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What is the value of sec^2(tan^(-1)2)+co...

What is the value of `sec^2(tan^(-1)2)+cosec^2(cot^(-1)3)`?

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USHA PUBLICATION-PRACTICE PAPER-PRACTICE PAPER
  1. Let X, Y be non-empty sets such that abs(X)=m and abs(Y)=n. If mltn, t...

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  2. What is the value of sec^2(tan^(-1)2)+cosec^2(cot^(-1)3)?

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  3. With 4 different elements how many different determinant of order 2 ca...

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  4. If A is a square matrix of order 3 such that abs(A)=5, then what is th...

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  5. If f(x)=(1+2x)^(frac[1][x]),xne0 is continuous at x=0, then what is th...

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  6. Write the least value of f(x)=ax+frac[b][x], where agt0,bgt0 andxgt0.

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  7. Write the value of intfrac[(x^2+1)dx][1+x^4].

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  8. What will be the substitution for which the equation frac[dy][dx]+p(x)...

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  9. If veca=2vecb and vecc=-3vecb, then what is the angle between veca and...

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  10. What is the number of independent constants that occur in the general ...

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  11. Show that the relation R on Z – {0} defined by R={(m,n)|frac[m][n] is ...

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  12. Show that the function f:RRrightarrowRR defined by f(x)={(x^2-frac[1][...

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  13. Solve for x, cos^(-1)x +sin^(-1)((x)/(2)) =(pi)/(6).

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  14. Prove that cos^(-1)(frac[b+acosx][a+bcosx])=2tan^(-1)(sqrt(frac[a-b][a...

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  15. A diet for a sick person must contain at least 4000 units of vitamins,...

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  16. 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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  17. Find inverse of the following matrices by elementary row/column operat...

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  18. If A =[[1,-2,2],[3,1,-1]] B[[2,4],[1,2],[3,-1]] "verify" "that" (AB)^...

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  19. Without expanding prove that |[1,a,a^(2),-bc],[1,b,b^(2),-ca],[1,c,c^(...

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

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