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What is the principal value of sin^(-1)(...

What is the principal value of `sin^(-1)(sinfrac[5pi][6])`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Write the minimum value of n such that frac[d^n][dx^n](3x^4+5)^(20)=0

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  2. Write the direction cosines of the normal to the plane x-2y+2z-10=0

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  3. What is the principal value of sin^(-1)(sinfrac[5pi][6])

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  4. For what value of lambda, the vectors veca=3hati+4hatj and vecb=8hati+...

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  5. If underset(n)(I) is an identity matrix of order n, then k being a nat...

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  6. What is the value of int0^picos^(101)xdx?

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  7. If A is a singular matrix, then what is A(adjA)?

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  8. Minimize:Z=6x1+7x2 "Subject to":x1+2x2 ge 4 x1,x2 ge 0

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  9. Show that if R is an equivalence relation on X then dom R=rngR =X.

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  10. Prove that: cos^(-1)(12/13)+sin^(-1)(3/5)=sin^(-1)(56/65)

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

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  12. Let f be a real function. Prove that f(x)-f(-x) is an odd function and...

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  13. If A=[{:(3,1),(-1,2):}] then prove that A^(2)-5A+7I=O

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  14. Express as a sum of a symmetric and a skew symmetric matrix: [[4,-3],[...

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  15. If ABC is a triangle, then prove that abs[[tanA,1,1],[1,tanB,1],[1,1,...

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  16. Evaluate abs[[1,a,bc],[1,b,ca],[1,c,ab]]-abs[[1,a,b^2],[1,b,b^2],[1,c,...

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  17. Find the inverse of the matrix [[1,2],[3,4]]

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  18. Find the number of critical points of f(x)=frac[abs(x-1)][x^2]

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  19. If f(x)={(ax^2+b if x lt1),(1 if x=1),(2ax-b if xgt1):} is continuous...

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  20. Find the equation of the tangent to the curve x = y^2-1 at the point w...

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