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Prove that ^nPr=^(n-1)Pr+r^(n-1)P(r-1)(n...

Prove that ``^nP_r=`^(n-1)P_r+r^(n-1)P_(r-1)`(notation used are in their usual meaning).

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Prove that .^(n)P_(r)=.^(n-1)P_(r)+r.^(n-1)P_(r-1) .

.^(n-1)C_(r)+^(n-1)C_(r-1)=

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show that ^nC_r+ ^(n-1)C_(r-1)+ ^(n-1)C_(r-2)= ^(n+1)C_r

Show that , .^(n)P_(r)=n.^(n-1)P_(r-1)=(n-r+1).^(n)P_(r-1) .

Show that , .^(n)C_(r)=(n-r+1)/(r).^(n)C_(r-1) .

(n)p_(r)=k^(n)C_(n-r),k=

If .^(n)P_(r)=x.^(n)C_(r) x=

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UNITED BOOK HOUSE-JADAVPUR VIDYAPITH-EXERCISE
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  2. tan25^@=a prove that (tan155^@-tan115^@)/(1+tan155^@.tan115^@)=(1-a^2)...

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  3. Prove that tan70^(@)=2tan50^(@)+tan20^(@).

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  4. a=(1+i)/sqrt2then a^6+a^4+a^2+1=?

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  5. x(x-3)=4,has two roots alphaand betathen alpha^2+beta^2=?

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  6. Find the area of the triangle formed by the straight lin x cosalpha+ys...

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  7. Straight line px-qy=r intercept the coordinate axis at the point (a,0)...

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  8. A relation R defined on the set of natural no as follows R={(x,y),x+5y...

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  9. cos(beta-gamma)+cos(gamma-alpha)+cos(alpha-beta)=-3/2 show that cosalp...

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  10. sintheta+sinphi=a,costheta+cosphi=bshow that tan((theta-phi)/2)=+-sqrt...

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  11. If cos theta=(acosphi+b)/(a+bcosphi)(theta,phiacute angle)show that ta...

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  12. In a triangle ABC if a cos^2(C/2)+c cos^2(A/2)=((3b)/2)show that sides...

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  13. If w be a imaginary cube root of uniyt and a+b+c=0 then show that (a+b...

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  14. An equilateral triangle in the Argan plane has vertix as z1,z2and z3wh...

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  15. If the equation x^2+px+qr=0and x^2+qx+pr=0(p!=q,r!=0)has same root the...

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  16. Prove that ^nPr=^(n-1)Pr+r^(n-1)P(r-1)(notation used are in their usua...

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  17. How many way will be made from the word JADAVPUR taking al the letters...

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  18. If a,b,c are in G.P and x,y are the arithmetic mean of a and b aand b,...

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  19. Sum of the reciprocal intercepts on the axes by a moving straight lin...

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  20. Distance of the straight line 4x+3y=5 cosalphaand 6x-8y=5 sinalphafrom...

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