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Engineering Entrance · Practice Sheet 32

Sheet code: UAE-ENGINEERING-S32 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Find term number 7 of a geometric progression with first term 3 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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2.
Physics
Calculate the potential energy of a 6 kg object at a height of 16 m (g = 9.8 m/s²).
Formula:Gravitational Potential Energy
$PE = mgh$
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3.
Physics
Find the momentum of a 41 kg body moving at 32 m/s.
Formula:Linear Momentum
$p = mv$
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4.
Physics
A body moving at 2 m/s accelerates at 7 m/s² for 3 s. Find the distance travelled.
Formula:Equation of Motion (s = ut + ½at²)
$s = ut + \tfrac{1}{2}at^{2}$
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5.
Physics
If 4,326 J of work is done in 24 s, find the power.
Formula:Power
$P = \dfrac{W}{t}$
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6.
Mathematics
In an arithmetic progression with first term 18 and common difference 10, find term number 9.
Formula:AP nth Term
$a_n = a + (n-1)d$
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7.
Physics
Find the kinetic energy of a 13 kg object moving at 5 m/s.
Formula:Kinetic Energy
$KE = \tfrac{1}{2}mv^{2}$
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8.
Mathematics
Find term number 3 of a geometric progression with first term 3 and common ratio 2.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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9.
Mathematics
If f(x) = 3x³ + 4x² + 9x, find f′(5).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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10.
Mathematics
Evaluate ∫ from 0 to 5 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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11.
Physics
Find the kinetic energy of a 8 kg object moving at 8 m/s.
Formula:Kinetic Energy
$KE = \tfrac{1}{2}mv^{2}$
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12.
Mathematics
Evaluate log base 5 of 15,625.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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13.
Physics
If 4,342 J of work is done in 31 s, find the power.
Formula:Power
$P = \dfrac{W}{t}$
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14.
Chemistry
Find the molarity of a solution containing 3 mol of solute in 2.5 L of solution.
Formula:Molarity
$M = \dfrac{n}{V}$
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15.
Mathematics
Find the sum of the first 5 terms of a GP with first term 4 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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16.
Physics
An object starts at 2 m/s and accelerates at 7 m/s² for 8 s. Find its final velocity.
Formula:Equation of Motion (v = u + at)
$v = u + at$
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17.
Mathematics
Find the binomial coefficient C(7, 4) — the coefficient of x^4 in (1 + x)^7.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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18.
Physics
A body moving at 4 m/s accelerates at 1 m/s² for 8 s. Find the distance travelled.
Formula:Equation of Motion (s = ut + ½at²)
$s = ut + \tfrac{1}{2}at^{2}$
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19.
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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20.
Physics
Find the voltage across a 19 Ω resistor carrying a current of 2 A.
Formula:Ohm's Law
$V = IR$
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