IIT-JEE · Practice Sheet 40

1. 1.

   Mathematics

   Find the binomial coefficient C(9, 4) — the coefficient of x^4 in (1 + x)^9.

   Formula:Binomial Coefficient

   $\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$

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2. 2.

   Physics

   Find the electrical power when 148 V drives a current of 11 A.

   Formula:Electrical Power

   $P = VI$

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3. 3.

   Mathematics

   In an arithmetic progression with first term 20 and common difference 5, find term number 6.

   Formula:AP nth Term

   $a_n = a + (n-1)d$

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4. 4.

   Chemistry

   Find the molarity of a solution containing 1 mol of solute in 2 L of solution.

   Formula:Molarity

   $M = \dfrac{n}{V}$

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5. 5.

   Mathematics

   For the quadratic 3x² − 3x − 8 = 0, find the sum and product of its roots.

   Formula:Vieta's Formulas (roots)

   $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

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6. 6.

   Physics

   A body moving at 2 m/s accelerates at 5 m/s² for 10 s. Find the distance travelled.

   Formula:Equation of Motion (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^{2}$

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7. 7.

   Physics

   Find the electrical power when 34 V drives a current of 19 A.

   Formula:Electrical Power

   $P = VI$

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8. 8.

   Physics

   An object starts at 18 m/s and accelerates at 8 m/s² for 12 s. Find its final velocity.

   Formula:Equation of Motion (v = u + at)

   $v = u + at$

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9. 9.

   Mathematics

   If f(x) = 4x³ + 6x² + 7x, find f′(3).

   Formula:Derivative of a Polynomial

   $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

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10. 10.

    Physics

    A constant force of 108 N moves an object 26 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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11. 11.

    Mathematics

    Find the slope of the line through (5, 5) and (-7, -2).

    Formula:Slope of a Line

    $m = \dfrac{y_2-y_1}{x_2-x_1}$

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12. 12.

    Mathematics

    Find the binomial coefficient C(5, 2) — the coefficient of x^2 in (1 + x)^5.

    Formula:Binomial Coefficient

    $\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$

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13. 13.

    Chemistry

    How many moles are present in 32 g of oxygen gas (O₂) (molar mass = 32 g/mol)?

    Formula:Number of Moles

    $n = \dfrac{m}{M}$

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14. 14.

    Physics

    A constant force of 100 N moves an object 29 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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15. 15.

    Mathematics

    Find the distance between the points (1, -5) and (1, 2).

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

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16. 16.

    Physics

    Find the kinetic energy of a 15 kg object moving at 3 m/s.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2}mv^{2}$

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17. 17.

    Physics

    A projectile is launched at 21 m/s at 45° to the horizontal. Find its range (g = 9.8 m/s²).

    Formula:Projectile Range

    $R = \dfrac{u^{2}\sin 2\theta}{g}$

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18. 18.

    Chemistry

    98 mL of a 5 M solution is diluted to 161 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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19. 19.

    Physics

    An object starts at 4 m/s and accelerates at 6 m/s² for 6 s. Find its final velocity.

    Formula:Equation of Motion (v = u + at)

    $v = u + at$

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20. 20.

    Physics

    A projectile is launched at 11 m/s at 45° to the horizontal. Find its range (g = 9.8 m/s²).

    Formula:Projectile Range

    $R = \dfrac{u^{2}\sin 2\theta}{g}$

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