GATE · Practice Sheet 25

1. 1.

   Mathematics

   Find the slope of the line through (-5, 6) and (-4, -2).

   Formula:Slope of a Line

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

   View formula →
2. 2.

   Mathematics

   Evaluate ∫ from 1 to 5 of 3x^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 →
3. 3.

   Mathematics

   Find the sum of the first 13 terms of an AP with first term 7 and common difference 9.

   Formula:AP Sum of n Terms

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

   View formula →
4. 4.

   Mathematics

   Find term number 7 of a geometric progression with first term 3 and common ratio 3.

   Formula:GP nth Term

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

   View formula →
5. 5.

   Physics

   A projectile is launched at 27 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 →
6. 6.

   Mathematics

   In an arithmetic progression with first term 19 and common difference 6, find term number 7.

   Formula:AP nth Term

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

   View formula →
7. 7.

   Mathematics

   Find the distance between the points (3, 0) and (-6, 4).

   Formula:Distance Between Two Points

   $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

   View formula →
8. 8.

   Quantitative Aptitude

   Find the HCF and LCM of 26 and 11.

   Formula:LCM & HCF

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

   View formula →
9. 9.

   Quantitative Aptitude

   What is 60% of 160?

   Formula:Percentage of a Number

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

   View formula →
10. 10.

    Physics

    A force of 553 N acts on an area of 23 m². Find the pressure.

    Formula:Pressure

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

    View formula →
11. 11.

    Mathematics

    Find the distance between the points (-4, 2) and (8, 2).

    Formula:Distance Between Two Points

    $d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

    View formula →
12. 12.

    Mathematics

    Evaluate ∫ from 0 to 4 of 3x^2 dx.

    Formula:Definite Integral of a Power

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

    View formula →
13. 13.

    Physics

    Find the force required to accelerate a 39 kg mass at 12 m/s².

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

    $F = ma$

    View formula →
14. 14.

    Mathematics

    Evaluate log base 10 of 10,000.

    Formula:Logarithm Evaluation

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

    View formula →
15. 15.

    Quantitative Aptitude

    A vehicle covers 306 km in 6 hours. Find its average speed.

    Formula:Speed, Distance & Time

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

    View formula →
16. 16.

    Quantitative Aptitude

    What is 15% of 720?

    Formula:Percentage of a Number

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

    View formula →
17. 17.

    Physics

    Find the kinetic energy of a 12 kg object moving at 4 m/s.

    Formula:Kinetic Energy

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

    View formula →
18. 18.

    Mathematics

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

    Formula:Derivative of a Polynomial

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

    View formula →
19. 19.

    Mathematics

    Find term number 4 of a geometric progression with first term 5 and common ratio 2.

    Formula:GP nth Term

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

    View formula →
20. 20.

    Mathematics

    For the quadratic 4x² + 5x + 9 = 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 →

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