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Two tangents are drawn from the point (-2, -1) to the parabola y2=4x. if α is the angle between these tangents then tan α=

A box contains 6 tickets. Two of the tickets carry a prize of Rs. 5/-each, the other four a prize of Rs. 1/- if one ticket is drawn. The mean value of prize is

The equation of the line joining the points represented by 2-3i and -3+4i in the Argand plane is

The derivative of Tan-1√(1+x2)-1/x w.r.to Tan-12x√(1-x2)/(1-2x2) at x=0 is

In ΔABC , if a=7, b=7√3 and right angled at C, then c=

If A,B are acute angles, tan A=5/12, cos B=3/5, then cos (A+B)=

d/dx{Tan-1(x/1-√1-x2)}=

If A+B+C=1800 then sin A+sin B+sin C=

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

The equation of trajectory of a projectile is y = 10x - (5/9) x2. If we assume g =10 ms-2, the range of projectile (in meter) is

A pipe having an internal diameter ‘D’ is connected to anther pipe of same size. water flows into the second pope through ‘n’ holes, each of diameter ‘d’. If the water in the first pipe has speed ‘V’, the speed of water leaving the second pipe is

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

A moving electron has 4.55 x 10-25 joules of kinetic energy. The wavelength of the electron is (mass = 9.1 x 10-31 kg and h = 6.6 x 10-34 kg m2 sec-1)

The equation ax2+bx+c=0 (a,bR) and x3-2x2+2x-1=0 have two roots common.Then a+b must equal to

If the points (0,0), (2,0), (0,4), (1,k) are concyclic then k2-4k=

If a=4i+6j and b=3j+4k then the vector form of the component of a along b is

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

Suppose E and F are two events of a random experiment. If the probability of occurrence of E is 1/5 and the probability of occurrence of F given E is 1/10, then the probability of non-occurrence of at least one of the events E and F is :

if f(x)=a2x-a-2x/a2x+a-2x, then f(x) is

If the roots of (3m+1)x2+2(m+1)x+m=0 are equal then m=

tan 750- tan 300- tan 750. tan 300=

The equation Sin-1 x- Cos-1 x=Cos-1 (√3/2) has

The equation of the auxiliary circle of x2/16-y2/25=1 is

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

If p=(2, 1, 3), q=(-2, 3, 1), r=(3, -2, 4) and j is the unit vector in the direction of y-axis then (2p+3q-4r). j=

The solution set of (5+4cosθ)(2cosθ+1) = 0 in the interval [0,2π],is

If α,β,γ are the roots of x3-px2+qx-r=0 then α4+β4+γ4=

The total number of real tangents that can be drawn to the ellipse 3x2+5y2=32 and 25x2+9y2=450 passing through (3, 5) is

Axes are coordinate axes and area of maximum rectangle inscribe in the ellipse is 16 and e= √15/4 then equation of ellipse

What is the hybridization state of the central atom in the conjugate acid of NH3?

If the expression x2-(5m-2)x+(4m2+10m+25)=0 can be expressed as a perfect square,then m=

If 5x2+λy2=20 represents a rectangular hyperbola, then λ is equal to

In a parallelogram, the ends of one diagonal are (3, -4) and (-6, 5). If the second diagonal has one end at (-2, 1) then its other end is

How many different combination of 5 can be formed 6 men and 4 women on which exact 3 men and 2 women serve

If x = sint; y = sin pt then (1-x2) (d2y/dx2) -x(dy/dx) +p2y =

The effect due to uniform magnetic field on a freely suspended magnetic needle is as follows :

If A=(3, 2, 5), B=(3, 4, 5) and C=(3, 4, 7) are the vertices of a triangle ABC, then its circumcentre is

If the area of the triangle formed by the points (1,2), (2,3), (x,4) is 40sq.unit, then x is

If α , β, γ are the roots of x3 + 2x2 - 3x - 1 = 0 then α-2 + β-2 + γ-2 =

The orthocentre of triangle formed by the lines x + 3y = 10 and 6x2 + xy - y2 = 0 is:

If u=(ax+by)2-(x2+y2) and a2+b2=1 then uxx+uyy=

In a full wave rectifier output is taken across a load resistor of 800ohm.If the resistance of diode in forward biased condition is 200 ohm,the efficiency of reflection of rectification of ac power into dc power is

The derivative of (ax+b)cx+d w.r.to x is

If m tan(θ-300)= n tan(θ+1200), then cos 2θ=

When a wire of length 10 m is subjected to a force of 100 N along its length, the lateral strain produced is 0.01 x 10-3 m. The Poisson's ratio was found to be 0.4. if the area of cross-section of wire is 0.025 m2, its Young's modulus is

If the area of the triangle formed by the points (10, 2), (-3, -4) and (x, 1) is 5 square units, then the value of x is

The value of k so that 3x4+4x3+2 x2+10x+k is divisible by x+2 is

If 23+43+63+….+(2n)3=kn2(n+1)2, then k=

The line 4x + 6y + 9=0, touches the parabola y2=4x at the point

The solution set of ,when x≠0 and x≠3 is

The domain of Cos-1 (2/2+sinx) in [0,2π] is

If n is a positive integer, then value of (3n+2)nC0+(3n-1) nC1+(3n-4) nC2+……..+ 2(nCn) is

