GATE · Practice Sheet 6

1. 1.

   Physics

   A force of 764 N acts on an area of 26 m². Find the pressure.

   Formula:Pressure

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

   View formula →
2. 2.

   Quantitative Aptitude

   In how many ways can 2 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 2.)

   Formula:Combinations

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

   View formula →
3. 3.

   Physics

   A projectile is launched at 39 m/s at 45° to the horizontal. Find its range (g = 9.8 m/s²).

   Formula:Projectile Range

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

   View formula →
4. 4.

   Quantitative Aptitude

   What is 60% of 280?

   Formula:Percentage of a Number

   $\text{Value} = \dfrac{P}{100}\times N$

   View formula →
5. 5.

   Mathematics

   Find the sum of the first 13 terms of an AP with first term 10 and common difference 10.

   Formula:AP Sum of n Terms

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

   View formula →
6. 6.

   Physics

   If 2,750 J of work is done in 26 s, find the power.

   Formula:Power

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

   View formula →
7. 7.

   Mathematics

   If f(x) = 1x³ + 6x² + 3x, find f′(4).

   Formula:Derivative of a Polynomial

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

   View formula →
8. 8.

   Mathematics

   For the quadratic 5x² − 7x − 7 = 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 →
9. 9.

   Quantitative Aptitude

   A vehicle covers 186 km in 6 hours. Find its average speed.

   Formula:Speed, Distance & Time

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

   View formula →
10. 10.

    Mathematics

    Evaluate log base 5 of 25.

    Formula:Logarithm Evaluation

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

    View formula →
11. 11.

    Quantitative Aptitude

    Find the simple interest on ₹4,000 at 12% per annum for 1 year(s).

    Formula:Simple Interest

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

    View formula →
12. 12.

    Mathematics

    Find the slope of the line through (0, -7) and (6, -6).

    Formula:Slope of a Line

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

    View formula →
13. 13.

    Mathematics

    Evaluate log base 3 of 243.

    Formula:Logarithm Evaluation

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

    View formula →
14. 14.

    Mathematics

    In an arithmetic progression with first term 13 and common difference 7, find term number 23.

    Formula:AP nth Term

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

    View formula →
15. 15.

    Physics

    If 4,383 J of work is done in 21 s, find the power.

    Formula:Power

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

    View formula →
16. 16.

    Physics

    A constant force of 82 N moves an object 10 m in the direction of the force. Calculate the work done.

    Formula:Work Done

    $W = F\,d$

    View formula →
17. 17.

    Physics

    Find the force required to accelerate a 47 kg mass at 6 m/s².

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

    $F = ma$

    View formula →
18. 18.

    Mathematics

    If f(x) = 5x³ + 1x² + 2x, find f′(2).

    Formula:Derivative of a Polynomial

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

    View formula →
19. 19.

    Mathematics

    Evaluate ∫ from 0 to 4 of 1x^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 →
20. 20.

    Physics

    A body moving at 3 m/s accelerates at 3 m/s² for 8 s. Find the distance travelled.

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

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

    View formula →

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