\(\frac{860}{3}\)
\(\frac{680}{3}\)
\(\frac{608}{3}\)
\(\frac{680}{3}\)
Correct answer is B
a = 153 - 1st term, 6th term = \(\frac{17}{27}\)
nth term = arn
Sn = a(1 - rn) where r < 1
6th term = 153\(\frac{1 - 0.4^4}{1 - 0.4}\)
= \(\frac{680}{3}\)
A pyramid is constructed on a cuboid. The figure has
Twelve faces
Thirteen vertices
Fourteen edges
Fifteen edges
Sixteen edges
Correct answer is E
The pyramid has 8 edges in itself while the cuboid has 12 edges. When merging the two shapes together, the edge of the base of the pyramid becomes same as the edges of the top of the cuboid.
Hence, the new structure will have (12 + 8) - 4 = 16 edges.
6 km/h
8 km/h
9 km\h
11 km\h
13 km\h
Correct answer is B
Let the average speed for the first 4 km = x km/h.
Hence, the last 5 km, speed = (x + 2) km/h
Recall: \(Time = \frac{Distance}{Speed}\)
Total time = 1 hour.
\(\therefore \frac{4}{x} + \frac{5}{x + 2} = 1\)
\(\frac{4(x + 2) + 5x}{x(x + 2)} = 1\)
\(9x + 8 = x^{2} + 2x\)
\(x^{2} + 2x - 9x - 8 = 0 \implies x^{2} - 7x - 8 = 0\)
\(x^{2} - 8x + x - 8 = 0\)
\(x(x - 8) + 1(x - 8) = 0\)
\(x = -1; x = 8\)
Since speed cannot be negative, x = 8km/h.
100000
1000000
120000
30000
350000
Correct answer is A
The canal's width = 10cm = 100mm (given) The speed of water = 1000mm 10mm = 1cm 1000mm = 100cm The adjacent sea must give speed x width = 1000 x 100 = 100,000
If \(3x - \frac{1}{4})^{\frac{1}{2}} > \frac{1}{4} - x \), then the interval of values of x is
x > \(\frac{1}{3}\)
x < \(\frac{1}{3}\)
x < \(\frac{1}{4}\)
x < \(\frac{9}{16}\)
x > \(\frac{9}{16}\)
Correct answer is E
\(3x - (\frac{1}{4})^{-\frac{1}{2}} > \frac{1}{4} - x\)
= \(3x - 4^{\frac{1}{2}} > \frac{1}{4} - x\)
= \(3x - 2 > \frac{1}{4} - x\)
= \(3x + x > \frac{1}{4} + 2 \implies 4x > \frac{9}{4}\)
\(x > \frac{9}{16}\)