(cos θ+ sin θ)2+(cos θ- sin θ)2 =

The heat of formation of SO2(g) is -297.8 kJ mol-1.The enthalpy change in the decomposition of 1 mole SO2(g) to its constituent elements is

The domain of √(x-1)(x-2)(x-3) is

The lines (a+b) x+(a-b)y=2ab, (a-b)x+(a+b)y=2ab,x+y=0 form an isosceles triangle whose vertical angle is

The roots of 6x6-25x5+31x4-31x2+25x-6=0 are

(l1,m1,n1) and (l2,m2,n2) are D’rs of two lines inclined at an angle 1200 then D.C’s of the line bisecting the angle between them are

If 3x2+8xy-ky2+29x-3y+18 is resolvable into two linear factors then k=

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 probability that a randomly chosen number from the set of first 100 natural numbers is divisible by 4 is

The lines 2x+3y = 6,2x+3y = 8 cut the x-axis at A,B respectively.A line L=0 drawn,through the point(2,2) meets the x-axis at C in such a way that abscissa of A,B and C are in the arithmetic progression.Then the equation of L=0 is

If a circle cuts the parabola y2 = 4ax in four points, then the algebraic sum of oridinates of the four points is

The coil in a MCG has an area of 4cm2 and 500 turns.The intensity of magnetic induction is 2T.when a current of 10-4A is passed through it,the deflection is 200.The couple per unit twist is(N-m)

If p and q are the coefficients of xn in (1+x)2n-1 and (1+x)2n respectively then 2p=

The points at which the tangent to the circle x2 + y2=13 is perpendicular to the line 2x + 3y +21=0 is:

The lengths of the chords of the circle x2+y2-2x-6y-15=0 which make an angle of 600 at (1, 3) and the locus of the midpoints of all such chords are

Two equal sides of an isosceles triangle are given by equation 7x-y+3=0 and x+y-3=0 and its third side passes through the point (1, 0).The equation of the third side is

If α,β,γ,δ are the roots of the equation 3x4-8x3+2x2-9=0 then

A right angled isosceles triangle is inscribed in a circle x2+y2-4x-2y-11=0.Then the length of the side of the triangle is

(1+ω)(1+ω2) )(1+ω3)(1+ω4)(1+ω5) (1+ω6)...(1+ω3n)=

The locus of the midpoint its of chords of x2/a2-y2/b2=1 which pass through the focus (ae, 0) is

The curve y=a2+bx has minimum at (2, -1) on it. Then (a, b)=

The number of non-zero terms in the expansion of (1+3√2x)9+(1+3√2x)9is equal to:

An organic compound X on treatment with pyridium dichromate in dichloromethane gives compound Y.Compound Y reacts with I2 and alkali to form idoform.The compound X is

The vectors (1, -1, 1), (0, 1, 1), (0, 0, 2) are

The equation of the straight line passing through the intersection of x+2y-19=0, x-2y-3=0 and at a distance of 5 unit from (-2, 4) 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

Let P be a point on the circle x2+y2=9, Q a point on the line 7x+y+3=0, and the perpendicular bisector of PQ be the line x-y+1=0. Then the coordinates of P are

The distance of (1,-2) from the common chord of x2+y2-5x+4y-2=0 and x2+y2-2x+8y+3=0 is

If y= acos (log x)+b sin (log x) then x2y2+xy1+y=

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

The equation whose roots are the Arithmetic mean and twice the H.M between the roots of the equation x2+ax-b=0 is

The angle between the curves xy=4 and x2-y2=15 at the point (-4, -1) is

The derivative of cot-1(cosec x-cot x) w.r.to x is

When a positively charged particle enters a uniform magnetic field with uniform velocity, its trajectory can be : 1) a straight line 2) a circle 3) a helix

If the product of the roots of the equation 5x2-4x+2+k(4x2-2x-1)=0 is 2,then k=

If A and B are square matrices of size n x n such that A2 – B2 = (A – B)(A + B), then which of the following will be always true

The angle of elevation of the summit of a mountain at a point A is 450. After walking 200 mt from A towards the mountain along a road included at 150, it is observed that the angle of elevation of the summit is 600. The height of the mountain is

3 red and 4 white balls of different sizes are arranged in a row at random. The probability that no two balls of the same colour are together is

By substituting y=vx,the transformed equation of (x+y)dx+(y-x)dy=0

Two cards aredrawn from a pack. The probability that one of them is a club and the other is not a club is

In the reaction AlCl3+Cl-→[AlCl4]-,AlCl3 acts as

Let a and b be nonzero reals such that a .Then the equation of the line passing through the origin and point of intersection of x/a+y/b=1 and x/b+y/a=1 is

The equation of the line passing through the point of intersection of the lines x+y-5=0, 2x-y+4=0 and having intercepts numerically equal is

In a ?ABC, AB =6, BC =5, CA =4 and AP bisects angle A. If P lies on BC then BP =

2 cosh 3 cosh 5=

If -3,1,8 are the roots of px3+qx2+rx+s=0 then the roots of p(x-3)3+q(x-3)2+r(x-3)+s=0 are

The side of an equilateral triangle increases at the uniform rate 0.05 cm/sec. the rate of increase in the area of the triangle when the side is 20 cm is

If α1,α2,α3 respectively denotes the moduli of the complex number -i , (1+i) / 3 and -1+i then their increasing order is

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