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The number of turns in primary and secondary coils of a transformer is 50 and 200. If the current in the primary coil is 4 A, then the current in the secondary coil is

If cos 2θ+cos 8θ= cos 5θ then θ=

A system absorbs 10kJ of heat and does 4kJ of work. The internal energy of the system

If f : R --->R and g : R ---> R are defined by f(x) = x -[x] and g(x) = x- [x] for x belongs to R where [x] is the greatest integer not exceeding x then for every x belongs to R f(g(x)) is equal to

The dispersive powers of the materials of two lenses forming an achromatic combination are in the ratio of 4:3. Effective focal length of the two lenses is +60 cm then the focal lengths of the lenses should be

Sin (2Tan-13/4) =

What is the quantity of electricity (in Coulombs) required to deposit all the silverfrom 250 mL of 1 M AgNO3 solution

The value of x, where x > 0 and tan ( sec-1(1/x ) )= sin ( tan-1 2) is

If a tangent to the circle x2+y2+4x-4y+4=0 makes equal intercepts on the coordinate axes then the equation of that tangent is

(tan 230+ tan220)/(1- tan 230 .tan220)=

The equation of the circle whose center lies on the x-axis and which passes through the points (0,1),(1,1) is

If a gas contains only three molecules that move with velocities of 100,200,500 ms-1.What is the rms velocity of that gas in ms-1

The locus of the midpoints of chords of the circle x2+y2=25 which touch the circle (x-2)2+(y-5)2=289 is

The roots of the equation 2(a2+b2)x2+2(a+b)x+1=0 are

If a=2i-j+3k, b=-i+4j-2k, c=i+j+7k and xa+yb=c then (x, y)=

In ΔABC , if A=750, B=450, C=√3, then b=

Two parallel sides of a rectangle are being lengthened at the rate of 2 cm/sec while the other two sides are shortened in such a way that the area of the rectangle is 50sq. cm. the rate of change of the perimeter when the length of an increasing side 5 cm is

A sonometer consists of two wires of same material whose radii are in the ratio2:3.The tension in thick wire is 4 times the tension in thin wire.If V is velocity of transverse were in thin wire,then the velocity of transverse wave in thick wire is

The equation of the normal at a point hose eccentric angle is 3π/2+θ to the ellipse x2/9+y2/4=1 is

If the product of two of 6x4-29x3+40x2-7x-12=0 is 2 then the roots are

x2+y2+kx+(1-k)y+5=0 represents a circle with radius less than or equal to 5.Then number of integral values of ‘k’ are

The condition that the lines joining the origin to the points of intersection of x/a+y/b=1, 5(x2+y2+bx+ay)=9ab are at a right angles is

During electrolytic reduction of aluminia,the reaction at cathode is

If n=3m then the coefficient of xn in the expansion of log(1+x+x2) is

The equation of the circle passing through the points (1, 1), (2, -1), (3, 2) is

What is the correct order of occurrence (% by weight) in air of Ne, Ar and Kr ?

If A, B, C, D are the lengths of normals to the curves 1.y=4x2 at (-1, 4) 2. Y=x3+1 at (1, 2) 3. Y=x3/2-x at (1,1) 4. 2x2+3xy-2y2=8 at (2, 3) then the ascending order of A,B,C,D is

If P(x)is a polynomial of 3rd degree and P’’(1)=0, P’’’(1)=6 then P’’(0)=

A body is thrown vertically upward with an initial velocity u reaches maximum height in 6 sec.The ratio of distance travelled by the body in the first and seventh second is :

The points (k,2-2k), (1-k,2k) and (-4-k,6-2k)are collinear. Then k =

A whistle of frequency 540Hz rotates in a horizontal circle of radius 2m at an angular speed of 15rad/s. The highest frequency heard by a listener away from the circle at rest with respect to the centre of circle (velocity of sound in air=330m/s)

