The minimum value of sin6 x+ cos6 x is
1
3/4
1/4
3/2
The objective and eyepiece of an astronomical telescope are double convex lenses with refractive index 1.5. When the telescope is adjusted to infinity, the separation between the two lenses is 16 cm. If the space between the lenses is now filled with water and again telescope is adjusted for infinity, then the present separation between the lenses is
8 cm
16 cm
24 cm
32 cm
A parallel plate capacitor has a capacitance of 10 micro farads without dielectric. A dielectric of dielectric constant 2 is used to fill exactly half the thickness between the plates. The capacitance in micro farads,now is
10
20
15
13.33
All the three oxygen atoms of ozone are utilized in the oxidation of
K2MnO4
Moist I2
Acidified FeSO4
Acidified SnCl2
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)
none
A 1.0 HP IP motor pumps out water from a well of 30m and fills water tank of volume 2238 litres at a height of 10 m from the ground. The running time of the motor to fill the empty water tank is: (g= 10 ms-2)
5 min
10 min
15 min
20 min
Consider the function f(x)=x sin(1/x),x≠0 and f(0) =0,then
it is continuous for all real values of x
it is discontinuous everywhere
f(x) exists and discontinuous at x=π/2
none of these
The maximum potential that can be measured with a voltameter of resistance 1000Ω is 6V.Resistance that must be connected to measure a potential of 30V with it is
2000Ω in series
12000Ω in series
6000Ω in series
4000Ω in series
I : If the points (2,-1), (5,k) are conjugate with respect to the parabola x2 = 8y then k = 7 II: If the lines 2x + 3y + 12 = 0,x – y + k = 0 are conjugate with respect to the parabola y2 = 8x then k = -12
Only I is true
Only II is true
Both I and II are true
Neither I nor II true
The equation of the tangent to the curve (x/a)2/3+(y/b)2/3 =1 at (a cos3θ, b sin3θ ) is
ax cos θ+by sinθ = a2cos4+b2sin4θ
ax cosθ-by sinθ = a2cos4-b2sin4θ
x/acosθ+y/bsinθ=1
x/acosθ-y/bsinθ=1
If ω is a complex cube root of unity, then sin[(ω10+ω23)π-π/4]=
1/√2
1/2
√3/2
The equation of the circle passing through the points (1, 1), (2, -1), (3, 2) is
x2+y2+2x+3y=0
x2+y2-5x-y+4=0
x2+y2-x-y=0
x2+y2-ax-by=0
If the equation of the hyperbola whose focus is (2, 4), eccentricity is 5 and directrix is 4x-3y+1=0 is 15x2-24xy+8y2+ax+by+c=0 then the ascending order of a, b, c is
a, b, c
b, c, a
c, a, b
c, b, a
An observer is moving away from a sound source of frequency 100 Hz. If the observer is moving with a velocity 49m/s and the speed of sound in air is 330m/s, the observed frequency is
149 Hz
100 Hz
91 Hz
85 Hz
In Ramsden eyepiece, the two planoconvex lenses each of focal length / are separated by a distance 12 cm. The equivalent focal length (in cm) of the eyepiece is
10.5
12.0
13.5
15.5
The radius of one circle is twice the radius of another circle whose centres are (2,0),(1,2) respectively cutting orthogonally.Then the radius of the first circle is
5
3
2
The radius of the circle which touches y-axis at (0, 0) and passes through the point (b, c) is:
|b|/2(b2+c2 )
(b2+c2)/2
(b2+c2)/|2c|
(b2+c2)/|2b|
Which of the following is not tetrahedral
BF4-
NH4+
CO32-
SO42-
If A+C =2B then(cos C - cos A) / (sin A -sin C) is equal to
cot B
cot 2B
tan 2B
tan B
Through the point (2, 3) a straight line is drawn making positive intercept on the coordinate axes. The area of the triangle thus formed is least, when the ratio of the intercepts on the x and y axes is
1:2
3:1
3. 2:3
None
If A,B,C are the minimum values of 2x3-3x2-12x+5, x3-9x2+24x-12,x3-6x2+9x+1 then the ascending order of A,B,C is
A, B, C
B, C, A
C, A, B
A, C, B
x grams of water is mixed in 69 g of ethanol. Mole fraction of ethanol in the resultant solution is 0.6. What is the value of x in grams ?
