The number of coins 1.5 cm in diameter and 0.2cm thick to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm is:
380
450
472
540
Six bells commence tolling together and toll at intervals 2,4,6,8,10 and 12 seconds respectively. In 30 minutes how many times they toll together.
4
10
15
16
The L.C.M. (Lowest (or Least) Common Multiple) of two numbers is 45 times to their H.C.F (Highest Common Factor). If one of the numbers is 125 and sum of L.C.M. and H.C.F. is 1150, the other number is:
215
220
225
235
Maximam no of hydrgen bonds existed in water:
4
3
2
1
None of above.
Let z=x+iy be a complex no. where x and y are integers. Then the area of rectangle whose vertices are the roots of the equation žz3+zž3=350 (ž is the conjucate of z)is..
48
32
40
80
The locus of the orthocentre of the triangle formed by the lines (1 + p)x – py + p(1 + p) = 0, (1 + q)x – qy +
q(1 + q) = 0 and y = 0, where p ? q, is
A Hyperbola
A Paarabola.
An ellipse.
A straightline
None of above.
If (1+i/1-i)^m = 1, then m =
4
5
6
7
p.q,r and in A.P. and each is numerically less than unity.
let x = 1 + p + p^2 +....¥
y = 1 + q + q^2+.....¥
and z = 1 + r + r^2 +.....¥ Then x, y, z are in
A.P
G.P
H.P
None of these.
If is a, ß y are roots of the equation x^3 + qx + r = 0, then (1+a) (1+ß) (1+y)=
qr
1+q-r
-q/r
1+qr
How should we define f(x) = log(1 + ax) - log (1-bx)/x at x = 0 so as to make it continuous there f(0) =
a-b
log a + log b.
a + b.
log(a/b).
None of these.
A real, non-zero solution to the system of equation 1+ x + x^2 +.....+ x^20=0 1 + x + x^2 +....+ x^16 =0 is
-2
1
2
-1
The equation to the tangent to the curve (x/a)^n + (y/b)^n = 2 at (a, b) is:
x/a + y/b =2
x/a + y/b =1/2
x/b + y/a=2
ax + by =2
log tan 1' + log tan 2' +....+ log tan 89' =
1
0
tan 1'
tan 89'
The set of all integers under the operation * defined by a*b = a + b + 1 is a group. Its identify is:
-1
-2
1
0
The set of positive integers including zero is not a group under addition because:
closure fails
associative law does not hold
there is no identify
there is no inverse
In the group C= {0,1,3,4,5} under addition modulo 6, subgroup is:
{0,1,3}
{0,4,5}
{0,2,4}
{0,3,5}
ò cos Öx dx =
Öx sin Öx
2[Öx sin Öx + cosÖx]
2[x sin Öx +cos Öx)
x sin Öx /2
If y^2(2a -x) = x^3, then dy/dx at (a, a) is:
1/a
1/2a
1
2
sin^-1(1/Ö5) + cos^-1 3=
p/3
p/2
p/6
p/4
The letters of the word TREASON are arranged in a row in all possible ways. How many of them begin with T and end with N?
60
120
240
720
The probability that an event A happens in a trial is 0.4. Three Independent trials are made. The probability that A happens at least once is:
0.216
0.784
0.064
0.936
Two events A and B occur with probabilities 0.25 and 0.50. The probability that they occur simultaneously is 0.14. What is the probability that neither of them occurs?
0.39
0.61
0.72
0.28
How many diagonals can be drawn in a polygon of n sides?
n(n-1)/2
n(n+1)/2
n(n-3)/2
n(n+3)/2
Define a function f : A ® B as follows: f(x) = x-2/x-3 Then f^-1 (x) =
x - 3/x-2
2x -1/3x - 2
x + 2/x + 3
2 - 3x/1 - x
The tangents drawn at the extremities of a focal chord of a parabola:
intersect on the tangent at the vertex
intersect on the directrix
intersect at an angle of 45'
are parallel
If all red, boiled crabs are dead and all red, dead crabs are boiled does it follow that all dead, boiled crabs are red?
yes
no
insufficient data
inconsistent data
Let A = [2 ,4, 6, 8] and define R = [(2, 4) (4,2) (4, 6), (6,4)]. Then R is:
reflexive
symmetric
transitive
anti-symmetric
Which of the following assertion is not true?
The cross product of vectors is not commutative
If a set has n element its power set has 2^n elements
In a box product the dot and the cross cannot be interchanged
Matrix multiplication is associative
What is the locus of the centre of a circle which touches externally two given circles?
A parabola
an ellipse
A hyperbola
A circle
The equation to the hyperbola with eccentricity 2 and foci at (+ 2, 0) is :
3x^2 -y^2 =3
x^2 - y^2 = 4
x^2/4 -y^2/9 =1
x^2/1 - y^2/4 =1