IIT-JEE · Practice Sheet 26

1. 1.

   Mathematics

   Find the distance between the points (0, 7) and (-3, 5).

   Formula:Distance Between Two Points

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

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2. 2.

   Mathematics

   Evaluate log base 2 of 32.

   Formula:Logarithm Evaluation

   $\log_{b}(b^{k}) = k$

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3. 3.

   Physics

   Find the momentum of a 34 kg body moving at 9 m/s.

   Formula:Linear Momentum

   $p = mv$

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4. 4.

   Physics

   A projectile is launched at 24 m/s at 30° 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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5. 5.

   Quantitative Aptitude

   In how many ways can 3 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 3.)

   Formula:Combinations

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

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6. 6.

   Mathematics

   Evaluate ∫ from 2 to 5 of 4x^1 dx.

   Formula:Definite Integral of a Power

   $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

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7. 7.

   Quantitative Aptitude

   A vehicle covers 372 km in 6 hours. Find its average speed.

   Formula:Speed, Distance & Time

   $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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8. 8.

   Chemistry

   Find the pressure of 2 mol of an ideal gas at 282 K in a 9 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

   Formula:Ideal Gas Law

   $PV = nRT$

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9. 9.

   Physics

   Find the voltage across a 2 Ω resistor carrying a current of 20 A.

   Formula:Ohm's Law

   $V = IR$

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10. 10.

    Chemistry

    Find the molarity of a solution containing 3 mol of solute in 0.5 L of solution.

    Formula:Molarity

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

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11. 11.

    Mathematics

    For the quadratic 3x² + 7x + 4 = 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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12. 12.

    Physics

    A force of 175 N acts on an area of 8 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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13. 13.

    Physics

    Find the kinetic energy of a 17 kg object moving at 17 m/s.

    Formula:Kinetic Energy

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

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14. 14.

    Physics

    If 2,635 J of work is done in 24 s, find the power.

    Formula:Power

    $P = \dfrac{W}{t}$

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15. 15.

    Chemistry

    How many moles are present in 234 g of sodium chloride (NaCl) (molar mass = 58.5 g/mol)?

    Formula:Number of Moles

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

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16. 16.

    Mathematics

    Evaluate ∫ from 1 to 3 of 2x^1 dx.

    Formula:Definite Integral of a Power

    $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

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17. 17.

    Mathematics

    Find the distance between the points (0, 8) and (8, -1).

    Formula:Distance Between Two Points

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

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18. 18.

    Physics

    Find the kinetic energy of a 7 kg object moving at 18 m/s.

    Formula:Kinetic Energy

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

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19. 19.

    Mathematics

    Find the sum of the first 11 terms of an AP with first term 17 and common difference 7.

    Formula:AP Sum of n Terms

    $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

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20. 20.

    Physics

    A constant force of 90 N moves an object 15 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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