54
36
180
18
In an experiment on photoelectric emission from a metallic surface, wavelength of incident light is 2xl0-7 m and stopping potential is 2.5 V. The threshold frequency of the metal (in Hz) approximately (charge of electron e= 1.6 x 10-19 C Planck's constant h = 6.67 x 10-34 J-s)
12 x 1015
9 x 1015
9 x 1014
12 x 1013
If α,β are the roots of ax2+bx+c=0;α+h,β+h are the roots of px2+qx+r=0;and D1,D2 the respective discriminants of these equations,then D1:D2=
a2:p2
b2:q2
c2:r2
The locus of middle points of chords of the hyperbola 2x2-3y2=5 which passes through the point (1,-2) is
3x2-y2-x-4y=0
x2-3y2-4x-y=0
3x2-2y2-6x-2y=0
2x2-3y2-2x-6y=0
A (2, 3),B(3, -5) are two vertices of a Δ ABC. C is a point on the line L=3x+4y-5=0. Then the locus of the centroide of Δ ABC is a line parallel to
AB
BC
AC
L=0
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
The distance between the parallel lines 16x2+24xy+ly2+kx-12y-21=0 is
7/√5
2/√5
√7/5
The frequency of a tuning fork A is 2% greater than that of standard fork K.The frequency of another tuning fork B is 3% less than K.When A and B are vibrated together 6 beats per second are heard per second. The frequencies of A and B are
122.4Hz,116.4Hz
132.4Hz,116.4Hz
142.4Hz,116.4Hz
152.4Hz,116.4Hz
The roots of the equation x3 - 3x - 2 = 0 are
-1,-1,2
-1 ,1,-2
-1,2,-3
-1,-1,-2
If (2, 1),(-1, -2),(3, 3) are the midpoints of the sides BC,CA,AB of Δ ABC, then the equation of AB is
x-y=1/2
x+y=1
x-y=9
x=y
If y = sin-1 x-sin-1√1- x2 then d2y/dx2=
2/√1- x2
2x/ (1- x2)3/2
2/ (1- x2)3/2
-2x/ (1- x2)3/2
A magnifying glass is made of a combination of convergent lens of power +20 diopters and a divergent lens of power -4 diopters .If the image is formed atleast distance of distinct vision (25cm), the magnifying power is
4
7
A rectangle ABCD is inscribed in a circle with a diameter lying along the line 3y=x+10. If A=(-6, 7), B=(4, 7) then the area of the rectangle is
80 sq. unit
40 sq. unit
160 sq. unit
20 sq. unit
The points at which the tangent to the circle x2+y2=13 is perpendicular to the line 2x+3y+21=0 is
(2,3)
(2,-3)
(3,-2)
(3,2)
In ΔABC , if a=7, b=7√3 and right angled at C, then c=
2√3
√21
8
14
d/dx{Tan-1(acos x-bsin x/b cos x+a sin x)}=
-1
-1/2
A straight line which makes equal intercepts on positive X and Y axes and which is at a distance 1 unit from the origin intersects the straight line y =2x+3+√2 at (x0, y0). Then 2x0+y0=
3+√2
√2-1
0
In a committee consisting of 25 members, everyone is proficient in Mathematics or Physics or both .Among them 19memers are proficient in mathematics and 16 are proficient in Physics. If a person is chosen at random from the commitee, the probability that he is proficient both in Mathematics and Physics is
0.4
0.8
1.9
0.2
If 2,-2,4 are the roots of ax3+bx2+cx+d=0 then the roots of 8ax3+4bx2+2cx+d=0 are
2,-2,4
1/2,-1/2,1/4
1,-1,2
4,-4,8
A point is moving on y = 4-2x2. The x-co-ordinate of the point is decreasing at the rate of 5 units per second. Then the rate at which y co-ordinate of the point is changing when the point isat (1, 2) is :
5 unit/s
10 unit/s
15 unit/s
20 unit/s
If the sum of the squares of the roots of the equation x2-(sin α-2)x-(1+sin α)=0 is least,then α=
