NEET Class neet Answered

Qn.# (10)

log(243729 )  ≈ log( 2.437 × 10⁵ ) = log ( 2.437 ) + log (10⁵ )

From Table of logarithms , log(2.437) = 0.3868

log(243729 )  ≈  0.3868 + 5.0000 = 5.3868

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Qn. #11

If line joining (x₁, y₁) and (x₂, y₂) is divided by a point P in the ratio m:n , then

Coordinate of P is  [  ( m x₂ + n x₁ ) / (m+n) , ( m y₂ + n y₁ ) / (m+n) ]

If line joining (5, 9) and (2, 3) is divided by a point P in the ratio 2:3 , then

Coordinate of P is  [  ( 2 × 2 + 3 × 5 ) / (2+3) , ( 2 × 3 + 3 × 9 ) / (2+3)   ]  = ( 19/5 , 33/5 )

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Qn. #12

If triangle have vertices (x₁, y₁) , (x₂, y₂) and (x₃, y₃) , then area of triangle is

A = (1/2) [ x₁ ( y₂ - y₃ ) + x₂ (y₃ - y₁ ) + x₃ ( y₁-y₂) ]

If vertices of triangle are ( 0, 0 ) , (2, -3) and (4, 5 ) , then

A = (1/2) [ 2 (5) + 4 (3 ) ] = 11 sq. units

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Qn. #13

Let the line be  y = m x + c  ..........................(1)

If the required line is perpendicular t o the given line whose slope is (1/2) , then slope of required line is -2 .

Hence , m = -2

Hence the required line be  y = -2x + c

If this required line passes through (-2, 1) , then we get

1 = -2 (-2 ) + c  or c = -3

Hence the required line is 2x+y +3 = 0

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Qn. #14

Let y = e^x cosx

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Qn.#15

Let y = sinx  log(x)

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Qn # 16

Let y = 3 x - 4 + ( 2/x ) + ( 5 / x² )

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Qn # 17

Let u = logx and dv =  x dx

du = dx/x   and v = (1/2) x²