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If (–2, 1), (a, 0), (4, b) and (1, 2) are the vertices of a parallelogram, then
(i) Find a
(ii) Find b
(iii) Area of the parallelogram.

Which of the following is correct statements?
(i) 3(sinθ – cosθ)⁴+ 6(sinθ + cosθ)² + 4(sin⁶θ + cos⁶θ) is independent of θ.
(ii) If cosecθ – sinθ = a³, secθ – cosθ = b³, then a²b²(a² + b²) = 2

A Only (i)
B Only (ii)
C Both (i) and (ii)
D Neither (i) nor (ii)

Study the Venn diagram given below.
(1) Rectangle represents males.
(2) Triangle represents educated.
(3) Circle represents urban.
(4) Square represents civil servants.

Who among the following is neither a civil servant nor educated but is urban and a male?

A 2
B 3
C 6
D 12

A leak at the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 litres per minute. When the tank is full, the inlet is opened and due to the leak, the tank gets empty in 8 hours. The capacity of the tank is

A5260 litres
B5760 litres
C5846 litres
D6970 litres

If α, β be two zeroes of the quadratic polynomial ax² + bx – c = 0, then find the value of .

A
B
C
D

If 2 men and 7 women can do a piece of work in 4 days, 4 men and 2 women can do the same work in 5 days, then in how many days 6 men and 27 women can do the same work?

A
B
C
DNone of these

For what value of a, the roots of the equation 2x² + 6x + a = 0, satisfy the condition <2 (where α and β are the roots of equation).
A a < 0
B –1 < a < 0
C –1 < a < 1
D None of these

A boat goes 32 km upstream and 36 km downstream in 7 hours. In 9 hours, it can go 40 km upstream and 48 km downstream. If x represents the speed of the boat in still water in km/hr and y represents the speed of the stream in km/hr, then_______.

A x + y = 12, x – y = 8
B x + y = 5, x – y = 11
C x + y = 6, x – y = 10
D x + y = 10, x – y = 6

A rectangular park is 100 m by 50 m. It is surrounded by semicircular flower beds all round. Find the cost of levelling the semicircular flower beds at 60 paise per m².

A ₹ 31425
B ₹ 28260
C ₹ 352.40
D ₹ 282.60