π/4
π/3
π/2
π/6
(sin 4θ)/(sin θ)=
8cos3θ-4cosθ
8sin3θ-4sinθ
4cos3θ-8cosθ
4sin3θ-8sinθ
There are four balls of different colours and four boxes of colours same as those of the balls. The number of ways in which the balls, one each in a box could be placed such that a ball does not go to a box of its own colour is
6
9
24
If 1,ω,ω2 are the cube roots of unity, then (a+bω+cω2)/ (c+aω+bω2) is equal to:
ω
ω2
ω3
If ax2+2hxy+by2=1 then (hx+by)3y2=
k2-ab
ab-h2
The radius of the circle r = √3 sinθ + cos θ is :
If α,β,γ are the angles made by a line with coordinate axes then cos2α+ cos2β + cos2γ+1=
If the points (0,0),(2,0),(0,4),(1,k) are concyclic then k2-4k=
-3
The equation of the normal to the curve y=3x2+4x-6 at (1, 1) is
X+10y-11=0
x-10y+12=0
X+y-9=0
In a ΔABC, cos[(B+2C+3A)/2]+cos[(A-B)/2] is equal to
d/dx{√(1+sin x/1-sin x)}=
1/(1+sin x)
1/(1-sin x)
1/ (1+cos x)
1/ (1- cos x)
Two charges each of 100 micro coulomb are separated in a medium of relative permittivity 2 by a distance of 5cm.The force between them is
1.8x104N
1.8x104dyne
3.6x105N
0.36x105N
If the product of the roots of x3+kx2-3x+4=0 may be -1 then k=
7/2
9/2
-7/2
-9/2
The points (2a,4a), (2a,6a) and ((2+√3)a,5a are the vertices of an
equilateral triangle
obtuse angled triangle
isosceles triangle
acute angled triangle
cos 250 - cos650=
√2 cos 200
√2 sin 200
√3 cos 200
√3 sin 200
1 /3 – 1! + 1 / 4.2! + 1 / 5.3! +………. =
1 /2
1 /4
1/6
1/8
Carbogen to
pure form of carbon
COCl2
mixture of CO and CO2
mixture of O2 and CO2
The position vector of the centroid of the triangle formed by the points 2a+3b, 5a+4b, 2a-b is
3a+2b
3b-2a
4a+7b
5b-2a
Let an=10n / n! for n=1,2,3.................. Then the greatest value of n for which an is the greatest is
11
If tan2 A= 2 tan2 B+1, then cos 2A+ sin2 B=
The value of k such that the lines 2x-3y+k=0, 3x-4y-18=0 and 8x-11y-33=0 are concurrent, is
-7
-20
Chemisorption involves
Bi-layered
zero layered
Uni layered
Multi layered
If n ≥ 2, then 3.C0 – 5.C1 + 7.C2 – ……+(-1)n(2n +3).Cn=
If the lines x+ky+3=0 and 2x-5y+7=0 intersects the coordinates axes in concyclic points then k =
-2/5
-3/5
-5/3
If a number x is selected from natural numbers 1 to 100,then the probability for x+100/x >29 is
41/50
47/50
39/50
37/50
An aeroplane flying at a height of 300 metres above the ground passes vertically above another plane at an instant when the angles of elevation of two planes from the same point on the ground are 600 and 450 respectively. The height of the lower plane from the ground is
100√3
100/√3
50
150(√3+1)
The pairs of lines (a-λ)x2+2hxy+(b-λ)y2=0, ax2+2hxy+by2=0 are
Parallel
Perpendicular
Equally inclined
Such that one pair bisects the angles between the other
4 Tan-1 1/5- Tan-1 1/239 =
π
3π/4
If 3x-2y+4=0 and 2x+5y+k=0 are conjugate lines w.r to the ellipse 9x2+16y2=144 then the value of k is
5/2
-5/2
A catalyst increases the rate of reaction because it :
increases the activation energy
decreases the energy barrier for reaction
decreases the collision diameter
increases the temperature coefficient
The nearest point on the circle x2+y2-6x-4y-12=0 from (-5, 4) is
(1, 1)
(-1, 1)
(-1, 2)
(-2, 2)
