The radical axis of the circle x2+y2+4x-6y=12 and x2+y2+2x-2y-1=0 divides the line joining the centers of the circles in the ratio
-3:7
-27:17
3:7
27:17
Two cylinders 'A' and 'B' fitted with pistons contain equal number of moles of an ideal mono-atomic gas at 400 K. The piston of 'A' is free to move while that of 'B' is hold fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in 'A' is 42 K, the rise in temperature of the gas in 'B' is
21 K
35 K
42 K
70 K
In Freundlich adsorption isotherm, the intercept is equal to
k
log k
1/n
log x/m
The base of an equilateral triangle is x+y=2 and the vertex is the point (2, -1). The equations to the remaining sides are
y+1=(2±√3)(x+2)
y-1= (2±√3) (x-2)
y+1=(2±√3) (x-2)
y+1=(1(1±√3) (x-2)
The relation between the coefficient of real expansion (γr) and coefficient of apparent expansion (γa) of a liquid and the coefficient of linear expansion (αg) of the material of the container is
γr = αg + γa
γr = αg + 3γa
γr = 3αg + γa
γr = 3(αg + γa )
The orthocentre of the triangle formed by the points(2,-1,1), (1,-3,-5), (3,-4,-4) is
(2,-1,1)
(1,-3,-5)
(3,-4,-4)
(2,-8/3,-8/3)
A bar magnet of 10 cm long is kept with its north (N)-pole pointing North. A neutral point is formed at a distance of 15 cm from each pole. Given the horizontal component of earth's field is 0.4 Gauss, the pole strength of the magnet is
9 amp-m
6.75 amp-m
27 amp-m
13.5 amp-m
The roots of x3+x2-2x-2=0 are
-1,±√2
0,1,2
-2,-1,1
1,±i
A clock which keeps correct time at 200C, is subjected to 400C. If coefficient of linear expansion of the pendulum is 12x 10-6 /0C. How much will it gain or lose time
10.3 s/day
20.6 s/day
5 s/day
20 min/day
The function f(x) = xe-x (x ∈R) attains a maximum value at x = …….
2
1/e
1
3
x2-y2+5x+8y-4=0 represents
parabola
Ellipse
hyperbola
none
The solution set of ,when x≠0 and x≠3 is
{1,2}
{1,-1}
{1,5}
{4,-1}
If 2x2-3xy+y2=0 represents two sides of a triangle and lx+my+n=0 is the third side then the locus of incentre of the triangle is
3x2+2xy-3y2=0
2x2+3xy+y2=0
3x2-2xy-3y2=0
2x2-3xy-2y2=0
If the points (0,0),(2,0),(0,4),(1,k) are concyclic then k2-4k=
-1
0
-3
If p1,p2,p3 are the product of perpendiculars from (0,0) to xy+x+y+1=0, x2-y2+2x+1=0, 2x2+3xy-2y2+3x+y+1=0 respectively then ascending order of p1,p2,p3 is
p1,p2,p3
p3,p2,p1
p2,p3,p1
p1,p3,p2
Hydrolysis of NCI3 gives NH3 and X. Which of the following is X ?
HClO4
HClO3
HOCl
HClO2
The spheres of different materials one with double the radius and one-fourth wall thickness of the other are filled with ice.If the time taken for complete melting of ice in the larger radius one is 25 minutes and that for smaller one is 25 minutes,the ratio of thermal conductivities of materials of larger sphere to smaller sphere is:
4:5
5:4
25:8
1:25
When an unknown resistance of 4Ω are connected in the left and right gaps of a meterbridge,the balance point is obtained at 50cm.The shift in the balance point if a 4 Ω resistance is now connected in parallel to the right gap is
14.6cm
34.6cm
16.7cm
66.7cm
A speaks truth in 80%of the cases and B in 60% of the cases. The percentage of the cases of which they likely to contradict each other in stating the same fact is
44%
55%
80%
20%
In the reaction BCl3+PH3→[Cl3B←PH3] the lewis base is
BCl3
PH3
Both PH3 & BCl3
Electron
A black body radiates energy at the rate of E watt/m2 at a high temperature T K. When the temperature is reduced to (T/2) K, the radiant energy is
E/2
2E
E/4
E/16
The number of 4 digited numbers that can be formed using the digits 0,1,2,3,4,5 that are divisible by 5 when repetition is allowed is
