A to Z Exams

If a=3i-j-2k, b=2i+3j+k then (a+2b)x(2a-b)=

If cos 2θ+cos 8θ= cos 5θ then θ=

If (a+bx)ey/x=x,then x3y2=

The equations of the tangents to the hyperbola 3x2-4y2=12 which are parallel to the line 2x+y+7 =0 are

If sin θ+ cos θ=a then sin4 θ+ cos 4 θ=

If a=2i+j-3k, b=i-2j+k then the vector of length 2√3 and perpendicular to both a and b is

8sin4θ=

If x= a {cos θ + log tan (θ/2)} and y = a sin θ then dy/dx=

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=

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

A: The polar of (2, 3) with respect to the circle x2+y2-4x-6y+5=0 is 2x+3y=0 R: The polar of (x1, y1) with respect to the circle S=0 is S1=0

The coefficient of xr in (1+x)2/(1-2x)3 is

In measuring the circumfence of a circle, there in an error of 0.05 cm. if with this error the circufence of the circle is measured of the circle is measured as c cm, then the percentage error in area is

The locus of the midpoint of the chord of the circle x2+y2=25 which subtends a right angle at (2,-3) is

The equation to the pair of tangents drawn from (3,-2) to the parabola y2 = x  is

The probabilities of problem being solved by two students are 1/2 and 1/3.Find the probability of the problem being solved.

d/dx{Tan-1(acos x-bsin x/b cos x+a sin x)}=

If three complex numbers are in A.P. then they lie on

The equation of the tangent to the curve y=x+9/x+5 so that is passes through the origin is

If cos  α+ cos β=0= sin α + sin β then cos(α - β)=

If α,β,γ are the roots of the equation x3+px2+qx+r=0,then Σ(α-β)2=

Match the following Parabola Focus y2 –x – 2y + 2 = 0 (1,2) y2 – 8x – 4y – 4 = 0 (-2,5) x2 + 4x – 8y + 28 = 0 (1,-1) x2 – 2x – 8y – 23 = 0 (5/4,1)

If tan(α+θ)= ntan(α-θ), then (n+1)sin 2θ=

The radii of two circles are 2 units and 3 units.If the radical axis of the circles cuts one of the common tangents of the circles in P then ratio in which P divides the common tangent is

The locus of the middle points of the chords of the circle x2+y2=8 which are at a distance of √2 units from the centre of circle is

 If x -y+ 1 = 0 meets the circle x2 + y2 + y - 1 = 0 at A and B, then the equation of the circle with AB as diameter is

If the tangent at any point on the curve x4+y4=a4 cuts off intercepts  p and q on the coordinates axes then p-4/3+q-4/3=

The value of k for which the points A(1, 0, 3), B(-1, 3, 4), C(1, 2, 1) and D(k, 2, 5) are coplanar is

A tangent to the circle x2+y2=4 meets the coordinate axes at P and Q. The locus of mindpoint of PQ is

If sin-1 (3/5)+sin-1(5/13)= sin-1 x, then x=

The shortest distance between the straight line passing through the point A=(6, 2, 2) and parallel to the vector(1, -2, 2) and the straight line passing through A’=(-4, 0, 1) and parallel to the vector (3, -2, -2) is

u = u(x, y) = sin (y+ax) - (y+ax)2 ===>

cos (θ + α).cos (θ - α)+ sin (θ + α). sin(θ - α)=

1.2+2.3+3.4+….n terms

If A=i+2j+3k, B=3i+4j+7k and C= 2i+3j+5k are collinear, then the ratio in which B divides is

The points (1, 6) and (12, 9) are two opposite vertices of a parallelogram. The other two vertices lie on the line 3y =11x+k. Then k=

If θ is the angle between the curves y2=4ax, ay=2x2 at (a, 2a) then tan θ=

If the points (0,0), (3,√3), (x,y) form an equilateral triangle, then (x,y)=

If the roots of x2+bx+c=0 are two consecutive integers then b2-4c=

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 :

The area of the triangle formed by the points (a,b+c), (b,c+a), (c,a+b) is

Equation of the latusrectum of the parabola x2 + 8x + 12y + 4=0 is

The equation whose roots are those of xn+xn-2+xn-5+m=0 with contrary signs (n is even as n≥6)

If α+β=-2 and α3+β3=-56 then the quadratic equation whose roots α,β is

The equation of the circle with centre (3, -2) and radius 3 is

A person of height 180 cm starts from a lamp post of height 450 cm and walks at the constant rate of 4 km per hour. The rate at which his shadow increases is

The equation of the circle passing through the point (1, 2) cutting the circle x2+y2-2x+8y+7=0 orthogonally and bisects the circumference of the circle x2+y2=9 is

If |x|

The internal centre of similitude of the two circles x2+y2+6x-2y+1=0, x2+y2-2x-6y+9=0 is

When a circular oil drop expands on water, its area increases at the uniform rate of 40sq. cm per minute. The rate of increase in the radius when the radius 5 cm is

The value of k,so that the sum and products of the roots of 2x2+(k-3)x+3k-5=0 are equal is

