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IIT-JEE · Practice Sheet 34

Sheet code: IIT-JEE-S34 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
If f(x) = 5x³ + 5x² + 1x, find f′(1).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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2.
Physics
A body moving at 12 m/s accelerates at 3 m/s² for 7 s. Find the distance travelled.
Formula:Equation of Motion (s = ut + ½at²)
$s = ut + \tfrac{1}{2}at^{2}$
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3.
Mathematics
Find the binomial coefficient C(9, 2) — the coefficient of x^2 in (1 + x)^9.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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4.
Quantitative Aptitude
In how many ways can 4 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 4.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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5.
Physics
Calculate the potential energy of a 50 kg object at a height of 50 m (g = 9.8 m/s²).
Formula:Gravitational Potential Energy
$PE = mgh$
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6.
Mathematics
Find the sum of the first 6 terms of a GP with first term 2 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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7.
Mathematics
Find term number 4 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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8.
Physics
Find the kinetic energy of a 15 kg object moving at 7 m/s.
Formula:Kinetic Energy
$KE = \tfrac{1}{2}mv^{2}$
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9.
Mathematics
Find term number 3 of a geometric progression with first term 6 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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10.
Mathematics
For the quadratic 3x² − 6x + 3 = 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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11.
Mathematics
Find the binomial coefficient C(7, 2) — the coefficient of x^2 in (1 + x)^7.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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12.
Physics
An object starts at 1 m/s and accelerates at 7 m/s² for 5 s. Find its final velocity.
Formula:Equation of Motion (v = u + at)
$v = u + at$
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13.
Mathematics
If f(x) = 5x³ + 6x² + 2x, find f′(2).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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14.
Quantitative Aptitude
A vehicle covers 351 km in 9 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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15.
Physics
Find the electrical power when 143 V drives a current of 9 A.
Formula:Electrical Power
$P = VI$
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16.
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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17.
Mathematics
In an arithmetic progression with first term 20 and common difference 4, find term number 21.
Formula:AP nth Term
$a_n = a + (n-1)d$
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18.
Chemistry
A solution is made by dissolving 10 g of solute in 104 g of solvent. Find the mass percentage of the solute.
Formula:Mass Percentage
$\%\,\text{mass} = \dfrac{\text{solute}}{\text{solution}}\times 100$
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19.
Quantitative Aptitude
In how many ways can 2 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 2.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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20.
Chemistry
A solution is made by dissolving 22 g of solute in 108 g of solvent. Find the mass percentage of the solute.
Formula:Mass Percentage
$\%\,\text{mass} = \dfrac{\text{solute}}{\text{solution}}\times 100$
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