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Let vec(a) =hat(i) +2hat(j) +hat(k),vec(...

Let `vec(a) =hat(i) +2hat(j) +hat(k),vec(b) =hat(i) -hat(j) +hat(k) and vec(c ) =hat(i) +hat(j) -hat(k) `, vector in the plane of `vec(a) and vec(b) ` whose projection on `vec(c ) ` is `1/(sqrt(3))` is ______.

A

3i+j-3k

B

4i+j-4k

C

i+j-2k

D

4i-j+4k

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The correct Answer is:
D
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HIMALAYA PUBLICATION-COMMON ENTRANCE TEST -2015-QUESTION BANK
  1. int(0)^(pi//4)log ((sin x +cos x )/(cosx))dx is equal to

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  2. Area bounded by y = x^(3) ,y = 8 and x = 0 is .

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  3. Let vec(a) =hat(i) +2hat(j) +hat(k),vec(b) =hat(i) -hat(j) +hat(k) and...

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  4. The mean devision from the data 3,10,10,4 ,7,10,5 is

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  5. The probability distribution of X is : {(X:,0,1,2,3),(P(X),0.2,k,k,...

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  6. If the function g(x) is defined by g(x) = (x^(200))/(200) +(x^(199...

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  7. A box contains 6 red numbers from 1 through 6 and 4 white marbles ...

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  8. lim(x rarr 0) (1- cos x)/(x^(2)) is :

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  9. f(x)= {(3x-8,"If " x le 5),(2k,"if" x gt 5):} is continuous, find k

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  10. If f(x)=2x^(2), find (f(3.8)-f(4))/(3.8-4) :

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  11. If x = ct and y = c/t , find (dy)/(dx) at t = 2 .

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  12. A balloon which always remains spherical is being inflated by pumping ...

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  13. int (sin^(2)x)/(1+cos x) dx is equal to

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  14. Evaluate : int e^(x) ((1 + sin x)/( 1+ cos x)) dx

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  15. If 1, w, w^(2) are three cube roots of unity, then (1 - w+ w^(2)) (1 +...

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  16. Solve for x tan^(-1) ((1-x)/(1+x))=(1)/(2) tan^(-1)x, x gt 0

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  17. The system of linear equations x+y+z = 6, x+2y+3z = 10 and x + 2y +az ...

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  18. The value of tan (1^(@)) + tan (89^(@)) is

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  19. If ((x+1)^(2))/(x^(3)+x)=A/x +(Bx+C)/(x^(2)+1) then "cosec"^(-1) (1/A...

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  20. The remainder obtained when 1! + 2! + 3!+….+ 11! is divided by 12 is

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