If ax2+6xy+9y2+4x+12y+3=0, x2-bxy+y2+2y+2=0, 3x2+11xy+10y2+7x+13y+c=0 represents pairs of straight lines then the ascending order of a,b,c is
a,b,c
b,c,a
c,a,b
b,a,c
The angle between the curves y=x2 and y=4-x2 is
tan-1(6/13)
tan-1(3/4)
tan-1(5/√3)
tan-1(4√2/7)
In Millikans oil drop experiment, an oil drop of radius r charge q falls under the gravity with a terminal velocity Vg and moves up with a terminal velocity Ve in the uniform vertical electric field of intensity E. If η is coefficient of viscosity of air, the charge of oil drop is
4πηr(Vg+Ve)/E
4πηr(Ve-Vg)/E
6πηr(Vg+Ve)/E
6πηr(Ve-Vg)/E
If the position of vectors of P, Q are respectively 5a+4b and 3a-2b then QP=
2a+6b
2a-6b
2a+5b
2a-5b
If y= {(3x-5)2/3(x2+1)3/2/(2x+3)5/2(3x2-1)1/3}then dy/dx=
y[2/3x-5+3x/x2+1-5/2x+3-2x/3x2-1]
y[2/3x-5+3x/x2+1-5/2x+3+2x/3x2-1]
y[2/3x-5-3x/x2+1-5/2x+3+2x/3x2-1]
y[2/3x-5+3x/x2+1+5/2x+3-2x/3x2-1]
In a series LCR a.c circuit R=50Ω and the impedance Z=100Ω. Then the phase difference between the current and applied voltage is (in radius)
π/6
π/4
π/3
π/2
The 7th term of loge(5/4) is
1/7?47
-1/7?47
1/7
-1/7
Let f(x)=1/|x| for |x| ≤1, f(x)=ax2+b for |x|>1. If f is differentiable at any point, then
a=-1/2,b=3/2
a=-1/2,b=1/2
a=1,b=-1
a=1/2,b=1/2
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
1+(1+2)/2!+(1+2+22)/3!+(1+2+22+23)/4!+ ....... =
e2+e
e2
e2-1
e2-e
Through the vertex O of the parabola y2 = 4ax a perpendicular is drawn to any tangent meeting it at P and the parabola at Q.Then OP.OQ =
A2
2a2
3a2
4a2
If the line 7x+2y-8=0, 2x+y-1=0,3x+4y+6=0 are concurrent,then the point of cncurrence is
(2, -3)
(6, 11)
(78/47, -181/47)
(-13/5, 2/5)
The fundamental physical quantities that have same dimensions in the dimensional formula of torque and angular momentum are
mass, time
time, length
mass, length
time, mole
If cos200=K and cosx = 2k2-1,then the possible values of x between 00 and 3600 are
1400
400 and 1400
400 and 3200
500 and 1300
If (x+1)/(2x-1)(3x+1)=A/(2x-1)+B/(3x+1), then 16A+9B is equal to :
4
5
6
8
A certain number of beats are heard when two tuning forks of natural frequencies n1 and n2 are sounded together. The number of beats heard when one of the forks is loaded :
increases
Decreases
Remains constant
may increase or decrease
In how many ways 4 sovereigns be given away, when there are 5 applicants and any applicant may have either 0,1,2,3or4 sovereigns?
