IIT-JEE · Practice Sheet 32

1. 1.

   Physics

   Find the voltage across a 18 Ω resistor carrying a current of 16 A.

   Formula:Ohm's Law

   $V = IR$

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2. 2.

   Mathematics

   Find the binomial coefficient C(9, 4) — the coefficient of x^4 in (1 + x)^9.

   Formula:Binomial Coefficient

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

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3. 3.

   Quantitative Aptitude

   In how many ways can 2 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 2.)

   Formula:Permutations

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

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4. 4.

   Mathematics

   Evaluate log base 2 of 16.

   Formula:Logarithm Evaluation

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

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5. 5.

   Physics

   Find the electrical power when 188 V drives a current of 10 A.

   Formula:Electrical Power

   $P = VI$

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6. 6.

   Mathematics

   For the quadratic 3x² − 7x − 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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7. 7.

   Mathematics

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

   Formula:GP nth Term

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

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8. 8.

   Mathematics

   Evaluate ∫ from 1 to 4 of 3x^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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9. 9.

   Physics

   A constant force of 73 N moves an object 32 m in the direction of the force. Calculate the work done.

   Formula:Work Done

   $W = F\,d$

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10. 10.

    Physics

    Find the kinetic energy of a 1 kg object moving at 19 m/s.

    Formula:Kinetic Energy

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

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11. 11.

    Mathematics

    In an arithmetic progression with first term 20 and common difference 6, find term number 9.

    Formula:AP nth Term

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

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12. 12.

    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 4.)

    Formula:Combinations

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

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13. 13.

    Chemistry

    Find the pressure of 4 mol of an ideal gas at 340 K in a 7 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).

    Formula:Ideal Gas Law

    $PV = nRT$

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14. 14.

    Mathematics

    Evaluate log base 5 of 625.

    Formula:Logarithm Evaluation

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

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15. 15.

    Physics

    A force of 922 N acts on an area of 32 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Physics

    A projectile is launched at 31 m/s at 45° to the horizontal. Find its range (g = 9.8 m/s²).

    Formula:Projectile Range

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

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17. 17.

    Physics

    An object starts at 16 m/s and accelerates at 9 m/s² for 11 s. Find its final velocity.

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

    $v = u + at$

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18. 18.

    Mathematics

    In an arithmetic progression with first term 2 and common difference 6, find term number 23.

    Formula:AP nth Term

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

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19. 19.

    Mathematics

    Evaluate ∫ from 2 to 4 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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20. 20.

    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 5?

    Formula:Probability (two dice)

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

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