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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
- What is intfrac[sin^8x-cos^8x][1-2sin^2xcos^2x]dx?
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- Write the minimum value of n such that frac[d^n][dx^n](3x^4+5)^(20)=0
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- Write the direction cosines of the normal to the plane x-2y+2z-10=0
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- What is the principal value of sin^(-1)(sinfrac[5pi][6])
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- For what value of lambda, the vectors veca=3hati+4hatj and vecb=8hati+...
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- If underset(n)(I) is an identity matrix of order n, then k being a nat...
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- What is the value of int0^picos^(101)xdx?
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- If A is a singular matrix, then what is A(adjA)?
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- Minimize:Z=6x1+7x2 "Subject to":x1+2x2 ge 4 x1,x2 ge 0
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- Show that if R is an equivalence relation on X then dom R=rngR =X.
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- Prove that: cos^(-1)(12/13)+sin^(-1)(3/5)=sin^(-1)(56/65)
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- Solve sin^(-1)(1-x)-2sin^(-1)x=frac[pi][2]
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- Let f be a real function. Prove that f(x)-f(-x) is an odd function and...
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- If A=[{:(3,1),(-1,2):}] then prove that A^(2)-5A+7I=O
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- Express as a sum of a symmetric and a skew symmetric matrix: [[4,-3],[...
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- If ABC is a triangle, then prove that abs[[tanA,1,1],[1,tanB,1],[1,1,...
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- 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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- Find the inverse of the matrix [[1,2],[3,4]]
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- Find the number of critical points of f(x)=frac[abs(x-1)][x^2]
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- If f(x)={(ax^2+b if x lt1),(1 if x=1),(2ax-b if xgt1):} is continuous...
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