IIT-JEE · Practice Sheet 24

1. 1.

   Mathematics

   For the quadratic 3x² + 1x + 7 = 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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2. 2.

   Mathematics

   Find term number 3 of a geometric progression with first term 2 and common ratio 3.

   Formula:GP nth Term

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

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3. 3.

   Physics

   An object starts at 1 m/s and accelerates at 7 m/s² for 9 s. Find its final velocity.

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

   $v = u + at$

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4. 4.

   Mathematics

   Find term number 7 of a geometric progression with first term 6 and common ratio 2.

   Formula:GP nth Term

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

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5. 5.

   Physics

   Find the momentum of a 45 kg body moving at 33 m/s.

   Formula:Linear Momentum

   $p = mv$

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6. 6.

   Physics

   A projectile is launched at 32 m/s at 60° 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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7. 7.

   Physics

   Find the density of an object with mass 278 g and volume 31 cm³.

   Formula:Density

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

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8. 8.

   Physics

   Find the kinetic energy of a 6 kg object moving at 6 m/s.

   Formula:Kinetic Energy

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

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9. 9.

   Physics

   Find the voltage across a 45 Ω resistor carrying a current of 20 A.

   Formula:Ohm's Law

   $V = IR$

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10. 10.

    Mathematics

    Find the distance between the points (7, 2) and (1, 1).

    Formula:Distance Between Two Points

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

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11. 11.

    Mathematics

    Evaluate log base 10 of 100,000.

    Formula:Logarithm Evaluation

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

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12. 12.

    Mathematics

    Find the binomial coefficient C(10, 3) — the coefficient of x^3 in (1 + x)^10.

    Formula:Binomial Coefficient

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

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13. 13.

    Chemistry

    33 mL of a 5 M solution is diluted to 388 mL. Find the new concentration.

    Formula:Dilution

    $M_1V_1 = M_2V_2$

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14. 14.

    Chemistry

    How many moles are present in 22 g of carbon dioxide (CO₂) (molar mass = 44 g/mol)?

    Formula:Number of Moles

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

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15. 15.

    Physics

    Calculate the potential energy of a 37 kg object at a height of 26 m (g = 9.8 m/s²).

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    Physics

    Find the density of an object with mass 67 g and volume 2 cm³.

    Formula:Density

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

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17. 17.

    Mathematics

    Evaluate ∫ from 0 to 3 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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18. 18.

    Quantitative Aptitude

    A vehicle covers 335 km in 5 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

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19. 19.

    Chemistry

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

    Formula:Molarity

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

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20. 20.

    Mathematics

    In an arithmetic progression with first term 1 and common difference 6, find term number 6.

    Formula:AP nth Term

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

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