IIT-JEE · Practice Sheet 29

1. 1.

   Physics

   Calculate the potential energy of a 20 kg object at a height of 19 m (g = 9.8 m/s²).

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
2. 2.

   Mathematics

   Find the binomial coefficient C(7, 3) — the coefficient of x^3 in (1 + x)^7.

   Formula:Binomial Coefficient

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

   View formula →
3. 3.

   Quantitative Aptitude

   In how many ways can 3 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 3.)

   Formula:Permutations

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

   View formula →
4. 4.

   Physics

   Find the electrical power when 195 V drives a current of 5 A.

   Formula:Electrical Power

   $P = VI$

   View formula →
5. 5.

   Mathematics

   Find the sum of the first 18 terms of an AP with first term 6 and common difference 9.

   Formula:AP Sum of n Terms

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

   View formula →
6. 6.

   Physics

   Find the density of an object with mass 62 g and volume 16 cm³.

   Formula:Density

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

   View formula →
7. 7.

   Mathematics

   Find the sum of the first 4 terms of a GP with first term 3 and common ratio 2.

   Formula:GP Sum of n Terms

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

   View formula →
8. 8.

   Physics

   Find the force required to accelerate a 20 kg mass at 8 m/s².

   Formula:Newton's Second Law (F = ma)

   $F = ma$

   View formula →
9. 9.

   Chemistry

   Find the molarity of a solution containing 0.5 mol of solute in 2.5 L of solution.

   Formula:Molarity

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

   View formula →
10. 10.

    Physics

    If 2,818 J of work is done in 24 s, find the power.

    Formula:Power

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

    View formula →
11. 11.

    Physics

    Find the kinetic energy of a 11 kg object moving at 11 m/s.

    Formula:Kinetic Energy

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

    View formula →
12. 12.

    Physics

    Find the momentum of a 19 kg body moving at 35 m/s.

    Formula:Linear Momentum

    $p = mv$

    View formula →
13. 13.

    Mathematics

    Evaluate ∫ from 0 to 4 of 2x^2 dx.

    Formula:Definite Integral of a Power

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

    View formula →
14. 14.

    Mathematics

    Evaluate log base 5 of 625.

    Formula:Logarithm Evaluation

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

    View formula →
15. 15.

    Chemistry

    Find the pressure of 4 mol of an ideal gas at 235 K in a 15 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

    View formula →
16. 16.

    Physics

    Find the momentum of a 45 kg body moving at 9 m/s.

    Formula:Linear Momentum

    $p = mv$

    View formula →
17. 17.

    Physics

    Calculate the potential energy of a 28 kg object at a height of 41 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
18. 18.

    Physics

    Find the density of an object with mass 373 g and volume 8 cm³.

    Formula:Density

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

    View formula →
19. 19.

    Physics

    Find the electrical power when 113 V drives a current of 13 A.

    Formula:Electrical Power

    $P = VI$

    View formula →
20. 20.

    Mathematics

    For the quadratic 1x² − 5x − 8 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)

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

    View formula →

© FormulaWon — formulawon.app · Answers & step-by-step working available on the solutions sheet.