60
65
70
75
The point on y=x2+7x+2 which is closest to the line y=3x-3 is
(-2, -4)
(-2, -8)
(2, 8)
(2, 4)
The condition that the pair of tangents drawn from the origin to the circle x2+y2+2gx+2fy+c=0 may be at right angles is
g2+f2+c=0
g2+f2=c
g2+f2=2c
2(g2+f2)=c
The term in the independent of x in the expansion of (3+2x)44, is
4th term
5th term
1st term
7th term
The midpoint of a chord 4x+5y-13=0 of the ellipse 2x2+5y2=20 is
(2, -1)
(-2,1)
(-2, -1)
(2, 1)
Which of the following is not correct
Iodine oxidises sodium thiosulphate to sodium tetrathionate
Sodium thiousulphate is soluble in water
Ozone is used to identify the presence of unsaturation in alkenes
Sodium thiosulphate reacts with iodine to form sodium sulphate
The centre of mass of three particles of masses 1 kg, 2 kg and 3 kg is at (2, 2, 2).The position of the fourth mass of 4 kg to be placed in the system as that the new centre of mass is at (0, 0, 0) is :
(-3,-3,-3)
(-3,3,-3)
(2,3,-3)
(2,-2,-3)
If the number of common tangents of the circles x2+y2+8x+6y+21=0, x2+y2+2y-15=0 are 2,then the point of their intersection is
(8,5)
(8,-5)
(-8,-5)
(-4,-3)
(a+b).a’+(b+c).b’+(c+a).c’=
0
1
2
3
The radiation emitted by a star A is 10,000 times that of the sun. If the surface temperatures of the sun and the star A are 6000 K and 2000 K respectively, the ratio of the radii of the star A and the sun is:
300 : 1
600 : 1
900: 1
1200 : 1
The equation to the locus of point of intersection of the line y-mx=√(4m2+3), my+x = √(4+3m2) is
x2+y2=12
x2+y2=7
x2+y2=1
x2+y2=4
The domain of the function √1/cos |x| is
R-{π/2}
R-{π/2, 3π/2}
R-{(2n+1)π/2: n? Z}
R-{nπ: n? Z}
A whistling engine is approaching a stationary observer with a velocity of 110m/s. The velocity of sound is 330m/s. The ratio of frequencies as heard by the observer as the engine approaches and recedes is
2:1
3:6
4:1
4:3
A wire carrying a current of 140 ampere is bent into the form of a circle of radius 6cm.The flux density at a distance of 8 cm on the axis passing through the centre of the coil and perpendicular to its plane is(in wb/m2(approximately))
πx10-4
2 πx10-4
π/2 x 10-4
1/ πx10-4
If α,β,γ are the roots of x3-px+q=0, then α6+β6+γ6=
-2p3-3p3
-2p3+3p3
2p3-3p3
2p3+3p3
A charge of 4 μC is placed in a uniform electric field of intensity 100N/C. The force acting on the charge is
25x106N
4x10-4N
4x104N
25x10-6N
(tan 230+ tan220)/(1- tan 230 .tan220)=
-1
75% of first order reaction is completed in 32 minutes 50% of the reaction would have been completed in
24 min
16 min
18 min
The roots of 2x4+x3-6x2+x+2=0 are
1,1,-2,-1/2
1,1±√3i/2, 3±√5/2
1,-1,-2,-1/2,3,1/3
2,1/2,3,1/3
If the locus of mid points of the chords of the parabola y2=4ax which passes through a fixed point (h, k) is also a parabola then its length of latusrectum is
a
3a
7a/2
2a
There are 25 st5amps numbered from 1 to 25 in a box. If a stamp is drawn at random from the box, the probability that the number on the stamp will be a prime number is
7/25
8/25
9/25
6/25
If P (A) =0.4, P (B) =0.5, P(C) =0.6, P (A∩B) =0.2, P (B∩C) =0.3, P (C∩A) =0.25, P (A∩B∩C) =0.1then P (AUBUC) =
0.1
0.9
0.85
0.8
The number of tangents that can be drawn from (6, 0) to the circle x2+y2-4x-6y-12=0 are
If f=x2yz+y2zx+z2xy then fxyz=
2x
2(x+y+z)
An aircraft gun can take a maximum of three shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first, second and third shot are 0.5,0.4,0.3 respectively. The probability that the gun hits the place is
0.79
0.488
0.6976
0.784
Match the appropriate pairs from Lists I and II: List-I List-II 1.NItrogen molecules A.continuous spectrum 2.Incandescent solids B.Absorption spectrum 3.Fraunhoffer lines C.Band spectrum 4.Electric arc between iron rods D.Emission spectrum
