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Let f = {(1,3), (2,4), (3,7)} and g = {(...

Let f = {(1,3), (2,4), (3,7)} and g = {(3,2), (4,3), (7,1)} determine gof?

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If f:{1, 3, 4} to {1,2,5} and g:{1,2,5} to {1, 3} given by f = {(1, 2), (3, 5), (4, 1)} and g = {(1, 3), (2, 3), (5, 1)}. Write down gof.

Let f={(1,a),(2,b),(3,c),(4,d)} and g={(a,x),(b,x),(c,y),(d,x)} Determine gof and fog if possible. Test whether fog=gof.

If the mappings f and g are given by f={(1,2),(3,5),(4,1) and g={(2,3),(5,1),(1,3)}, then write fog.

If the mapping f and g are given by f= {(1,2), (3, 4), (5, 6), (7, 8)}, g={(2, 5),(4, 7),(6, 3),(8, 1)} then find (i) gof (ii) fog. Hence show that composition of functions is not commutative.

If A = {1, 2, 3), B = {4, 5, 6, 7) and f = {(1,4),(2,5), (3,6)} is a function from A to B.b State whether f is one-one or not.

Let S = {1,2,3). Determine whether the functions f :'S rarr S defined as below have inverses. Find f^(-1) , if it exists. (i) f= {(1, 1), (2, 2), (3, 3)] (ii) f = {(1,2),(2,1),(3, 1), (iii) f = {(1,3), (3, 2), (2,1)]

Let A={1,2,3}, B={4,5,6,7} and let f={(1,4),(2,5),(3,6)} be a function from A to B. State whether f is one-one or not.

If A = {1, 2, 3}, B = {4, 5, 6, 7} and f = {(1, 4), (2, 5), (3, 6)} is a function from A to B. State whether f is one-one or not.

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Solve graphically: Maximize Z=5x+6y subject to 2x+3yle6,x, yge0

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  2. Solve sin^(-1)(1-x)-2sin^(-1)x=frac[pi][2]

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  3. Let f = {(1,3), (2,4), (3,7)} and g = {(3,2), (4,3), (7,1)} determine ...

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  4. Prove that abs[[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2abs[[a,b,c]...

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  5. If abs((a,b,a-b),(b,c,b-c),(2,1,0))=0 , then prove that a,b,c are in G...

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  6. Verify that A=[[a,b],[c,d]] satisfies the equation A^2-(a+d)A+(ad-bc...

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  7. Solve : [[7,6,x],[2,x,2],[x,3,7]] = 0

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  8. Verify that [AB]^T = B^T A^T whereA=[[1,2,3],[3,-2,1]],B=[[1,2],[2,0],...

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  9. Prove the inequality x^2e^(-x^2) le e^(-1),x in R.

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  10. Prove that d/dxlntan(pi/4+x/2)=secx.

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  11. Determine the point on the curve y = ln x, at which the tangent will b...

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  12. Find the angle of intersection of two curves y =2^x and y=5^x

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  13. If 2y=x(1+(dy)/(dx)), then show that y(2) is a constant.

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  14. Find the solution of the following differential equations: (4x+6y+5)dx...

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  15. int(xe^x)/(1+x^2)dx

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  16. Solve dy/dx-y=e^x.

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  17. Evaluate int(-2)^2abs([x])dx.

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  18. intdx/(sqrtx-root(3)(x))(x=t^6)

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  19. Find the co-ordinates of the foot of the perpendicular from the point ...

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  20. Show that [veca+vecbvecb+veccvecc+veca] = 2[vecavecbvecc]

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