GATE · Practice Sheet 21

1. 1.

   Physics

   A body moving at 5 m/s accelerates at 3 m/s² for 2 s. Find the distance travelled.

   Formula:Equation of Motion (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^{2}$

   View formula →
2. 2.

   Quantitative Aptitude

   Find the simple interest on ₹13,000 at 8% per annum for 5 year(s).

   Formula:Simple Interest

   $SI = \dfrac{P\times R\times T}{100}$

   View formula →
3. 3.

   Mathematics

   For the quadratic 1x² − 8x − 4 = 0, find the sum and product of its roots.

   Formula:Vieta's Formulas (roots)

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

   View formula →
4. 4.

   Physics

   An object starts at 15 m/s and accelerates at 6 m/s² for 12 s. Find its final velocity.

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

   $v = u + at$

   View formula →
5. 5.

   Quantitative Aptitude

   In how many ways can 4 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 4.)

   Formula:Permutations

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

   View formula →
6. 6.

   Physics

   If 117 J of work is done in 30 s, find the power.

   Formula:Power

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

   View formula →
7. 7.

   Physics

   A projectile is launched at 23 m/s at 60° to the horizontal. Find its range (g = 9.8 m/s²).

   Formula:Projectile Range

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

   View formula →
8. 8.

   Physics

   A force of 815 N acts on an area of 44 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

   View formula →
9. 9.

   Mathematics

   Find the slope of the line through (-2, 6) and (8, -5).

   Formula:Slope of a Line

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

   View formula →
10. 10.

    Physics

    A body moving at 14 m/s accelerates at 1 m/s² for 10 s. Find the distance travelled.

    Formula:Equation of Motion (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^{2}$

    View formula →
11. 11.

    Quantitative Aptitude

    Find the simple interest on ₹49,000 at 12% per annum for 4 year(s).

    Formula:Simple Interest

    $SI = \dfrac{P\times R\times T}{100}$

    View formula →
12. 12.

    Mathematics

    Find the sum of the first 17 terms of an AP with first term 20 and common difference 6.

    Formula:AP Sum of n Terms

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

    View formula →
13. 13.

    Physics

    An object starts at 18 m/s and accelerates at 4 m/s² for 7 s. Find its final velocity.

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

    $v = u + at$

    View formula →
14. 14.

    Mathematics

    Evaluate log base 5 of 625.

    Formula:Logarithm Evaluation

    $\log_{b}(b^{k}) = k$

    View formula →
15. 15.

    Mathematics

    For the quadratic 3x² + 5x + 3 = 0, find the sum and product of its roots.

    Formula:Vieta's Formulas (roots)

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

    View formula →
16. 16.

    Physics

    Find the voltage across a 13 Ω resistor carrying a current of 14 A.

    Formula:Ohm's Law

    $V = IR$

    View formula →
17. 17.

    Mathematics

    For the quadratic 4x² + 5x − 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 →
18. 18.

    Mathematics

    Evaluate ∫ from 0 to 3 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 →
19. 19.

    Quantitative Aptitude

    Find the HCF and LCM of 36 and 12.

    Formula:LCM & HCF

    $\text{LCM}\times\text{HCF} = a\times b$

    View formula →
20. 20.

    Quantitative Aptitude

    A vehicle covers 469 km in 7 hours. Find its average speed.

    Formula:Speed, Distance & Time

    $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

    View formula →

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