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Solve frac[dx][dy]=frac[3x-7y+7][3y-7x-3...

Solve `frac[dx][dy]=frac[3x-7y+7][3y-7x-3]`

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Solve (x+y+1)frac[dy][dx]=1

Prove that the lines frac[x+3][2]=frac[y+5][3]=frac[z-7][-3] and frac[x+1][4]=frac[y+1][5]=frac[z+1][-1] are coplanar. Find the equation of plane containing them.

Find the shortest distance between the lines frac[x][2]=frac[y][-3]=frac[z][1] and frac[x-2][3]=frac[y-1][-5]=frac[z+2][2] .

If y=tan^(-1)(frac[1+sinx][1-sinx])^(frac[1][2]) and z=log(frac[1+cosx][1-cosx]) , then prove that frac[dy][dx]=frac[-sinx][4]

Find the foot of the perpendicular drawn from the point (5,7,3) to the line frac[x-15][3]=frac[y-29][8]=frac[z-5][-5] . Find the length of the perpendicular.

Are the lines frac[x][1]=frac[y][2]=frac[z][3] and frac[x-1][-2]=frac[y-2][-4]=frac[z-3][-6] parallel?

Write the order and degree of the differential equation frac[dy][dx]= [1+(frac[d^2y][dx^2])^2]^(frac[2][3]

Find the equation of the plane containing the line frac[x+3][3]=frac[y-1][4]=frac[z-2][-2] and the point (0,2,4).

Solve dy/dx=x+y

USHA PUBLICATION-PREVIOUS YEAR QUESTION 2017-PREVIOUS YEAR QUESTION
  1. Solve by Cramer’s rule 2x-y=2, 3x+y=13

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  2. If the matrix A is such that [[1,-1],[2,3]]A=[[-4,1],[7,7]], find A.

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  3. Find the inverse of the following matrix: [[0,0,2],[0,2,0],[2,0,0]]

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  4. If P(n-1,3):P(n+1,3)=5:12, find n.

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  5. A cricket team consisting of 11 players is to be chosen from 8 batsmen...

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  6. Write the principal value of sin^(-1)frac[1][2]+cos^(-1)(-frac[1][2])

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  7. Five boys and four girls randomly stand in a line. Find the probabilit...

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  8. If a random variable X has a binomial distribution B(8,frac[1][2]), th...

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  9. If (a + bx)e^(y/x) = x, then show that x^3d/dx (dy/dx) = (x dy/dx - ...

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  10. A cylindrical open water tank with a circular base is to be made out o...

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  11. Evaluate intfrac[dx][cosx(1+2sinx)]

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  12. Solve frac[dx][dy]=frac[3x-7y+7][3y-7x-3]

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  13. Prove the following by vector method. An angle inscribed in a semi-cir...

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  14. Show that hatitimes (vecatimeshati)+hatjtimes(vecatimeshatj)+hatktime...

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  15. Show that the line joining the points (0,2,-4) and (-1,1-2) and the l...

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  16. Solve the following LPP graphically: Maximize: Z=4x1+3x2 subject to x1...

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  17. Prove the following: [[(b+c)^2,a^2,bc],[(c+a)^2,b^2,ca],[(a+b)^2,c^2...

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  18. Show that: C1^2+2C2^2+3C3^2...+nCn^2=frac[(2n-1)!][{(n-1)!}^2

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  19. The probability that a student will pass the final examination in both...

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  20. If P (A) = 0.4,P (B | A)= 0.3 and P (B^c | A^c)=0.2. find P (A | B )

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