1-C,2-A,3-B,4-D
1-B, 2-A, 3-D, 4-C
1-D, 2-A, 3-B, 4 -C
1-A, 2-C, 3-D, 4 -B
If α,β are the roots of x2-p(x+1)-c=0 then (α2+2α+1/α2+2α+c )+(β2+2β+1/β2+2β+c)=
A potentiometer wire of length 100 cm has a resistance of 10 Ω. It is connected in series with a resistance and a cell of emf 2V and of negligible internal resistance. A source of emf 10 mV is balanced against a length of 40 cm of the potentiometer wire. The value of external resistance is:
790Ω
890Ω
990Ω
1090Ω
The equation x2 - 3xy + λy2 + 3x - 5y + 2 = 0, where λ is a real number, represents a pair of straight lines. If θ is the angle between these lines then cosec2 = θ
9
10
100
P and Q are two points on the line x-y+1=0. If OP=OQ=6 then length of median of Δ OPQ through O is
1/2
1/√2
none
For the estimation of sulphur by Carius method, the organic compound is heated in Carius tube with
BaCl2/Fuming HNO3
BaCl2/H2SO4
AgCl/HCl
CaCl2/HCl
The maximum value of x4+3x3-2x2-9x+6 is
11
3/8
12
Bag A contains 3 white and 2 black balls. Bag B contains 2 white and 4 black balls. One bag is selected at random and a ball is drawn from it. The probability that it is white is
52/77
76/155
89/198
7/15
The equation of the circle passing through the point of intersection of the circles x2+y2-3x-6y+8=0, x2+y2-2x-4y+4=0 and touching the line x+2v=5 is
x2+y2-x-2y=0
x2+y2+4=0
138 g of ethyl alcohol is mixed with 72 g of water. The ratio of mole fraction of alcohol to water is
3:4
1:2
1:4
1:1
The equation of the circle passing through (-7, 1) and having centre at (-4, -3) is
x2+y2+8x+6y=0
x2+y2+4x-16y-101=0
x2+y2-4x-6y=0
x2+y2=5
If the lines 2x + 3y + 12 = 0,x – y + 4k = 0 are conjugate with respect to the parabola y2 = 8x then k =
7/2
-12
-2
If the circles x2+y2+2x+c=0 and x2+y2+2y+c=0 touch each other then c=
1/4
If A+B+C= 1800 then cos A+cos B+ cos C=
1+4sin A/2sin B/2 sin C/2
1+4 cos A/2cos B/2sin C/2
1+ 4 cos A/2 cos B/2 cos C/2
1+ 4cos A/2sin B/2 cos C/2
The area of the triangle whose vertices are (a,θ),(2a,θ+π/3) and (3a,θ+2π/3) is (in sq.unit)
7√3a2/4
5√3a2/4
3√3a2/4
√3a2/4
A 20F capacitor is charged to 5V and isolated. It is then connected in parallel with an uncharged 30F. The decrease in the energy of the system will be
25 J
100 J
125 J
150 J
If α,β are the roots of x2+ax-b=0 and γ,δ are the roots of x2+ax-b=0 then (α-γ)(β-γ)(α-δ)(β-δ)=
b2
2b2
3b2
4b2
The roots of x4-12x3+34x2-12x+1=0 are
2±√3, 3±2√2
2±√3,4±√15
-1,-2,-1/2,√3±√5/2
A quantity of heat Q is supplied to a mono atomic ideal gas which expands at constant pressure. The fraction of heat that goes into work done by the gas is :
2/5
3/5
2/3
If (1, a), (b, 2) are conjugate points with respect to the circle x2 + y2 = 25, then4a + 2b is equal to :
25
50
150
The angle between the curves y2=x, x2=y at (1, 1) is
tan-3/4
tan-4/3
If cosec θ-sin θ=m, sec θ-cos θ=n then (m2n)2/3+(mn2)2/3=
Circum centre of the ?le formed by the points (2, -5), (2, 7), (4, 7) is
(1,3)
(-2, -3)
(3, 1)
(7, 5)
The point on the parabola y2 = 36x whose oridinate is three times its abscissa is
(4, 12)
(-4, 12)
(4, -12)
(-4, -12)
The area of the triangle formed by (a, a), (a + 1, a + 1), (a + 2, a) is
a3
√2
One number is selected at random from 1 to 100. The probability that it is a prime number is
-1/4
1/8
5/14
The area bounded by the curve y=x(x-1)2,y-axis and the line y=2 is
10/3
5/3
20/3
The number of real solutions of Tan1 x+Tan 1 (1/y) = Tan1 3 is
(1,4)
(4,13)
(2,1)
none of these
A set contains (2n+1) elements. The number of subsets of the set which contain more than n elements is
2n
2n+1
2n-1
22n
If A=sin2θ + cos4θ, then for all values of θ, where
1 ≤ A ≤ 2
(3/4) ≤ A ≤ 1
