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Assertions (A) :The line vecr=vec(a1)+la...

Assertions (A) :The line `vecr=vec(a_1)+lamda vec (b_1)` and `vecr=vec(a_2)+mu vec (b_2)` are perpendicular , when `vecb_1 . vecb_2=0`
Reason (R) : the angle `theta` between the lines `vecr=vec(a_1)+lamda vec (b_1)` and `vecr=vec(a_2)+mu vec (b_2)` is given by `cos theta = (vecb_1 . vecb_2)/(abs(vecb_1)abs(vecb_2))`

A

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

B

Both Assertion (A) and Reason (R) are true , but Reason (R) is not the correct explanation of the Assertion (A).

C

Assertion (A) is true, but Reason (R) is false.

D

Assertion (A) is false, but Reason (R) is true.

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XII BOARDS PREVIOUS YEAR-QUESTION PAPER 2023-Question
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  2. The integrating factor for solving the differential equation x (dy)/(...

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  3. Assertions (A) :The line vecr=vec(a1)+lamda vec (b1) and vecr=vec(a2)+...

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  4. Assertions (A): All trigonometric functions have their inverses over t...

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  5. If xy=e^(x-y), prove that (dy)/(dx)=(y(x-1))/(x(y+1)).

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  6. Find the domain of y=sin^-1(x^2-4)

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  7. Evaluate : cos^-1[cos(-(7pi)/(3))]

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  8. If the projection of the vector hati+hatj+hatk on the vector p hati+ha...

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  9. Find the point on the curve y^2=8x for which the abscissa and ordinate...

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  10. Find the vector equation of the line passing the point (2,1,3) and per...

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  11. The equation of a line are 5x-3=15y+7=3-10z. Write the direction cosin...

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  12. Find int(2)/((1-x)(1+x^2))dx

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  13. Evaluate int(1/3)^1 (x-x^3)^(1/3)/x^4dx

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  14. Evaluate : int1^3 {abs(x-1)+abs(x-2)}dx

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  15. Maximize Z = 5x + 3y subject to the constraints: 3x + 5y le 15, 5x + 2...

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  16. From a lot of 30 bulbs which include 6 defective bulbs, a sample of 2 ...

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  17. Find the particular solution of the differential equation (dy)/(dx)=(...

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  18. Find the general solution of the differential equation e^xtanydx+(1-...

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  19. Evaluate: int(pi/4)^(pi/2)e^(2x)((1-sin2x)/(1-cos2x))dx

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  20. Evaluate: int(-2)^2 x^2/(1+5^x)dx

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