200
300
900
2160
The roots of x3-6x2+7x+2=0, one root being 2+√5 are
-8/3,2+√7,2-√72
2,2+√5,2-√5
-1,1+2,1-2
-1+√2,1+√2,1-2
If α,β,γ are the roots of the equation x3+qx+c=0 the equation whose roots are -α-1,-β-1,-γ-1 is
rx3-qx2+1=0
rx3+qx2+1=0
rx3-qx2-1=0
A person standing on the bank of a river observes that the angle of elevation of the angle of elevation of the top of a tree on the opposite bank of river is 600 and when he retires 40 meters away from the tree then the angle of elevation becomes 300, the breadth of river is
20 m
30 m
40 m
60 m
The solution of excot y dx+(1-ex)cosec2ydy=0 is
(ex+1)cot y=c
(ex-1)cot y=c
(2ex-1)cot y=c
(ex-2)cot y=c
If nεN, n is odd then n(n2-1) is divisible by
24
64
17
676
(1+ω)(1+ω2) )(1+ω3)(1+ω4)(1+ω5) (1+ω6)...(1+ω3n)=
23n
22n
2n
The capacity of a parallel plate condenser consisting of two plates each 10 cm square and are separated by a distance of 2mm is (Take air as the medium between the plate):
88.5 x 10-13 F
44.42 x 10-12 F
4.42 x 10-11 F
8.85 x 10-13 F
The distance of (1, -2) from the common chord of x2 + y2 – 5x + 4y – 2 =0 and x2 + y2 – 2x + 8y + 3 =0
The order of decrease in atomic radii for Be;Na;Mg is
Na>Mg>Be
Mg>Na>Be
Be>Na>Mg
Be>Mg>Na
X,Y,Z hydrocarbons molecular formula are CH4, C2H4, C2H2, these three are passed through porcelain tube containing ammonical cuprous chloride. The out coming gases would be
X,Y
Y,Z
X,Z
X,Y,Z
The ratio in which (5,4,-6) divides the line segment joining (3,2,-4),(9,8,-10) is
2:1
1:2
2:3
3:2
If tan (πcos x) = cot (π sinx) then cos(x-π/4) =
± 1/2
± 1/√2
± 1/2√2
(a+2b)2+(aω+2bω2)2+(aω2+2bω)2=
8ab
9ab
11ab
12ab
The electrolytic conductance of 0.01 M solution of acetic acid is 0.000163 Scm-1 at 298k. The % of dissociation of acetic acid at 298K.Given Am0 of acetic acid =390.7 Scm-2/mole at 298K.
4.6
1.63
3.37
4.17
If y=(ax+b/cx+d) then 2y1y3=
y2
y22
3y22
4y22
Under the application of force, a steel wire (Y = 19 x 1010Nm-2) of 5 m in length suffers an elongation of 1 mm. The potential energy stored per unit volume in this process, in joules per m3 is :
1.9 x103
9.5 x 103
3.8 x 103
If B,A, A+B are acute angles, sin(A+B)=12/13, sin B=5/13 then sin A=
119/169
-119/69
169/119
-169/119
If Tr+1 is the term independent of x in (3x-5/x3)8 then r=
4
tan x + tan(x + π/3)+tan(x+2π/3)=3⇒tan3x=
CaCl2+C2H5OH→CaCl2xC2H5OH,in this ‘x’ is
6
The intersection of the sphere x2+y2+z2-3x+3y+4z=8 is the same as the intersection of one of the sphere and the plane
2x-y-z=1
x-y-z=1
x-2y-z=1
x-2y-2z=1
The weight in grams of a non-volatile solute (M.wt:60) to be dissolved in 90 g of water to produce a relative lowering of vapour pressure of 0.02 is
8
10
The equation of the parabola whose axis is parallel to y –axis and passing through (4, 5) (-2, 11), (-4, 21) is
X2 -4x -2y + 10 = 0
X2 – 2x –y +5 = 0
X2 - 4x – 2y + 10 = 0
Y2 – 2x – 3y + 4 = 0
If an error of 0.01 cm is made while measuring the radius 10cm of a circle, then the relative error in the area is
0.02π sq.cm
4.4sq.cm
0.4π cm
0.6π cm
If tan β= n tan α / 1+(1-n)tan2 α, then tan(α - β)=
(1+n)tan α
(1-n)tan α
-(1+n)tan α
–(1-n) tan α
The length of the latus rectum of the parabola 2y2+3y+4x-2=0 is
1/3
3/2
d/dx{x1/x}=
x1/x-2(1+log x)
x1/x-2(1-log x)
1+log x
x1/x-2
A whistle of frequency 540 Hz rotates in a horizontal circle of radius 2 m at an angular speed of 15 rad/s. The highest frequency heard by a listener at rest with respect to the centre of circle (velocity of sound in air = 330 ms-1)
590 Hz
594 Hz
598Hz
602 Hz
If 2 tan A+cot A=tan B, then cot A+2tan(A-B)=
1/2
If x2+y2+2gx+2fy+9=0 represents a circle with centre (1, -3) then radius=
