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Let A = R × R and * be the binary oper...

Let A = R × R and * be the binary operation on A defined by (a, b) * (c, d) = (a+c,b+d). Show that * is commutative and associative. Find the identity element for * on A.

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Let A = N×N and ⋅ be the binary operation on A defined by(a, b) ⋅(c, d) = (a + c, b + d) . Show that ⋅ is commutative and associative. Find the identity element for ⋅ on A, if any.

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Let A = Q xxQ and ** be a binary operation on A defined by (a, b) ** (c,d) = (ad + b, ac). Prove that ** is closed on A = QxxQ . Find (i) Identity element of (A, **) , (ii) The invertible element of (A,**).

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Let R_0 denote the set of all non-zero real numbers and let A=R_0xxR_0 . If * is a binary operation on A defined by (a ,\ b)*(c ,\ d)=(a c ,\ b d) for all (a ,\ b),\ (c ,\ d) in Adot Find the identity element in A .

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. If a line makes angles alpha,beta,gamma with the positive direction of...

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  2. Find a Vector in the direction of vec a= hat i-2 hat j that has magni...

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  3. Let A = R × R and * be the binary operation on A defined by (a, b) *...

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  4. Find the inverse of the matrix A=[1 3 3 1 4 3 1 3 4]

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  5. If [2x3][1 2-3 0][x3]=O , find x

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  6. Find the equation of the plane through the line of intersection of the...

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  7. A bag contains 4 red and 4 black balls, another bag contains 2 red and...

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  8. One kind of cake requires 200 g of flour and 25 g of fat, and anoth...

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  9. Using properties of determinants, prove that |[(a+1)(a+2),a+2,1],[(a...

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  10. Solve the differential equation x^2dy+(x y+y^2)dx=0 given y=1, when x=...

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  11. Find the particular solution of the differential equation x(dy)/(dx)+y...

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  12. From a lot of 15 bulbs which include 5 defectives, a sample of 2 bulbs...

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  13. Probability of solving specific problem independently by A and B are 1...

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  14. Find the area of the region in the first quadrant enclosed by the y-ax...

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  15. Evaluate : int0^(pi/2)(dx)/(1+sqrt(tanx))

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  16. Show that the four points A, B, C and D with position vectors4 hat i+...

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  17. Find the shortest distance between the lines vec r=( hat i+2 hat j+ h...

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  18. Find the derivative of (sinx)^x+sin^(-1)sqrt(x) w.r.t. x

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  19. If y=(xcos^(-1)x)/(sqrt(1-x^2))-logsqrt(1-x^2), then prove that (dy)/(...

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  20. Find int((x^2+1)e^x)/((x+1)^2)dx

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