AB,AC are tangents to a parabola y2= 4ax. If l1,l2,l3 are the lengths of perpendiculars from A,B,C on any tangent to the parabola,then

The orthocenter of the triangle formed by (0, 0), (3, 1), (1, 3) is

If the points (0,0) (3,√3), (p,q) form an equilateral triangle and q1,q2 ,are the two values of q, then q1+q2 =

If f={(a, 1), (b, -2), (c, 3)}, g={(a, -2), (b, 0), (c, 1)} then f2+g2=

7/5(1+1/?102 +1.3/1.2.1/104 +1.3.5/1.2.3.1/106 +...........∞)

A tuning fork vibrating with a sonometer wire of length 20cm produces 5 beats per second. The beat frequency does not change if the length of the wire is changed to 21 cm. The frequency of the tuning fork must be

The liquids at temperature 600C and 300C respectively have masses in the ratio 3 : 4 and their specific heats in the ratio 4 : 5. If the two liquids are mixed, the resultant temperature is:

If α,β are the roots of 3x2-5x+7=0 then α3+β3=

A motor car approaching a cliff with a velocity of 90 kmph sounds the horn and the echo is heard after 20 seconds.Assuming the velocity of sound in air to be 332m/s,the distance between the car and cliff when the horn is sounded is

The harmonic conjugate of (7,5) w.r.t. (4,2), (9,7) is

A flint glass prism is of refracting angle 50.Its refractive index for C line is 1.790 and for F line is 1.805.The angular dispersion of C and F lines is

If 2,3 are roots of 2x3+mx2-13x+n=0 then the other root is

If α,β,γ,δ are the roots of x4+px3+qx2+rx+s=0 then Σα2βγ

L and L’are ends of the latus rectum of the parabola x2 = 6y. the equation of OL and OL’ where O is the origin is

If x=-5+4i then x4+9x3+35x2-x+4=

H3O++OH-→2H2O

The locus of the centre of circle which touches the line x cos α+y sin α=p and circle (x-a)2+(y-b)2=c2 is

The equation of the normal to the curve 2x2-xy+3y2=18 at (3, 1) is

If the length of the tangets from two points A, B to a circles are 6, 7 respectively. If A, B are conjugate points then AB=

If an error of 0.02cm is made while measuring the radius 10cm of a sphere, then the error in the volume is

(2 cos θ-1) (2 cos 2θ-1) (2 cos 4θ-1) (2 cos 8θ-1)=

The equation of wave is y=10 cos2π(t/0.02-x/10),where ‘t’ is in seconds an x in cm.The phase difference between two points separated by a distance of 5 cm at any instant is

If the rate of change in the radius of a circle is 0.02 cm/sec, then the rate of change in the area of the circle when the radius is 5 cm is

The equation of the line passing through the point (-2, 1) and having intercepts whose product is 1 is

If x cos α= y cos(2π/3+ α)= z cos(4π/3+ α),then xy+yz+zx=

Two waves of wavelengths 2m and 2.02m respectively moving with the same velocity superpose to produce 2 beats/s.The velocity of the wave is

d/dx{sin2((1-x2)/(1+x2))}

The area bounded by the curve y=x(x-1)2,y-axis and the line y=2 is

A tangent to y2=7x is equally inclined with the coordinate axes.Then the area of the triangle formed by the tangent with the coordinate axes is

(1-ω)(1-ω2) (1-ω4) (1-ω5)(1-ω7) )(1-ω8)=

The two circles (x-a)2+(y-b)2=c and (y-b)2+x2=4c have only one real common tangent then

A solution of concentration "C" g equiv/litre has a specific resistance R, The equivalent conductance of the solution is

sin2200+ sin21000 +sin2 1400=

The straight line joining the points in Argand diagram given by 0+0i and 7+7i has equation

The molar capacity(Cp)of water at constant pressure is 75 J.K-1.mol-1.The increase in temperature (in K) of 100 g of water when 1 K.J. of heat is supplied to it is

