Verify: `(a/b+c/d)+e/f=a/b+\ (c/d+e/f) for\ a/b=\ (-2)/3, c/d=5/7a n d e/f=(-1)/6dot`

Let R be a relation on NxxN defined by (a , b)\ R(c , d)hArra+d=b+c\ if\ (a , b),(c , d) in NxxN then show that: (i)\ (a , b)R\ (a , b)\ for\ a l l\ (a , b) in NxxN (ii)\ (a , b)R(c , d)=>(c , d)R(a , b)for\ a l l\ (a , b),\ (c , d) in NxxN (iii)\ (a , b)R\ (c , d)a n d\ (c , d)R(e ,f)=>(a , b)R(e ,f)\ for all \ (a , b),\ (c , d),\ (e ,f) in NxxN

If A B C and DEF are two triangles such that A B C\ ~= F D E\ a n d\ A B=5c m ,\ /_B=40^0\ a n d\ /_A=80^0dot Then, which of the following is true? (a)D F=5c m ,\ /_F=60^0 (b) D E=5c m ,\ /_E=60^0 (c)D F=5\ c m ,\ /_E=60^0 (d) D E=5c m ,\ /_D=40^0

Construct a quadrilateral B D E F , where D E=4. 5 c m ,\ E F=3. 5 c m ,\ F B=6. 5 c m ,\ /_F=50^0a n d\ /_E=100^0dot

(a)/(b) = (c)/(d) = (e)/(f) = k(a, b, c, d, e, f gt 0) then (A) k = (a + c +e)/(b + d + f) (B) k = (a^(2) + c^(2) +e^(2))/(b^(2) + d^(2) + f^(2)) (C) k = (c^(2)e^(2))/(d^(2)f^(2)) (D) k = ((ace)/(bdf))^((1)/(3))

If a,b,c,d,e, f are A. M's between 2 and 12 , then find a + b + c +d + e +f.

Let A = (a,b,c),B= (b,d,e) and C = (e,f,g) , verify that : A nn B = B nn A

Let A = (a,b,c),B= (b,d,e) and C = (e,f,g) , verify that : A uu B = B uu A

The coefficient of (x^(3)* b^(6) * C^(8) *d^(9) *e *f) in the expansion of (a + b + c - d - e - f)^(31) is

In two triangles A B C\ a n d\ D E F , it is given that /_A=/_D ,\ /_B=/_E and /_C=/_Fdot Are the two triangles necessarily congruent?

Let A = (a,b,c),B= (b,d,e) and C = (e,f,g) , verify that : ( A nn B ) nn C = A nn (B nn C )