09:28

Find the number of cyphers at the end of C(2002, 2001)

06:28

Find the number of ways in which 94864 can be resolved as a product of two factors.

03:56

Find the number of ways in which we get a score of 11 by throwing three dice.

05:18

If sides AB, BC and CA of ∆ ABC have 3, 4, and 5 points respectively on them. Find

05:12

Find the maximum number of points into which four circles and four straight lines intersect.

04:31

Find the value of P(n,1) + P(n,2)/2! + P(n,3)/3! +....+P(n,n)/nl

04:52

Evaluate: ∫ {0, π/2} (sin x - cosx) dx / (1+ sin x cos x)

05:39

If a, b, c are in GP. The equations ax²+2bx+c=0 and dx²+2ex+f=0 have a common root, prove that...

06:16

If t_n=¼(n+2)(n+3) for n= 1,2,3 then find the value of 1/t_1+1/t_2+1/t_3+.........+1/t_2003

05:10

Find the sum of 1/(2.4)+(1.3)/(2.4.6)+(1.3.5)/(2.4.6.8)+...infinity

11:30

Find the value of range of common ratio if the sides of a triangle are in GP.

06:31

If α is a non real root of x^7=1, find the value of 1+3α+5α^2+7α^3+..+13α^6.

06:52

If z be a complex number having argument theta, 0,theta,π/2 and satisfying the equation

07:39

If z and w be two non zero complex numbers such that |zw|=1 and arg z - arg w=π/4, find bar(z)w

07:15

If x^2+x+1=0, find the value of (x+1/x)+(x^2+1/x^2)^2+...+(x^150+1/x^150)^150

06:43

If alpha, beta be the roots of equation ax^2+bx+c=0 and ∆=b^2-4ac. If (alph @ganitalayatutorial9

08:12

If alpha, beta be the roots of equation x^2+px+q=0 and x^2n+p^nx^n+q^n=0.....@ganitalayatutorial9

07:43

If a, b, c be sides of ∆ABC, such that x^2-2(a+b+c)x+3lambda(ab+bc+ca)=0

06:35

If log a = 4 , find the value of log (cu.rt a by sq.rt b). Here base is ab.

05:11

If n is a positive integer, prove that (1+I)^n+(1-i)^n = 2^(n/2+1)cos( nπ/4)

12:04

Solve the system of equations: log(xy)=3log x log y and 4log(x/y)=logx/logy (base 8 in all)

07:21

If alpha, beta, gamma be roots of x^3-3x^2+3x+7=0, find (alpha-1)/(beta-1) + in cu. rt of unity.

11:45

Find the greatest term in the expansion of (x+y)^18 when x=2 and y=1.

09:18

Find the value of m such that both roots of the equation x^2-6mx+9m^2-2m+2=0 may exceed 3

06:56

Integrate (1+sin log x)/(1+cos log x)

04:35

Indefinite integration

04:27

Integrate x^2/√(25-x^2)

05:13

Find dy/dx if sin(x+y)=xy

06:26

If y = cos^(-1)(8x^4-8x^2+1), find dy by dx.

07:21

A curve passes through (0,1) and its slope is 3 at x=0, satisfying the differential equation....

04:17

Find the greatest angle of triangle whose sides are sin alpha, cos alpha and sqrt(1+ ......

05:45

A telephone company has 500 subscribers on its list

15:19

Find the maximum and the minimum values of f(x) = sec x + 2 log(cos x)

07:15

If the function f(x)= 2x^3-9ax^2+12a^2x+1

09:31

Find the distance of point A(-2,3,1) from line PQ through P(-3,5,2) which makes equal angles with

06:49

If p=2i-3j+3k and q=4i-2j+k be two vectors and r be a vector perpendicular to p and q satis

31:30

If cos(α-3θ)/cos³θ = sin(α-3θ)/sin³θ = m, prove that cosα = 2/m - m.

06:22

Find the square root of x^2/y^2+y^2/x^2 + 1/2i.(x/y+y/x)+31/16

13:15

An aeroplane is flying along the line r̅ =λ(î-ĵ+k̂), where λ is a scalar and another plane ....

12:28

Show that the joins of points A(0,2,-1), B(1,0,0) and C(1,2,-2),

07:56

Two vertices of a triangle are (3,5-2) and (5,-1,4) and the medians through these vertices

14:16

Find the equations of two lines from the origin which intersect the line (x-3)/2=(y-3)/1=z/1

11:39

If a variable lines in two adjacent positions has direction cosines l,m,n and l+dl, m+dl, n+dl.

07:32

Find the foot of perpendicular from point (2,3,-8) to lines (4-x)/2 = y/6 = (1-z)/3. Also find

05:42

Find the angle between the lines whose direction cosines are given by l+m+n=0; l^2+m^2-n^2=0

04:39

Evaluate: int(-1/2, 1/2) {((x+1)/(x-1))^2 +((x-1)/(x+1))^2 -2}dx

10:42

Evaluate: int(1,3) [(|x+1|)/(|x-2|+|x-3|)]dx

08:54

Solve: dy/dx = cos(x+y) + sin(x+y)

13:19

Solve: y + d/dx(xy) = x(sin x + log x)

05:39

Prove that 3/1^2 +5/(1^2+2^2)+7/(1^2+2^2+3^2)+.....to n terms = 6n/(n+1)Prove that 3/1^2 +5/(1^2

07:53

Find the sum to n terms of the series cot^(-1) 3 + cot^(-1) 7 + cot^(-1) 13 + cot^(-1) 21+....

07:37

Find three digit numbers that are divisible by 5 as well as 9 and whose consecutive digits are in AP

04:19

In an AP of natural number, the sum of first nine terms is greater than 200 but less than 220.

06:14

If e^{(sin^2 x + sin^4 x + sin^6 x+.....)log 2} satisfies the equation x^2 -9x + 8=0, find value

13:24

In an examination, the maximum marks for each of the three paper is 50 each. The maximum marks

07:31

Find the number of non negative integral solution of x+y+3z=30

04:17

A student is allowed to select at most n books from a collection of (2n+1) books. If the number of

02:54

In how many ways can 12 different books to distribute equally among 4 different boxes.

04:41

If T_n be the number of all possible triangle formed by joining vertices of n sided regular polygo

02:48

Find the sum of all four digits numbers that can be formed by using 1, 2, 3, 4 and 5 without rept.