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IIT-JEE · Practice Sheet 19

Sheet code: IIT-JEE-S19 · 20 questions

Name: ______________

Date: ______________

1.
Physics
Find the density of an object with mass 317 g and volume 35 cm³.
Formula:Density
$\rho = \dfrac{m}{V}$
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2.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 9?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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3.
Physics
A body moving at 5 m/s accelerates at 1 m/s² for 10 s. Find the distance travelled.
Formula:Equation of Motion (s = ut + ½at²)
$s = ut + \tfrac{1}{2}at^{2}$
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4.
Physics
Find the momentum of a 18 kg body moving at 22 m/s.
Formula:Linear Momentum
$p = mv$
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5.
Physics
Find the voltage across a 31 Ω resistor carrying a current of 16 A.
Formula:Ohm's Law
$V = IR$
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6.
Mathematics
For the quadratic 5x² + 5x − 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.
Physics
If 184 J of work is done in 36 s, find the power.
Formula:Power
$P = \dfrac{W}{t}$
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8.
Chemistry
Find the pH of a solution with [H⁺] = 5×10⁻4 mol/L.
Formula:pH of a Solution
$pH = -\log_{10}[H^{+}]$
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9.
Mathematics
Find the slope of the line through (1, -3) and (-7, -5).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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10.
Physics
Find the force required to accelerate a 49 kg mass at 7 m/s².
Formula:Newton's Second Law (F = ma)
$F = ma$
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11.
Physics
Find the density of an object with mass 118 g and volume 24 cm³.
Formula:Density
$\rho = \dfrac{m}{V}$
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12.
Mathematics
If f(x) = 5x³ + 6x² + 4x, find f′(2).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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13.
Quantitative Aptitude
A vehicle covers 553 km in 7 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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14.
Physics
Calculate the potential energy of a 1 kg object at a height of 7 m (g = 9.8 m/s²).
Formula:Gravitational Potential Energy
$PE = mgh$
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15.
Chemistry
Find the molarity of a solution containing 1 mol of solute in 2 L of solution.
Formula:Molarity
$M = \dfrac{n}{V}$
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16.
Chemistry
99 mL of a 5 M solution is diluted to 336 mL. Find the new concentration.
Formula:Dilution
$M_1V_1 = M_2V_2$
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17.
Physics
Find the voltage across a 30 Ω resistor carrying a current of 17 A.
Formula:Ohm's Law
$V = IR$
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18.
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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19.
Mathematics
Find the slope of the line through (3, 2) and (-2, -6).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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20.
Chemistry
Find the pressure of 4 mol of an ideal gas at 400 K in a 20 L container (R = 0.0821 L·atm·mol⁻¹·K⁻¹).
Formula:Ideal Gas Law
$PV = nRT$
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