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Following are the steps of construction of a ΔPQR, given that QR = 3 cm, ∠PQR = 45° and QP - PR = 2 cm. Arrange them and select the correct option.
(i) Make an angle XQR = 45° at point Q of base QR.
(ii) Join SR and draw the perpendicular bisector of SR say AB.
(iii) Draw the base QR of length 3 cm.
(iv) Let bisector AB intersect QX at P. Join PR.
(v) Cut the line segment QS = QP - PR = 2 cm from the ray QX.

A (iii) → (ii) → (i) → (v) → (iv)
B (iii) → (i) → (ii) → (v) → (iv)
C (iii) → (i) → (ii) → (iv) → (v)
D (iii) → (i) → (v) → (ii) → (iv)

The fluid contained in a bucket can fill four large bottles or seven small bottles. A full large bottle is used to fill an empty small bottle. What fraction of the fluid is left over in the large bottle when the small one is full?

A
B
C
D

Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

A 3 : 4
B 3 : 5
C 5 : 3
D None of these

If = k, then the value of k is
A 3
B 3²
C 3³
D

In the given figure (not drawn to scale), ΔABC, ΔEFG, ΔKIJ and ΔNMO are 4 different equilateral triangles. Find the perimeter of the figure, if side of square PDHL is 8 cm, AC = 4 cm, EG = 2 cm, KI = 3 cm and MO = 2 cm.


A34 cm
B64 cm
C43 cm
D52 cm

Select a figure from the options in which Fig. (X) is exactly embedded as one of its part.


A
B
C
D

In the given figure, it is given that
(i) AB ⊥ BF and EF ⊥ BF
(ii) AC = BC
(iii) KD is perpendicular to BC and DE

Find the measure of x.

A 75°
B 30°
C 60°
D 45°

Fill in the blanks and select the CORRECT option.
• Two cylindrical pots contain the same amount of milk. If their diameters are in the ratio 2 : 1, then the ratio of their heights is __P__.
• The volume of a sphere is equal to __Q__ the volume of a cylinder which has same height and diameter. (Radius of sphere = radius of cylinder)
• The slant height and base diameter of conical tomb are 25 m and 14 m respectively. The cost of white washing its curved surface at the rate of ₹ 210 per 100 m² is __R__

Kirti bought a dozen eggs to be used in a cake recipe. Only 1 egg is needed per cake. If 5 eggs remain in the carton, how many cakes did she make?

A6
B7
C11
D12

The average marks (out of 100) of boys and girls in an examination are 70 and 73 respectively. If the average marks of all the students in the examination is 71, then find the ratio of the number of boys to the number of girls.

A1 : 3
B2 : 1
C1 : 2
D3 : 1