A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length x. The maximum area enclosed by the park is
3x2/2
x3/8
x2/2
x2/2
At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote is
5040
6210
385
385
If the expansion in powers of x of the function is a0 + a1x + a2x2 + a3x3 + … , then an is
D.
(1-ax)-1(1-bx)-1 = (1+ax+a2x2+.....)(1+bx+b2x2+....)
therefore coefficient of xn = bn +abn-1 +a2bn-2 +.....+an-1b +an =
For natural numbers m, n if (1 − y)m (1 + y)n = 1 + a1y + a2y2 + … , and a1 = a2 = 10, then (m, n) is
(20, 45)
(35, 20)
(45, 35)
(45, 35)
The value of ,where [x] denotes the greatest integer not exceeding x is
af(a) − {f(1) + f(2) + … + f([a])}
[a] f(a) − {f(1) + f(2) + … + f([a])}
[a] f([a]) − {f(1) + f(2) + … + f(a)}
[a] f([a]) − {f(1) + f(2) + … + f(a)}
If the lines 3x − 4y − 7 = 0 and 2x − 3y − 5 = 0 are two diameters of a circle of area 49π square units, the equation of the circle is
x2 + y2 + 2x − 2y − 47 = 0
x2 + y2 + 2x − 2y − 62 = 0
x2 + y2 − 2x + 2y − 62 = 0
x2 + y2 − 2x + 2y − 62 = 0
Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the mid points of the chords of the circle C that subtend an angle of 2π/3 at its centre is
x2+y2 = 3/2
x2 + y2 = 1
x2+y2 = 27/4
x2+y2 = 27/4
If (a, a2 ) falls inside the angle made by the lines y =x/2, x >0 and y = 3x, x > 0, then a belongs to
(0,1/2)
(3, ∞)
(1/2, 3)
(1/2, 3)