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Find the point on the curve y^2=4x which...

Find the point on the curve `y^2=4x` which is nearest to the point (2, 1).

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To find the point on the curve \( y^2 = 4x \) that is nearest to the point \( (2, 1) \), we can follow these steps: ### Step 1: Define the point on the curve Let the point on the curve be \( P(x, y) \). Since the point lies on the curve \( y^2 = 4x \), we can express \( x \) in terms of \( y \): \[ x = \frac{y^2}{4} \] Thus, the point \( P \) can be represented as: ...
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XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. A particle starting with initial velocity of 26 m/sec moves with a ...

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  2. A body of mass 50 kg, suspended by two strings of lengths 30 cm and...

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  3. Find the point on the curve y^2=4x which is nearest to the point (2, 1...

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  4. Show that a cylinder of a given volume which is open at the top has...

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  5. If y=acos(logx)+bsin(logx), prove that x^2(d^2y)/(dx^2)+\ x(dy)/(dx)...

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  6. Verify Rolle's theorem for the function f(x)=\ x^2-5x+6 on [2, 3].

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  7. Using matrices, solve the following system of equations: 2x-y+z= -3, ...

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  8. Find the derivative of cos(2x+1) w.r.t. x from first principle.

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  9. Evaluate: \lim{x\rightarrow0}\ ((sqrt(1+x)\ -\ sqrt(1-x))/(sin^(-1)x))

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  10. Solve the following differential equation : ("x"^2-1)"dy"/("dx")+2"xy...

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  11. Using integration calculate the area of the region bounded by the t...

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  12. Evaluate int0^2(2x^2+\ x+5)dx as limit of a sum.

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  13. Solve the following differential equation: ("y"^2- "x"^2)"dy"=3"x y ...

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  14. Verify that "y"="Acos x"-"Bsinx" is solution of the differential eq...

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  15. A window is in the form of a rectangle surmounted by a semi-circle. ...

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  16. An open box, with a square base, is to be made out of a given quanti...

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  17. Find the intervals in which the function "f"("x")="x"^"3"- "12"x^2+ ...

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  18. Evaluate: int sqrt(tan theta) d theta

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  19. Using matrices, solve the following system of equations: 3"x"-"y"+"...

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  20. Differentiate sqrt ("tan x")" w.r.t x from first principle.

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