The value of the series cos 120 + cos 840 + cos 320 + cos 1560 is :
1/2
1/4
-1/4
-1/2
If cosh-1 x = loge (2+√3), then x is equal to
1
2
3
5
If m and M respectively denote the minimum and maximum of f(x) = (x - 1)2+ 3 for x ε [ -3, 1], then the ordered pair (m, M) is equal to
(-3, 19)
(3, 19)
(-19,3)
(-19,-3)
If 3x /(x-a) (x-b) = 2/(x-a) + 1/(x-b) then a:b =
1 : 2
-2 : 1
1 : 3
3 : 1
Which of the following equations gives a circle
r = 2 sinθ
r2 cos2θ = 1
r(4 cosθ + 5 sinθ) = 3
5 = r (1 + √2 cosθ)
∫ (sin6x/cos8x) dx is equal to
tan 7x+c
tan7x / 7 +c
sec7x+c
If the function y = sin-1 x, then ( 1 - x2 ) d2y / dx2 is equal to :
-x dy / dx
0
x dy / dx
x (dy / dx)2
Observe the statements given below : Assertion (A) : f (x) = xe-x has the maximum at x = 1Reason (R) : f’(1)= 0 and f” (1) < 0 Which of the following is correct
Both (A) and (R) are true and (R) is the correct reason for (A)
Both (A) and (R) are true and (R) is not the correct reason for (A)
(A) is true, (R) is false
(A) is false, (R) is true
The extreme values of 4 cos(x2) cos(π/3 + x2 ) cos(π/3 - x2) over IR are
-1, 1
-2, 2
-3, 3
-4, 4
The radius of the circle r = √3 sinθ + cos θ is :
4
The differential equation obtained by eliminating the arbitrary constants a and b from xy=aex + be-x is
x d2y/dx2 +2 dy/dx -xy =0
d2y/dx2 +2y dy/dx -xy =0
x d2y/dx2 +2 dy/dx +xy =0
d2y/dx2 + dy/dx -xy =0
If α is a non real root number of x6 = 1 then (α5 + α3 +α +1 ) / (α2 +1) is equal to
α2
-α2
α
If(1.5)n=(0.15)b=100, then 1/a-1/b is equal to:
2/3
Two consecutive sides of a parallelogram are 4x + 5y = 0 and 7x + 2y = 0. If the equation to one diagonal is 11x + 7y = 9, then the equation of the other diagonal is:
x + 2y = 0
2x + y = 0
x - y =0
none of these
Four numbers are chosen at random from {1, 2, 3, .... 40}. The probability that they are not consecutive, is
1/2470
4/7969
2469/2470
7965/7969
The pair of straight lines x2-3xy+2y2 = 0 and x2-3xy+2y2+ x -2 =0 form a
square but not rhombus
rhombus
parellelogram
rectangle but not a square
The length of the subtangent at (2, 2) to the curve x5 = 2y4 is
5/2
8/5
2/5
5/8
The condition for the coaxial system x2 + y2+ 2λx+ c = 0, where λ is a parameter and c is a constant, to have distinct limiting points, is
c = 0
c < 0
c = -1
c > 0
The lines 2x + 3y = 6, 2x + 3y = 8 cut the x-axis at A and B respectively, drawn through the point (2, 2) meets the x-axis as C in such a way that abscissae of A, B and C are in arithmetic progression. Then the equation of the line L is:
2x + 3y = 10
8x + 2y = 10
2x - 3y = 10
8x - 2y = 10
A polygon has 54 diagonals then the number of it's sides is
7
9
10
12
Suppose A, B are two points on 2x-y + 3=0 and P(l, 2) is such that PA = PB. Then the mid-point of AB is :
( -1/5, 13/5 )
( -7/5 , 9/5 )
( 7/5 , -9/5 )
( -7/5, -9/5 )
If C0, C1, C2,...... are binomial coefficients , then C1+C2+C3+C4+....+Cr+....+Cn is equal to :
2n
2n-1
22n
The condition f(x) = x3 + px2 + qx + r (xЄR) to have no extreme value, is
p2 <3q
2p2 <q
p2 < q/4
p2 > 3q
The number of ways of arranging 8 men and 4 women around a circular table such that no two women can sit together is
8!
4!
8!4!
7!8P4
The locus of the Z in the argand plane for which |z+1|2+|z-1|2=4, is a
straight line
pair of straight lines
circle
parabola
u = u(x, y) = sin (y+ax) - (y+ax)2 ===>
uxx = a2 . uyy
uyy = a2 uxx
uxx = -a2 . uyy
uyy = - a2 uxx
If P = (0, 1, 2), Q = (4, -2, 1), 0 = (0, 0, 0), then LPOQ is equal to:
π/2
π/4
π/6
π/3
The angle between the pair of lines 2x2+5xy+2y2+3x+3y+1=0,is:
cos-1(4/5)
tan-1(4/5)
A number n is chosen at random from S = {l,2,3,....,50}. Let A = {n ε S: n + 50/n > 27} and B = { n ε S: n is a prime number} and C = {n ε S: n is a square}.The correct order of their probability is
P(A) < P(B) < P(C)
P(A) > P(B) > P(C)
P(B) < P(A) < P(C)
P(A) > P(C) > P(B)
A bag X contains 2 white and 3 black balls and another bag Y contains 4 white and 2 black balls.One bag is selected at random and a ball is drawn from it.Then the probability for the ball chosen be white,is
2/15
7/15
8/15
14/15