If (2,3,4) is the centroid of the tetrahedron for which (2,3,-1), (3,0,-2), (-1,4,3) are three vertices then the fourth vertex is
(4,5,16)
(3,2,4)
(2,3,4)
(2,2,12)
A rectangular sheet of dimensions 30 cm * 80 cm four equal squares of side x cm are removed at the corners, and the sides are then turned up so as to form an open rectangle box. The value of x, so that the value of the box is the greatest is
20/3
10/3
15/2
5
Let A (4, 7, 8), B(2, 3, 4) and C(2, 5, 7) be the position vectors of the vertices of triangle ABC . The length of the internal bisector of the angle at A is
3/2√34
2/3 √34
1/2 √34
1/3 √34
P(-2, -1) and (0, -3) are the limiting points of a coaxal system of which C= x2+y2+5x+y+4=0 is a member. The circle S= x2+y2-4x-2y-15=0 is orthogonal to the circle C. The point where the polar P cuts the circle S is
(3, 6)
(-3, 6)
(-6, 3)
(6, 3)
The equation cos4x-(a+2)cos2x-(a+3) =0 possesses a solution if
a>-3
a
-3 ≤ a ≤-2
a is any positive integer
A 25 watt,220 volt bulb and a 100 watt,220 volt bulb are connected in series across 440 volt line
only 100 watt bulb will fuse
only 25 watt bulb will fuse
Both bulbs will not fuse
Both bulb will fuse
The centre of the circle passing through the points (0, 0), (1, 0) and touching the circle x2+y2=9 is
(3/2, 1/2)
(1/2, 3/2)
(-1/√2, 1/√2)
(1/2, -√2)
The mass of a balloon with its contents is 15kg. It is descending with an acceleration equal to half that of acceleration due to gravity. If it is to go up with the same acceleration, keeping the volume same, its mass should be decreased by
13 kg
l kg
0.75 kg
0.5 kg
If the sum of the roots of the equation 5x2-4x+2+k(4x2-2x-1)=0 is 6,then k=
13/17
17/13
-17/13
-13/11
A man has 7 relatives 4 women and 3 men.His wife also has 7 relatives 3 women and 4 men.The number of ways in which they can invite 3 men and 3 women so that they both invite three is
485
584
720
468
Let f be an injective function with domain{x, y ,z} and range {1,2,3}such that exactly one of the following statements is correct and the remaining are false. F(x)=1, f(y)≠1, f(z)≠2. The value of f1(1) is
x
y
z
The equation of the chord of the ellipse 2x2+3y2=6 having (1, -1) as its midpoint is
8x+9y-25=0
2x-3y-5=0
x+y-1=0
3x-2y-6=0
If there is an error of 0.05 cm, while measuring the side of equilateral triangles as 5 cm, then the percentage error in area is
2/3
If the first three terms of (1+ax)n are 1,6x,6x2 then (a,n)=
(2/3, 9)
(2/5, 8)
(3/2, 6)
(5/2, 3)
When a monochromatic light of frequency v is incident on a metal, stopping potential is V0. Frequency of the incident light for which stopping potential becomes 2V0 is
V
v+(eV0/h)
2v+(eV0/h)
v-(eV0/h)
9.2 grams of N2O4(g) is taken one liter vessel and heated till the following equilibrium is reached N2O4 (g)⇔2NO2(g).At equilibrium 50% of N2O4(g) is dissociated.The value of Kc is
0.2
0.1
0.4
The total mechanical energy of a harmonic oscillator of A=1m and force constant 200 N/m is 150J.Then
the minimum potential energy is zero
the minimum potential energy is 100J
the minimum potential energy is 50J
the miximum kinetic energy is 150J
The area of the triangle formed by the tangents from (1, 3) to the circle x2+y2-4x+6y+1=0 and its chord of contact is
250√3/37
125√3/37
250√3/17
125√3/17
If the polar of P with respect to the circle x2+y2=a2 touches the parabola y2=4ax, then the locus of P is
y2+2ax=0
y2+3ax=0
y2+ax=0
2y2+ax=0
If the tangent from a point P to the circle x2+y2=1 is perpendicular to the tangent from P to the circle x2+y2=3, then the locus of P is
a circle of radius 2
