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For what value of a the vectors 2 h...

For what value of ` a ` the vectors `2 hat i-\ 3 hat j+4 hat k` and `a hat i+6 hat j-8 hat k` are collinear?

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. For what value of x, the matrix [(5-x,x+1),(2,4)] is singular?

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  2. Write A^-1 for A=[(2,5),(1,3)]

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  3. For what value of a the vectors 2 hat i-\ 3 hat j+4 hat k and a h...

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  4. Write the direction cosines of the vector -2 hat i+ hat j-5 hat k

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  5. The length x of a rectangle is decreasing at the rate of 5 cm/minut...

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  6. Find the intervals in which the function f given f(x)=\ sin x+cosx ,\...

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  7. Write the principal value of tan^(-1)(1)+cos^(-1)(-1/2)

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  8. Suppose a girl throws a dice. If she gets 5 or 6 she tosses a coin thr...

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  9. A dietician wishes to mix two types of foods in such a way that the...

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  10. Let vec(a)=hat(i)+4 hat(j)+2hat(k), vec(b)=3 hat(i)-2 hat(j)+7 hat(k) ...

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  11. Find the coordinates of the point where the line through the points...

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  12. Two cards are drawn simultaneously (without replacement) from a wel...

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  13. Using matrices, solve the following system of equations: 2x+3y+3z=5;...

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  14. Find the area of the region {(x , y)\ : x^2+y^2lt=4,\ x+y\ geq2}

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  15. If the lines (x-1)/(-3)=(y-2)/(-2k)=(z-3)/2 and (x-1)/k=(y-2)/1-(z-3)...

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  16. Sand is pouring from a pipe at the rate of12\ c m^3//s . The falling s...

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  17. Write the value of tan(2tan^-1(1/5)) .

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  18. Find (dy)/(dx)\ if (x^2+y^2)^2=x y

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  19. If y=3cos(logx)+4sin(logx),\ then show that x^2dot(d^2\ y)/(dx^2)+...

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  20. If x^m y^n=(x+y)^(m+n), prove that (dy)/(dx)=y/x .

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