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IIT-JEE · Practice Sheet 20

Sheet code: IIT-JEE-S20 · 20 questions

Name: ______________

Date: ______________

1.
Physics
Find the kinetic energy of a 9 kg object moving at 15 m/s.
Formula:Kinetic Energy
$KE = \tfrac{1}{2}mv^{2}$
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2.
Physics
Find the force required to accelerate a 25 kg mass at 20 m/s².
Formula:Newton's Second Law (F = ma)
$F = ma$
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3.
Physics
Find the kinetic energy of a 17 kg object moving at 8 m/s.
Formula:Kinetic Energy
$KE = \tfrac{1}{2}mv^{2}$
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4.
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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5.
Physics
A projectile is launched at 25 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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6.
Mathematics
Find term number 5 of a geometric progression with first term 5 and common ratio 2.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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7.
Physics
A constant force of 173 N moves an object 8 m in the direction of the force. Calculate the work done.
Formula:Work Done
$W = F\,d$
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8.
Physics
If 4,447 J of work is done in 29 s, find the power.
Formula:Power
$P = \dfrac{W}{t}$
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9.
Mathematics
For the quadratic 1x² + 9x + 4 = 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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10.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 6?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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11.
Mathematics
Find the sum of the first 6 terms of a GP with first term 3 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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12.
Mathematics
Evaluate log base 5 of 125.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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13.
Physics
An object starts at 8 m/s and accelerates at 4 m/s² for 9 s. Find its final velocity.
Formula:Equation of Motion (v = u + at)
$v = u + at$
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14.
Quantitative Aptitude
A vehicle covers 704 km in 8 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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15.
Mathematics
Find the binomial coefficient C(9, 3) — the coefficient of x^3 in (1 + x)^9.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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16.
Chemistry
How many moles are present in 64 g of oxygen gas (O₂) (molar mass = 32 g/mol)?
Formula:Number of Moles
$n = \dfrac{m}{M}$
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17.
Mathematics
Find the distance between the points (-2, 6) and (-4, 0).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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18.
Mathematics
Evaluate log base 10 of 1,000,000.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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19.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 6?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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20.
Physics
Find the force required to accelerate a 10 kg mass at 2 m/s².
Formula:Newton's Second Law (F = ma)
$F = ma$
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