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Show that hatitimes (vecatimeshati)+hat...

Show that ` hatitimes (vecatimeshati)+hatjtimes(vecatimeshatj)+hatktimes(vecatimeshatk)=2veca`

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Prove that (vecaxxhati)^2+(vecaxxhatj)^2+(vecaxxhatk)^2=2veca^2 .

Prove that (vecaxxhati)^2+(vecaxxhatj)^2+(vecaxxhatk)^2=2veca^2

Find the value of lambda so that three vectors veca=2hati-hatj+hatk, vecb=hati+2hatj-3 hatk and vecc= 3hati +lambda vecj+5 hatk are coplanar.

If veca = hati+2hatj-hatk , vecb = hati+hatj+2hatk , vecc = 2hati-hatj then

Show that the vector area of the triangle whosse vertices have position vector veca,vecb,vecc is 1/2(vecaxxvecb+vecbxxvecc+veccxxveca) .

if veca=2hati-5hatj+8hatk, vecb=hati-3hatj-7hatk and vecc=-3hati+2hatj-hatk then find |veca+vecb+vecc|

Let veca = 2hati+hatj, vecb = -hati+3hatj+hatk and vecc = hati+2hatj+5hatk be three vectors. Find veccxxveca

Let veca = 2hati+hatj, vecb = -hati+3hatj+hatk and vecc = hati+2hatj+5hatk be three vectors. Find vecaxx(-vecb)

Let veca = 2hati+hatj, vecb = -hati+3hatj+hatk and vecc = hati+2hatj+5hatk be three vectors. Find (veca-vecb)xx(vecc-veca)

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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