle. Radius of the smaller circle is r. Given than 

Find the value of O₁ P in terms of r.

• a) 1. 2r
• b) r
• c) 0.8r
• d) Cannot be determined

Answer: 1. 2r

Question: A circle is touching the side BC of ΔABC at ‘T’ and touching AB and AC produced at Q and R respectively, then the value of AQ is

• a) QR
• b)

  

• c) AB + BC + AC
• d) None of these

Answer:

Question: In the figure

   AB = 15, CD = 8, AD = x, DE = 10, FG = y and CG = 6. The ratio x : y equal to 

• a) 1 : 2
• b) 1 : 3
• c) 2 : 1
• d) 3 : 2

Answer: 2 : 1

Question: In the figure

   CD = 8 cm CE = 10 cm, BE = 2cm, AB = 9, AD = b and DE = a. The value of a + b is 

• a) 13 cm
• b) 15 cm
• c) 12 cm
• d) 9 cm

Answer: 13 cm

Question: In the figure, AB is a diameter of the circle. TD is a tangent. If   

• a) 1200   
• b)1160       
• c) 1060 
• d) 1260

Answer: 1260

Question: In the figure given above, A and B are the centres of the two congruent circles with radius 17 units. If AB = 30 units, the length of the common chord DC is

• a) 25 units
• b) 18 units
• c) 10 units
• d) 16 units

Answer: 16 units

Question: Let X be any point on the side BC of a triangle ABC. If XM, XN are drawn parallel to BA and CA Meeting CA, BA in M, N respectively ; MN meets CB produced in T. Then -

• a) TB2 = TX × TC            
• b) TC2 = TX × TX       
• c) TX2 = TB × TC           
• d) TX2 = 2(TB × TC)

Answer: TX2 = TB × TC           

Question: In figure, D and E are the mid-points of sides AB and AC respectively of   

• a) 1100 
• b) 1200
• c) 700 
• d) 800

Answer: 1100 

Question: The exterior angle of a regular is 1/5 of its interior angle. Find the number of sides of the polygon

• a) 12
• b) 10
• c) 7
• d) 8

Answer: 12

Question: The exterior angle of a regular is 1/5 of its interior angle. Find the number of sides of the polygon

• a) 12
• b) 10
• c) 7
• d) 8

Answer: 12

Question: The difference between an exterior angle of n - 1 sided regular polygon and exterior angle of n + 2 sided regular polygon is 60. Find the value of n.

• a) 13
• b) 12
• c) 7
• d) 10

Answer: 13

Question: ABCD is a parallelogram inscribed is a circle, then it is a

• a) Rhombus
• b) Square
• c) Rectangle
• d) Trapezium

Answer: Rectangle

Question: The exterior angle of a regular is 1/5 of its interior angle. Find the number of sides of the polygon

• a) 12
• b) 10
• c) 7
• d) 8

Answer: 12

Question: The difference between an exterior angle of n - 1 sided regular polygon and exterior angle of n + 2 sided regular polygon is 60. Find the value of n.

• a) 13
• b) 12
• c) 7
• d) 10

Answer: 13