Q.1

The volume of a hemisphere is 19404 cmFind its diameter (in cm).

  • 42
  • 21
  • 84
  • 63
Q.2

Which of the following is a true statement?

  • Two similar triangles are always congruent.
  • Two similar triangles have equal areas
  • Two triangles are similar if their corresponding sides are proportional
  • Two polygons are similar if their corresponding sides are proportional
Q.3

Which of the following is the CORRECT option for the triangles having sides in the ratio of 3:4:6?

  • Acute angled
  • Obtuse angled
  • Right angled
  • Either acute or right angled
Q.4

Three cubes of iron whose edges are 6cm, 8cm and 10cm respectively are melted and formed into a single cube. The edge of the new cube formed is

  • 12 cm
  • 14 cm
  • 16 cm
  • 18 cm
Q.5

A circle has its centre at O . A tangent drawn from a point P , which is situated outside the circle, touches the circle at A. If PA = 4 cm & PO=5 cm, then the length of the radius of the circle is

  • 1 cm
  • 2 cm
  • 3 cm
  • 4 cm
Q.6

Δ PQR is right angled at Q. If m∠R = 60°, what is the length of PR (in cm), if RQ = 4√3 cm?

  • 8
  • 4
  • 8/√3
  • 8√3
Q.7

If an interior of a regular polygon is 170o, then the number of sides of the polygon is

  • 30
  • 20
  • 18
  • 27
Q.8

O is the center of the circle and two tangents are drawn from a point P to this circle at points A and B. If ∠AOP = 50°, then what is the value (in degrees) of ∠APB?

  • 60
  • 80
  • 90
  • 100
Q.9

What is the curved surface area (in cm²) of a hemisphere of diameter 42 cm?

  • 2332
  • 1778
  • 1556
  • 2772
Q.10

Which of the following condition is True about the similarity of triangle ABC & DEF given below?

  • 1
  • 2
  • 3
  • none
Q.11

Consider the following figure shown below and choose which of the following equation is correct about the similarity of both triangles?

  • 1
  • 2
  • 3
  • 4
Q.12

ABCD is a cyclic trapezium in which AD || BC. If ∠ABC = 70°, then ∠BCD is

  • 110°
  • 80°
  • 70°
  • 90°
Q.13

 In ΔDEF measure of angle E is 90 deg. If tanD = 4/3, and DE = 6cm, then what is the length (in cm) of side EF?

  • 10
  • 5
  • 8
  • 4
Q.14

A right circular conical structure stands on a circular base of 21m diameter and is 14m in height. The total cost of colour washing for its curved surface at Rs. 6 per sq. m. is
(Take Π = 22/7 )

  • 4365
  • 4465
  • 3465
  • 3365
Q.15

The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:The ratio of their volumes is

  • 27:20
  • 20:27
  • 4:9
  • 9:4
Q.16

BD and CE are two medians of the triangle ABC. If EO = 7 cm, then the length of CE is

  • 28 cm
  • 14 cm
  • 21 cm
  • 35 cm
Q.17

D and E are points on side AB and AC of ΔABC. DE is parallel to BC. If AD:DB = 2:5 and area of ΔADE is 8 sq cm, what is the ratio of area of ΔADE: area of quadrilateral BDEC?

  • (4:45)
  • (45:4)
  • (8:45)
  • (45:8)
Q.18

The area of a semicircle is 1925 cmCalculate its perimeter (in cm).

  • 360
  • 80
  • 160
  • 180
Q.19

An angle is greater than its complementary by 20°. What will be the measure of the angle?

  • 55°
  • 35°
  • 100°
  • 80°
Q.20

Two tangents PA and PB are drawn to a circle of centre O in such a way that angle AOB = 120 deg. Calculate the value of angle APB.

  • 40 deg
  • 50 deg
  • 60 deg
  • 80 deg
Q.21

In ΔPQR, L and M are two points on the sides PQ and PR respectively such that LM II QR. If PL=2cm; LQ=6cm and PM=1.5 cm, then MR in cm is

  • 0.5
  • 4.5
  • 9
  • 8
Q.22

Two adjacent sides of a parallelogram are 21 cms and 20 cms. The diagonal joining the end points of these two sides is 29 cms. The area of the parallelogram (in sq.cms) is

  • 240
  • 120
  • 210
  • 420
Q.23

The length of the radius of a circle with centre O is 5 cm and the length of the chord AB is 8 cm. The distance of the chord AB from the point O is

  • 2 cm
  • 3 cm
  • 4 cm
  • 15 cm
Q.24

If a cylinder of radius 7 cm and height 9 cm is melted and constructed into a cone of the same radius, what will be the height of this cone?

  • 54 cm
  • 9 cm
  • 27 cm
  • 13.5 cm
Q.25

The tangents drawn at points A and B of a circle with centre O, meet at P. If ∠AOB = 120° and AP = 6 cm, then what is the area of triangle (in cm2) APB?

  • 6√3
  • 8√3
  • 9
  • 9√3
Q.26

wooden bowl is in shape of a hollow hemisphere of internal radius 9 cm and thickness 1 cm. Find the total surface area of the bowl?

