
Find the coefficient of xr in the following (x+2)n+(x+2)n1(x+1)+(x+2)n2(x+2)2+.....+(x+1)n ...

The probability that a randomly chosen relation from a set A = {1, 2, . . . n}, n ≥ 1 to itself is a symmetric relation is (A) 2 n2+n/2 (B) 2 n2/2 (C) 2 nn2/2 (D) 2 n+1n2/2 ...

The equation of the circle passing through the points (0, 0),(0,b) and (a,b) is a) {{x}^{2}}+{{y}^{2}}+ax+by=0 b) {{x}^{2}}+{{y}^{2}}ax+by=0 c) {{x}^{2}}+{{y}^{2}}+x+3y=0 d) {{x}^{2}}+{{y}^{2}}+axby=0 ...

The equation of the tangent to the parabola {{y}^{2}}=4x+5 parallel to the line y=2x+7 is a) 2xy3=0 b) 2xy+3=0 c) 2x+y+3=0 d) None of these ...

The curve described parametrically by x={{t}^{2}}+t+1,y={{t}^{2}}t+1 represents a)A pair of straight lines b)An ellipse c)A parabola d)A hyperbola ...

Eccentricity of the parabola {{x}^{2}}4x4y+4=0 is__ e=0 __ e=1 __ e>4 __ e=4 ...

The axis of the parabola 9{{y}^{2}}16x12y57=0 is__ 3y=2 __ x+3y=3 __ 2x=3 __ y=3 ...

If f:R o R,,f(x)=2x1 and g:R o R, g(x)={{x}^{2}} then (gof),(x) equals ...

The period of the function f(x)=2cos frac{1}{3}(xpi ) is ...

Which of the following is an even function? ...

If f:R o R,, then f(x),=,x is ...

Domain of definition of the function f(x),=frac{3}{4{{x}^{2}}}+{{log }_{10}}({{x}^{3}}x),, is ...

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Let and c be two vectors perpendicular to each other in the xyplane. All vectors in the same plane having projections 1 and 2 along b and c respectively, are given by ...

this question is from coordinate geometry... if the straight lines y=43x ; ay=x+10 ; 2y+bx+9=0 represent the three consecutive sides of a rectangle then what is the value of ab? plz show the work out as well thnx in advance ...

The value of i log(x – i) + i2+i3 log(x +i) + i4( 2 tan1x), x> 0 is (A) 0 (B) 1 (C) 2 (D) 3 ...

The product of n positive numbers is unity.Then their sum is a.a positive integer b.divisible by n c.equal to n + 1/n d.never less than n Let the numbers be a1,a2,a3.......an Applying A.M>=G.M we get, a1+a2+a3+............ ...

Let f(x+y)=f(x).f(y) and f(x)=1+sin(3x).g(x) where g(x) is cont. , then f'(x) is a) f(x).g(0) b)3g(0) c) f(x).cos(3x) d)3f(x).g(0) e)3f(x).g(x) ...

A parabola is drawn touching the axis of x at the origin and having its vertex at a given distance k from the axis.Prove that the axis of the parabola always touches x2=8k(y2k). ...

If f(x+y)=f(x)f(y) for all x and y and f'(0) exists show that f'(x)=f'(x).f'(0) for all x ...

Consider a 25*25 grid of city streets. Let S be the points of intersection of the streets, and let P be the set of paths from the bottom left corner to the top right corner of which consist of only walking to the right and up ...

Point P(a, b) is in the first quadrant. A circle of radius r, centre P and containing points in each quadrant is drawn. If AK is the area inside the circle in the Kth quadrant, K=1, 2, 3, 4, then A1A2+A3A4= (a) ab (b) 2ab ( ...

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in how many ways we can make a 4 digit no. using 1,2,3,4 and what's the sum of all the numbers obtained?(repeatations not allowed) ...

If a,b,c be the pth,qth and rth terms of an HP respectively then prove the system of equations (bc)x + (ca)y + (ab)z = 0 px +qy + rz =0 and x+y+z=0 has ∞ number of solutions ...

Find incenter of a triangle whose sides are 7x5y+11=0, x + y 15=0,7x+17y+65=0 obtain the equation of the circle ...

If a,b,c are in AP ;b,c,a In GP then prove that 1/c , 1/a , 1/b are in ap ...

This is a great problem which you can probably approach in a number of different ways. All natural numbers are arranged as follows. 1 3 6 10 15 . 2 5 9 14 . . 4 8 13 . . . 7 12 . . . . 11 . . . . . and so on. Find the row and ...

In triangle ABC points L and M divide the sides AB and BC in the ratio 2:3 respectively. AM and LC intersect at point P. From point P, a line parallel to BA is drawn intersecting AC at D. Find the ratio AD:DC. Please show how ...

Three distinct numbers are selected uniformly at random from the tenterm geometric sequence with first term 10/9 and common ratio 2 . What is the expected value of their sum? ...