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

d/dx{(2x-3)/(3x+1)}=

The magnitude of the projection of the vector a = 4i - 3j + 2k on the line which makes equal angles with the coordinate axes is

The number of solutions of the system of equations 2x+y-z =7,x-3y+2z =1,x+4y-3z =5 is

The area (in square units) of the triangle formed by the lines x = 0,y = 0 and 3x + 4y = 12, is

In a class of 10 students, there are 3 girls A,B,C.The number of different ways that they can be arranged in a row such that no two of the three girls are consecutive is

The radical axis of the circles x2+y2-6x-4y-44=0 and x2+y2-14x-5y-24=0 is

The foot of the perpendicular from the point (3, 4) on the line 3x-4y+5=0 is

The orthocentre of the triangle formed by the points(2,1,5), (3,2,3), (4,0,4) is

If y=(1+x2)Tan-1x then y2=

If sin A= sin2 B and 2 cos2 A =3 cos2 B, then the ΔABC is

If the coefficients of (2r+1)th term and (4r+5)th term in the expansion of (1+x)10 are equal then r=

The circumcentre of the triangle formed by(0,0), (2, -1) and ( -1, 3) is (5/2,5/2). Then the orthocentre is

Write the descending order of the perpendicular distance of the line 2x-y+5=0 from A) (2, 1) B) (2, -1)   C (-2, 1) D (-2, -1)

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

If α,β,γ are the roots of a cubic equation satisfying the relations α+β+γ=2,α2+β2+γ2=6 and α3+β3+γ3=8 then the cubic equation is

If f(x)=x3-x, g(x)=sin 2x, then

The distance between the points (5, 3, 1), (3, 2, -1) is

For the parabola y2 +6y-2x+5 = 0(I) The vertex is (-2 , -3)(II) The directrix is y+3 = 0

If the origin is the centroid of the tetrahedron for which (2,-1,3), (-1,3,1), (3,4,-2) are three vertices then the fourth vertex is

sin 1200 cos 1500-cos 2400 sin 3300 is equal to :

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

Solution of differential equation dy/dx = (1+y2) (1+x2)-1is

The diameter x of a circle is found by measurements to be 5 cm with maximum error of 0.05 cm. the relevant error in the area is

The angle between the lines joining the origin to the points of intersection of 3x-y+1=0 and x2+2xy+y2+2x+2y-5=0 is

The locus of the midpoint of chords of the parabola y2 = 4ax parallel to the line y = mx + c is

The locus of the midpoint of the chords of the parabola y2= 6x which touch the circle x2 + y2 + 4x – 12 = 0 is

If the normal at (1,2) on the parabola again at the point (l2,2t), then the value of t is

If the foot of the perpendicular from (0,0,0) to a plane is (1,2,3), then the equation of the plane is

If the roots of a(b-c)x2+b(c-a)x+c(a-b)=0 are equal,then a,b,c are in

The equation of the circle passing through the points of intersection of the circlesx2+y2=5, x2+y2+12x+8y-33=0 and touching x-axis is

A pole of height h stands at one corner of a park in the shape of an equilateral triangle. If α is the angle which the pole subtends at the midpoint of the opposite side, the length of each side of the park is

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

The domain of sin-1(2x-7) is

(sin 3A+ sin A) sin A+ (cos 3A- cos A) cos A=

The equation of the circle passing through the intersection of the circles x2+y2=2ax and x2+y2=2by and having its centre on the x/a-y/b=2 is

If the lines 3x + 4y - 14 = 0 and 6x + 8y + 7 = 0 are both tangents to a circle, then its radius is

The value of √3cot 200- 4cos 200 is

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

The locus of the point of intersection of two tangents to the parabola y2 = 4ax which make the angle θ1 and θ2 with the axis so that cot θ1 + cos θ2 = k is

(sin 3θ/ sin θ)-(cos 3θ/ cos θ)=

The equation of the circle passing through (0,0) and the points of intersection of x2+y2-4x-6y+9=0 and x2+y2+4x-2y-4=

If α,β are the roots of ax2+bx+c=0 and γ,δ are the roots of lx2+mx+n=0,then the equation whose roots are αγ+βδ and αδ+βγ is

If the vectors i - 2xj - 3yk and i + 3xj + 2yk are orthogonal to each other, then the locus of the point (x, y) is

cos2 π/5+ sin2 4π/5=

The equation of tangent to the curve y=x+9/x+5 so that is passes through the origin is

I. In a class 25% of thestudents failed in mathematics, 30% failed in chemistry and 15% failed in both Mathematics and chemistry. If a student is selected at random failed in Mathematics, the probability that he failed in chemistry is 1/2 II: A bag contain 10 identical balls of which 4 are blue and 6 are red. 3 balls are taken out at random from the bag one after the other. The probability that all the 3 balls drawn are red is 1/6

The inverse of f(x)=10x-10-x/ 10x+10-x is

The condition that the lines joining the origin to the points of intersection of 2x+3y=k,3x2-xy+3y2+2x-3y-4=0 are at a right angles is