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The factors of 8a³ + b³ - 6ab + 1 are

A (2a + b - 1)(4a² + b² + 1 - 3ab - 2a)
B (2ab - b + 1)(4a² + b² - 4ab + 1 - 2a + b)
C (2a + b + 1)(4a² + b² + 1 - 2ab - b - 2a)
D (2a - 1 + b)(4a² + 1 - 4a - b - 2ab)

Which of the following is equivalent to 7.7 × 10^–6?

A 0.00000077
B 0.0000077
C 0.000077
D 0.00077

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__