If the length of the tangent from (2, 3) to circle x2+y2+6x+2ky-6=0 is equal to 7. Then k=

(13/1)+(13+23/1+3)+(13+23+33/1+3+5)+….. n terms

The area bounded by the curve xy=4,x-axis and the ordinates x=2,x=5 is

In the expansion of (1-2x+3x2)/(1-x)2coefficient of x20 is

If the tangents at (3, -4) to the circle x2+y2-4x+2y-5=0 w.r.t the circle x2+y2+16x+2y+10=0 in A and B, then the midpoint of AB is

The number of ways in which 5 boys and 4 girls can sit in a row so that all the girls come together and 2 particular girls never be together is

A compound microscope has an objective of focal length 4mm and an eye piece of focal length 25 mm. The objcetive produces a real image at a distance of 180mm. If the eye pieces is in normal adjustment the magnification is:

The equation of the latus rectum of the parbola x2 – 12x – 8y + 52 = 0 is

If [cos(θ1-θ2)/ cos(θ1+θ2)]+ [cos(θ3+θ4)/ cos(θ3-θ4)] =0, then tan θ3tan θ4=

Equation of the tangent line at y=a/4 to the curve y(x2+a2)=ax2 is

If α,β,γ are the roots of x3+x2+2x+3=0 then the equation whose roots β+γ,γ+α,α+β is

18 guests have to be seated half on each side of a long table. 4 particular guests desire to sit on one particular side and 3 others on the other side. Determine the number of ways in which the sitting arrangements cn be made

A lot consists of 12 good pencils, 6 with minor defects and 2 with major defects. A pencil is drawn at random. The probability that this pencil is not defective is

sin θ+ sin (θ + 1200)- sin (1200- θ)=

Coefficient of x4 in [(1-3x)2/(1-2x)] is

The quadrilateral formed by the pairs of lines 6x2-5xy-6y2=0, 6x2-5xy-6y2+x+5y-1=0 is

The frequency of a tuning fork x is 5% greater than that of a standard fork of frequency K.The frequency of another fork y is 3% less than that of K.When x and y are vibrated together 4 beats are heard per second.The frequencies of x and y are

4(cos3 100 +sin32 00) =

The points (-1, 5), (-2, 3), (5, 7), (6, 9) taken in order form

The value of the series cos 120 + cos 840 + cos 320 + cos 1560 is :

If x is very small, so that x4 and higher powers of x are neglected then √(x2+16)-√(x2+9)=

A bag contain 6 white and 4 black balls. A fair die is rolled and a number of balls equal to that appearing on the die is chosen from the bag at random. The probability that all the balls selected are white is

One ticket is selected at random from 100 tickets numbered 00,01,02,...99. Suppose A and B are the sum and product of the digits found on the ticket. Then P(A=7 | B=0) is given by

If the normal at ‘θ’ on the hyperbola x2/a2-y2/b2=1 meets the tansverse axis at G, the AG, AG’=

sin 2α+ sin2β+sin 2γ- sin 2(α+β+γ)=

sin4 π/8+ sin4 3π/8+ sin4 5π/8+ sin4 7π/8=

If 4l2-5m2+6l+1=0, then the line lx+my+1=0 touches the circle

If cot θ+ tan θ=m, sec θ -cos θ=n, then (m2n)2/3-(mn2)2/3=

The number of ways in which an examiner can assign 30 marks to 8 questions giving not less than 2 marks to any question is

'Natalite' is used as

The derivative of (log x)xw.r.to x is

In ΔABC, if A=900 then r2 +r3 =

The modules of (3+2i)(2-i)/ (1+i) is

Assertion (A) : At 300 K,kinetic energy of 16 g of methane is equal to the kinetic energy of 32 g of oxygen. Reason (R) : At constant temperature,kinetic energy of one mole of all gases is equal. The correct answer is:

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