The charge required to reduce 1 mole Cr2O7-2 to Cr+3 ions is
3F
3columb
6F
2x6.023x1023e
Which of the following, compounds is the reactant in Rosenmund's reduction
CH3CO2H
CH3CHO
CH3CH2Cl
CH3COCl
If 2x-y+3=0, 4x+ky+3=0 are conjugate with respect to the ellipse 5x2+6y2-15=0 then k=
Identify the reaction for which ΔH ≠ ΔE :
S (rhombic) + O2(g) → SO2(g)
N2(g) + O2(g) →2NO(g)
H2(g) + Cl2(g) → 2HCL(g)
CO(g) +1/2 O2(g) → CO2(g)
The equation of the chord of contact of the point (4, 2) with respect to the circle x2+y2-5x+4y-3=0 is
5x-3y-25=0
8x-2y-11=0
3x+8y-18=0
x-14y-6=0
If a point P moves such that its distances from the point A (1, 1) and the line x+ y + 2 = 0 are equal, then the locus of P is
a straight line
a pair of straight lines
a parabola
an ellipse
The sum of the slopes of the tangents to the parabola y2 = 8x drawn from the point (-2,3) is
-2
-3/2
In the extraction of copper, the slag formed in the blast furnace
CaSiO3
FesSio3
Ca3(PO4)2
MnSiO3
The equation of the normal to the curve 3y2=4x+1 at (1, 2) is
3x+y+5=0
3x+y-5=0
3x-y+5=0
3x-y-5=0
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
Ify=ae-bx cos(cx+d) then y2+2by1+(b2+c2)y=
The period of cos (5x/2) is
4π/5
2π/7
3π/2
4π/3
If the circles x2+y2+2ax+4ay-3a2=0 and x2+y2-8ax-6ay+7a2=0 touch each other externally, the point of contact is
(a, a)
(0, a)
(a, 0)
(-a, 0)
The slope of the tangent to the curve x2+y2 =4 at (√2, √2) is
The straight line joining the points in Argand diagram given by 0+0i and 7+7i has equation
y=x
y=7
x=7
y=0
An eraser weighing 2N is pressed against the black board with a force of 5N. If the co-efficient of friction is 0.4. How much force parllel to the black board is required to slide the eraser upwards
2N
2.8N
4N
4.8N
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)
If a=2i-3j-k, b=i+4j-2k then (a+b)x(a-b)=
20i-6j-22k
-20i+6j-22k
-20i-6j-22k
20i+6j-22k
The conjugate line of 3x+4y-45=0 with respect to x2+y2-6x-8y+5=0 which is perpendicular to x+y=0 is
x-y=8
x-y=2
x-y+2=0
x-y+8=0
(2i-3j+k).(i-j+2k)x(2i+j+k)=
-12
Molar conductivity of a solution 1.26 x 102Ω-1cm2mol-1 ,its molarity is 0.01.its specific conductivity will be
1.26 x 10-5
1.26 x 10-3
1.26 x 10-4
0.0063
The variable line x/a+y/b=1 is such that a+b=10, the locus of the midpoint of the portion of the line intercepted between the axes is:
x+y=10
10x+5y=1
x+y=5
5x+10y=1
If 1,2,3,4 are the roots of the equation x4+ax3+bx2+cx+d=0 then a+2b+c=
-25
The point on the curve y=x2+7x+2 which is closest to the line y=3x+2 is
(-2,8)
(0,2)
(-4,10)
If cos θ+ sin θ=a, then sin 2θ=
a2+1
a2-1
a2
A galvanometer of resistance 100Ω gives full scale deflection with 5mA current.To convert it into a 5 volt range voltmeter,the value of resistance connected in series is
1 mega ohm
10000 ohm
9999 ohm
900ohm
Which of the following is not correct regarding the properties of ionic compounds ?
Ionic compounds have high melting and boiling points
Their reaction velocity in aqueous medium is very high
Ionic compounds in their molten and aqueous solutions do not conduct electricity
They are highly soluble in polar solvents
The least value of (x-a) (x-b) occurs at x=
G.M of a,b
A.M of a, b
H.M of a, b
a+b