IIT-JEE · Practice Sheet 43

1. 1.

   Physics

   Find the density of an object with mass 64 g and volume 31 cm³.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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2. 2.

   Quantitative Aptitude

   In how many ways can 2 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 2.)

   Formula:Combinations

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

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3. 3.

   Physics

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

   Formula:Kinetic Energy

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

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4. 4.

   Chemistry

   How many moles are present in 36 g of water (H₂O) (molar mass = 18 g/mol)?

   Formula:Number of Moles

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

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5. 5.

   Chemistry

   95 mL of a 5 M solution is diluted to 208 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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6. 6.

   Physics

   An object starts at 7 m/s and accelerates at 8 m/s² for 11 s. Find its final velocity.

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

   $v = u + at$

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7. 7.

   Mathematics

   Evaluate ∫ from 1 to 5 of 1x^2 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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8. 8.

   Mathematics

   For the quadratic 1x² + 8x + 6 = 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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9. 9.

   Chemistry

   96 mL of a 10 M solution is diluted to 490 mL. Find the new concentration.

   Formula:Dilution

   $M_1V_1 = M_2V_2$

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10. 10.

    Mathematics

    Find term number 6 of a geometric progression with first term 4 and common ratio 2.

    Formula:GP nth Term

    $a_n = a\,r^{\,n-1}$

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11. 11.

    Mathematics

    For the quadratic 1x² + 0x − 9 = 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.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 8?

    Formula:Probability (two dice)

    $P = \dfrac{\text{favourable}}{\text{total}}$

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13. 13.

    Mathematics

    Evaluate log base 2 of 8.

    Formula:Logarithm Evaluation

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

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14. 14.

    Physics

    Find the momentum of a 20 kg body moving at 32 m/s.

    Formula:Linear Momentum

    $p = mv$

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15. 15.

    Physics

    Calculate the potential energy of a 5 kg object at a height of 14 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    Physics

    A body moving at 1 m/s accelerates at 5 m/s² for 6 s. Find the distance travelled.

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

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

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17. 17.

    Physics

    A constant force of 102 N moves an object 40 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

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18. 18.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 10?

    Formula:Probability (two dice)

    $P = \dfrac{\text{favourable}}{\text{total}}$

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19. 19.

    Mathematics

    In an arithmetic progression with first term 2 and common difference 8, find term number 11.

    Formula:AP nth Term

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

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20. 20.

    Mathematics

    Find the sum of the first 22 terms of an AP with first term 11 and common difference 4.

    Formula:AP Sum of n Terms

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

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