0 ≤ A ≤ 1
(1/4) ≤ A ≤ (1/2)
The magnitude of the force between parallel conductors, each of length 110 cm,carrying a current of 10A and separated by a distance of 10 cm is
22x10-5N
33x10-5N
44x10-5N
55x10-5N
If x4-6x3+3x2+26x-24 is divided by x-4 then the quotient is
x3-2x2-5x+6
x3-2x2+5x+6
x3+2x2-5x+6
Let v- = 2i- + j- - k- and u- = i- + 3k- . If u is any unit vector then the maximum value of the scalar triple product [u- v- w-] is
√10 + √6
√59
√60
The complex numbers sin x+ i cos 2x- i sin 2x are conjugate to each other for
x=nπ
x= (n+1/2) π
x=0
The chemical formula of 'tear gas is :
COCl2
CO2
Cl2
CCl3NO2
The angle of minimum deviation when light is incident at an angle of 450 on the refracting faces of an equilateral prism of refractive index 1.414 is
400
300
450
500
(√2+1)6+(√2-1)6=
198
992
99
The equation of the incircle of triangle formed by x=0,y=0 and (x/3)+(y/4)=1 is
x2+y2-4x-4y+4=0
x2+y2-2x-2y=0
x2+y2-2x-2y+1=0
x2+y2-4x-4y=0
The area bounded by y=cos x,y=x+1,y=0 is
3/2
5/2
If the line 3x - 2y + 6 = 0 meets X-axis and Y-axis respectively at A and B, then theequation of the circle with radius AB and centre at A is :
x2 + y2 + 4x + 9 = 0
x2 + y2 + 4x - 9 = 0
x2 + y2 + 4x + 4 = 0
x2 + y2 + 4x - 4 = 0
If the tangent at P on the circle x2+y2=a2 cuts two parallel tangents of the circle at A and B then PA. PB=
a2
If sinA + sinB = l, cosA - cosB = m, then the value of cos(A - B) =
(l2-m2)/(l2+m2)
(l2+m2)/(l2-m2)
2lm/(l2+m2)
2lm/(l2-m2)
The value of a such that x3+3ax2+3a2x+b is increasing on R-{-a} are
1, 2
a, b are any real numbers
-1, 2
±1
If cot θ=8/15 and θ does not lie in the first quadrant, then cos(300+ θ) +sin(450- θ)+cos(1200+ θ)=
(1/34)(23+7√3+7√2)
(1/34)(23+7√3-7√2)
(1/34)(23-7√2+7√3)
(1/34)(23-7√3-7√2)
Which of the following does not participate in carbylamine reaction?
KOH
Ethanal
Chloroform
Aniline
The Kc for the reaction A+B↔C is 4 and Kc for 2A+D↔C is 6. The value of Kc for C+D↔2B is
0.67
0.375
2.7
1.5
The area of the region bounded by the curves y=x2+2,y=x,x=0 and x=3 is
4/3 sq.unit
2/3 sq.unit
21/2 sq.unit
27 sq.unit
Coefficient of x10 in the expansion of (2 + 3x) e-x is :
-26/(10!)
-28/(10!)
-30/(10!)
-32/(10!)
sin θ+ sin (1200+ θ)+sin (θ - 1200)=
3/4
The equation of the bisector of the obtuse angle between the lines x-y+2=0,7x+y+1=0 is
2x-6y+9=0
8x-4y+11=0
2x+6y-9=0
8x+4y-11=0
A car of mass 400 kg and travelling at 72 kmph crashes into a truck of mass 4000 kg and travelling at 9 kmph, in the same direction. The car/bounces back at a speed of 18 kmph.The speed of truck after the impact is
9 kmph
18 kmph
27 kmph
36 kmph
If the slope of one of the lines 2x2+3xy+λy2=0 is 2 then the angle between the lines is
The length of the latus rectum of the parabola x2 + 4x – 8y + 28 = 0 is
16
If sinh x= cos θ and sin θ=2/3 then cosh x=
√13/3
√14/3
The point which divides the line segment joining the points( 1,-1,2), (2,3,7) in the ratio -2:3 is
(9,-8)
(13/7, 2/7, 15/7)
(-3/2, ½ ,9)
(4,-7,6)
The locus of the point of intersection of two tangents to the parabola y2 = 4ax which make an angle 300 with one another is
(x + a)2 = 3(y2 – 4ax)
(x + a)2 = y2 -4ax
3(x + a)2 = Y2 – 4ax
X + a = 0
A five digit number is formed by using the digits 0, 1,2,3,4 and 5 without repetetion.The probability that the number is divisible by 6 is
9/50
10/39
1/16
A gun is aimed at a target in line with its barrel. The target is released and allowed to fall under gravity, at the instant, the gun is fired. The bullet will :
pass above the target
pass below the target
hit the target
certainly hit the target
The number of sigma and pi bonds in peroxodisulphuric acid are, respectively
9 and 4
11 and 4
4 and 8
4 and 9