IIT-JEE · Practice Sheet 22

1. 1.

   Quantitative Aptitude

   A vehicle covers 106 km in 2 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

   View formula →
2. 2.

   Mathematics

   For the quadratic 4x² + 0x − 5 = 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 →
3. 3.

   Physics

   A force of 550 N acts on an area of 49 m². Find the pressure.

   Formula:Pressure

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

   View formula →
4. 4.

   Physics

   A body moving at 2 m/s accelerates at 4 m/s² for 8 s. Find the distance travelled.

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

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

   View formula →
5. 5.

   Mathematics

   If f(x) = 3x³ + 4x² + 7x, find f′(1).

   Formula:Derivative of a Polynomial

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

   View formula →
6. 6.

   Chemistry

   How many moles are present in 132 g of carbon dioxide (CO₂) (molar mass = 44 g/mol)?

   Formula:Number of Moles

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

   View formula →
7. 7.

   Physics

   A projectile is launched at 17 m/s at 45° to the horizontal. Find its range (g = 9.8 m/s²).

   Formula:Projectile Range

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

   View formula →
8. 8.

   Physics

   If 3,121 J of work is done in 32 s, find the power.

   Formula:Power

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

   View formula →
9. 9.

   Physics

   A body moving at 9 m/s accelerates at 8 m/s² for 7 s. Find the distance travelled.

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

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

   View formula →
10. 10.

    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 4.)

    Formula:Permutations

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

    View formula →
11. 11.

    Mathematics

    Evaluate ∫ from 2 to 3 of 5x^3 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 →
12. 12.

    Physics

    Find the electrical power when 143 V drives a current of 12 A.

    Formula:Electrical Power

    $P = VI$

    View formula →
13. 13.

    Physics

    Find the density of an object with mass 351 g and volume 50 cm³.

    Formula:Density

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

    View formula →
14. 14.

    Chemistry

    A solution is made by dissolving 26 g of solute in 134 g of solvent. Find the mass percentage of the solute.

    Formula:Mass Percentage

    $\%\,\text{mass} = \dfrac{\text{solute}}{\text{solution}}\times 100$

    View formula →
15. 15.

    Mathematics

    Find the sum of the first 5 terms of an AP with first term 12 and common difference 1.

    Formula:AP Sum of n Terms

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

    View formula →
16. 16.

    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 3.)

    Formula:Permutations

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

    View formula →
17. 17.

    Mathematics

    Evaluate ∫ from 0 to 5 of 4x^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 →
18. 18.

    Chemistry

    61 mL of a 1 M solution is diluted to 173 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

    View formula →
19. 19.

    Chemistry

    Find the molarity of a solution containing 1 mol of solute in 4 L of solution.

    Formula:Molarity

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

    View formula →
20. 20.

    Quantitative Aptitude

    In how many ways can 2 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 2.)

    Formula:Permutations

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

    View formula →

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