a circle of radius 4
a circle of radius3
If 2 Sin2x + √3 Cosx+1=0, then θ=
nπ ± 5π/6
2 nπ ± 5π/6
nπ ± 3π/4
2nπ ± 3π/4
The number of ways that all the letters of the word SWORD can be arranged such that no letter is in its original position is
44
32
28
20
Which of the following pair of ions have same paramagnetic moment
Cu2+ , Ti3+
Mn2+ , Cu2+
Ti4+ , Cu2+
Ti3+ , Ni2+
If y=4x-5 is a tangent to the curve y2=px3+q at (2, 3), then
p=2, q=-7
p=-2, q=7
p=-2, q=-7
p=2, q=7
If the lines 3x+y+2=0, 2x-y+3=0, 2x+ay-6=0 are concurrent then a=
7
The equation of the latus rectum of the parbola x2 – 12x – 8y + 52 = 0 is
X = 4
Y = 4
X = 6
Y = 2
The condition for f(x)= x3+px2+qx+r(x R) to have no extreme value, is
p2
2p2
An electron beam moving with a speed of 2x107ms-1 enters a magnetic field of induction 3x10-3T, directed perpendicular to its direction of motion. The intensity of electric field applied so that the electron beam is undeflected due to the magnetic field is
0.66x1010NC-1
12x104NC-1
1.5x104NC-1
6x104NC-1
Two charges of 50 μC and 100 μC are separated by a distance of 0.6m. The intensity of electric field at a point midway between them is
50x106V/m
5x106V/m
10x106V/m
10x10-6V/m
The magnetic oxide of iron is
Limonite
Siderite
magnetite
Haematite
The point of concurrence of the lines (3k+1) x-(2k+3)y+(9-k)=0 is
(1, 1)
(1, -1)
(3, 4)
(-2, 1)
If a= 2i+2j+k, b=i+j, c=3i+4k, d=12i+3j+4k then the descending order pf their magnitudes is
|d, |c|, |a|, |b|
|a, |b|, |c|, |d|
|d, |a|, |c|, |b|
|a, |b|, |d|, |c|
If |a+b|2=|a|2+|b|2 then the angle between a and b is
600
450
1200
When X amperes of current is passed through molten AlCl3 for 96.5 second,0.09g of alumunium is deposited.What is the value of X
10 ampere
20 ampere
30 ampere
40 ampere
If the latus rectum of a hyperbola x2/16-y2/p=1 is 41/2. If eccentricity e=
4/5
5/4
3/4
4/3
The acute angle made by the line joining the points (1, -3, 2), and (3, -5, 1) with the coordinate axes are
cos-1(2/3), cos-1(2/3), cos-1(1/3)
cos-1(3/2), cos-1(2/3), cos-1(2/3)
cos-1(1/3), cos-1(3/2), cos-1(1/3)
The equation of the circle which has both the axes as its tangents and which passes through the point(1,2)
x2+y2-2x+2y-1=0
x2+y2-2x+2y+1=0
x2+y2-2x-2y+1=
x2+y2-2x-2y-1=0
Tangents are drawn from the Point (-2, -1) to the hyperbola 2x2-3y2=6. Their equations are
3x-y+5=0, x-y+1=0
3x+y+5=0, x+y+1=0
3x-y-5=0, x-y-1=0
3x+y-5=0, x+y-1=0
If α,β,γ are the roots of the equation x3-px2+qx-r=0,then α3β3γ3=
pq+3r
pq-3r
p3-3pq+3r
r3
Limiting points of the coaxial system determined by the circles x2+y2+14x-8y-5=0, x2+y2+4x+2y+5=0 are
(2,1),(0,-3)
(-2,-1),(0,3)
(-2,-1),(0,-3)
(0,-3), (2,1)
sin 780 -sin 180 +cos 1320=
The equations of the tangents to the circle x2+y2=16 which are inclined at an angle of 600 to the x-axis is
y=√3x±8
x=√3x±8
2y=√3x-8
2x=√3x-8
If the lines 2x+3y+1=0, 3x+2y-1=0 intersect the coordinate axes in four concyclic points then the equation of the circle passing through these four points is
x2+y2+x-y-1=0
6(x2+y2)+x-y-1=0
x2+y2+6(x-y)-1=0
6x2+6y2+6x-6y-1=0
The values of the parameters a for which the quadratic equations (1-2a)x2-6ax-1=0 and ax2-x+1=0 have at least one root in common are
0,1/2
1/2,2/9
2/9
0,1/2,2/9
If the pairs of lines x2+2axy-y2=0, x2+2bxy-y2=0 are such that each pair bisects the angles between the other pair then ab=
(1+ cos π/10) (1+ cos 3π/10) (1+ cos 7π/10) (1+ cos 9π/10)=
1/4
1/8
1/16
2 Tan-1 1/3+Tan-1 1/7=
π
π/2
π/4
3π/4
If p and q are the lengths of the perpendiculars from the origin on the tangent and the normal to the curve x2/3+y2/3=a2/3, then 4p2+q2 =
a2
2a2
5a2