GATE · Practice Sheet 45

1. 1.

   Mathematics

   Evaluate ∫ from 1 to 5 of 2x^3 dx.

   Formula:Definite Integral of a Power

   $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

   View formula →
2. 2.

   Physics

   An object starts at 4 m/s and accelerates at 3 m/s² for 9 s. Find its final velocity.

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

   $v = u + at$

   View formula →
3. 3.

   Mathematics

   Find the slope of the line through (4, 6) and (3, -7).

   Formula:Slope of a Line

   $m = \dfrac{y_2-y_1}{x_2-x_1}$

   View formula →
4. 4.

   Physics

   Find the kinetic energy of a 18 kg object moving at 28 m/s.

   Formula:Kinetic Energy

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

   View formula →
5. 5.

   Quantitative Aptitude

   In how many ways can 3 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 3.)

   Formula:Combinations

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

   View formula →
6. 6.

   Physics

   A projectile is launched at 13 m/s at 30° to the horizontal. Find its range (g = 9.8 m/s²).

   Formula:Projectile Range

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

   View formula →
7. 7.

   Physics

   Find the voltage across a 44 Ω resistor carrying a current of 17 A.

   Formula:Ohm's Law

   $V = IR$

   View formula →
8. 8.

   Mathematics

   Evaluate ∫ from 2 to 5 of 2x^2 dx.

   Formula:Definite Integral of a Power

   $\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$

   View formula →
9. 9.

   Physics

   Find the electrical power when 185 V drives a current of 4 A.

   Formula:Electrical Power

   $P = VI$

   View formula →
10. 10.

    Quantitative Aptitude

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

    Formula:Combinations

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

    View formula →
11. 11.

    Physics

    Find the force required to accelerate a 12 kg mass at 11 m/s².

    Formula:Newton's Second Law (F = ma)

    $F = ma$

    View formula →
12. 12.

    Mathematics

    If f(x) = 2x³ + 1x² + 8x, find f′(4).

    Formula:Derivative of a Polynomial

    $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

    View formula →
13. 13.

    Physics

    If 4,243 J of work is done in 33 s, find the power.

    Formula:Power

    $P = \dfrac{W}{t}$

    View formula →
14. 14.

    Mathematics

    Find the sum of the first 7 terms of an AP with first term 18 and common difference 6.

    Formula:AP Sum of n Terms

    $S_n = \dfrac{n}{2}\,[2a+(n-1)d]$

    View formula →
15. 15.

    Mathematics

    For the quadratic 2x² + 1x − 1 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)

    $\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$

    View formula →
16. 16.

    Physics

    Find the force required to accelerate a 4 kg mass at 20 m/s².

    Formula:Newton's Second Law (F = ma)

    $F = ma$

    View formula →
17. 17.

    Mathematics

    Find term number 4 of a geometric progression with first term 6 and common ratio 3.

    Formula:GP nth Term

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

    View formula →
18. 18.

    Mathematics

    In an arithmetic progression with first term 6 and common difference 4, find term number 20.

    Formula:AP nth Term

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

    View formula →
19. 19.

    Physics

    An object starts at 11 m/s and accelerates at 2 m/s² for 3 s. Find its final velocity.

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

    $v = u + at$

    View formula →
20. 20.

    Mathematics

    If f(x) = 4x³ + 4x² + 5x, find f′(2).

    Formula:Derivative of a Polynomial

    $\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$

    View formula →

© FormulaWon — formulawon.app · Answers & step-by-step working available on the solutions sheet.