  • 1376.58 sq cms
  • 2064.87 sq cms
  • 344.15 sq cms
  • 1197.42 sq cms
Q.27

O is an centre of a circle. P is an external point of it at distance of 13cm from O. The radius of the circle is 5cm. Then the length of a tangent to the circle from P upto the point of contact is

  • √194cm
  • 10cm
  • 12cm
  • 8cm
Q.28

ΔPQR is right angled at Q. If cosP = 3/5, then what is the value of cosR ?

  • 3/4
  • 5/3
  • 4/5
  • 4/3
Q.29

Triangle ΔXYZ is similar to ΔPQR. If XY:PQ=5:If Area of ΔPQR is 5 sq cm, what is the area (in sq cm) of ΔXYZ?

  • 125
  • 120
  • 100
  • 64
Q.30

The ratio of curved surface area of a right circular cylinder to the total area of its two bases is 2 :If the total surface area of cylinder is 23100 cm2, then what is the volume (in cm3) of cylinder?

  • 247200
  • 269500
  • 312500
  • 341800
Q.31

In a triangle the length of the side opposite the right angle is 6 cm, what is the length of the side opposite to the angle which measures 30°?

  • 3 cm
  • 3√3 cm
  • 3/2 cm
  • (3/2)√3 cm
Q.32

The midpoints of AB and AC of a triangle ABC are X and Y respectively. If BC+XY=12 units, then BC­XY is

  • 10 units
  • 8 units
  • 6 units
  • 4 units
Q.33

In a rectangle

  • Diagonals bisect opposite angles
  • Consecutive sides are congruent
  • All sides are congruent
  • Diagonals form two congruent triangles
Q.34

Number of circles that can be drawn through three non-colinear points is

  • exactly one
  • two
  • three
  • more than three
Q.35

The amount of extension in a spring is proportional to the weight hung on it. If the weight of 5 kgs produces an extension of 0.4 cm, what weight would produce an extension of 5cm?

  • 6.25kgs
  • 62.5kgs
  • 4kgs
  • 40kgs
Q.36

In ΔDEF, G and H are points on side DE and DF respectively. GH is parallel to EF. If G divides DE in the ratio 3:2 and HF is 8 cm, then the length of DF is

  • 12 cm
  • 20 cm
  • 14 cm
  • 16 cm
Q.37

Thousand solid metallic spheres of diameter 6 cm are melted and recast into a new solid sphere. The diameter of the new sphere (in cm) is

  • 30
  • 90
  • 45
  • 60
Q.38

­ A wooden bowl is in shape of a hollow hemisphere of internal radius 8 cm and thickness 1 cm. Find the total surface area of the bowl?

  • 964.85 sq cms
  • 1125.14 sq cms
  • 1687.71 sq cms
  • 281.29 sq cms
Q.39

Volume of a cylinder is 13860 cubic cm. If circumference of its base is 132 cm, find the curved surface area of the cylinder?

  • 2640 sq cm
  • 3960 sq cm
  • 1320 sq cm
  • 660 sq cm
Q.40

The radius and height of a solid cylinder are increased by 2% each. What will be the approximate percentage increase in volume?

  • 6.76
  • 5.88
  • 6.12
  • 3.34
Q.41

In triangle ABC, BAC = 90 deg and AD is perpendicular to BC. If AD = 6cm and BD = 4cm, then the length of BC is

  • 10 cm
  • 12 cm
  • 13 cm
  • 15 cm
Q.42

If there are four lines in a plane, then what cannot be the number of points of intersection of these lines?

  • 0
  • 5
  • 4
  • 7
Q.43

If any two sides of a triangle are divided by the line in the same ratio, then the line must be _________________ to the third side of the triangle.

  • equal
  • parallel
  • perpendicular
  • non parallel
Q.44

The sum of the lengths of the edges of a cube is equal to four times the perimeter of a square. If a quarter of the numerical value of the volume of the cube is equal to the numerical value of the area of the square, then the length of one side of the square is

  • 27/16 units
  • 10.5 units
  • 9/4 units
  • 27 units
Q.45

The length of the common chord of two intersecting circles is 12 cm. If the diameters of the circles are 15 cm and 13 cm, then what is the distance (in cm) between their centers?

  • 7/2
  • 7
  • 7√2
  • 14
Q.46

A cone is hollowed out of a solid wooden cube of side 6 cm. The diameter and height of the cone is same as the side of the cube. What is the volume of the remaining cube?

  • 159.42 cubic cms
  • 323.15 cubic cms
  • 106.33 cubic cms
  • 210.66 cubic cms
Q.47

What is the circumference (in cm) of a circle whose area is 616 sq cm?

  • 44
  • 22
  • 66
  • 88
Q.48

A cylindrical vessel of radius 8 cm is partially filled with water. By how much will the water level rise if a sphere of radius 7 cm is completely immersed in this water?

  • 7.15 cm
  • 14.3 cm
  • 21.45 cm
  • 28.6 cm
Q.49

Point A (2, 1) divides segment BC in the ratio 2:Co-ordinates of B are (1, -3) and C are (4, y). What is the value of y?

  • 8
  • -7
  • -8
  • 7
Q.50

At what point does the line 2x - 3y = 6 cuts the Y axis?

  • (0, 2)
  • (-2, 0)
  • (2, 0)
  • (0, -2)
0 h : 0 m : 1 s