Practice/Question bank/JEE Main

JEE Main practice questions

NTA-style Physics, Chemistry and Maths MCQs with solutions. 2,688 questions in the bank.

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  1. 1Let f: R $\rightarrow$ R be a twice differentiable function satisfying f(2) = - 1, f '(2) = 4 and $\int_{2}^{3}\mspace{2mu}(3 -…Mathematics· Definite Integration· Easy
  2. 2$\int_{- \pi/2}^{\pi/2}\mspace{2mu}\sin^{10}x\left( 6x^{9} - 25x^{7} + 4x^{3} - 2x \right)$ dx equals.Mathematics· Definite Integration· Easy
  3. 3$\int_{2 - log3}^{3 + log3}\mspace{2mu}\frac{log(4 + x)}{log(4 + x) + log(9 - x)}$ dx is equal toMathematics· Definite Integration· Moderate
  4. 4If tan⁡$(\alpha + \beta) = \frac{1}{2}\ $and $tan(\alpha = \beta) = \frac{1}{3}$ then tan⁡$2\alpha\ is\ $(where $\alpha + \beta$ and…Mathematics· Definite Integration· Easy
  5. 5If $\int_{0}^{100}\mspace{2mu} f(x)dx = a,\ then\ \left. \ \sum_{r = 1}^{100}\mspace{2mu}\int_{0}^{1}\mspace{2mu} f(r - 1 + x)dx \right) =$Mathematics· Definite Integration· Moderate
  6. 6The value of $\int_{0}^{2\pi}\mspace{2mu} x\sin^{6}x{\ cos}^{4}$⁡x dx is equal to.Mathematics· Definite Integration· Moderate
  7. 7Area bounded by curves y^2 = x and y = | x | is given byMathematics· Definite Integration· Moderate· figure
  8. 8General solution of differential equation $x^{2}(x + y\frac{dy}{dx}) + (x\frac{dy}{dx} - y)\sqrt{x^{2} + y^{2}} = 0$ isMathematics· Differential equation· Moderate
  9. 9The slope of the tangent to curve $y = \int_{x}^{x^{2}}\mspace{2mu}\cos^{- 1}t^{2}dt\ at\ x = \frac{1}{\sqrt[4]{2}}$ isMathematics· Definite Integration· Moderate
  10. 10If y(x) is the solution of the differential equation $\frac{dt}{dx}$ = - 2 (y - 1), then $\lim_{x \rightarrow \infty}\mspace{2mu} y(x)$…Mathematics· Differential equation· Moderate
  11. 11Let $\frac{d}{dx}(f(x)) = \frac{e^{sinx}}{x},x > 0,\ If\ \int_{1}^{4}\mspace{2mu}\frac{2e^{sinx^{2}}}{x}$ dx = f(k) - f(1), then one of the…Mathematics· Definite Integration· Tough
  12. 12If the order and degree of differential equation $\left\lbrack 1 + \left( \frac{dy}{dx} \right)^{2} \right\rbrack^{5/2} =…Mathematics· Differential equation· Easy
  13. 13If the curve satisfying x(x + 1) $\frac{dy}{dx}$ - y = x(x + 1), passes through (1, 0), then the value of $\frac{5}{2}\left( \frac{5y}{4} -…Mathematics· Differential equation· Tough
  14. 14For any integer n, the integral $\int_{0}^{\pi}\mspace{2mu} e^{\sin^{2}x}\cos^{3}$(2n + 1)x dx has the value.Mathematics· Definite Integration· Moderate
  15. 15The solution of the differential equation $\frac{dy}{dx} = \frac{x + y}{x}$ satisfying the condition yMathematics· Differential equation· Moderate
  16. 16Value of $\int_{0}^{\pi/4}\mspace{2mu}\mathcal{l}n(1 + cos4x)$dx is.Mathematics· Definite Integration· Moderate
  17. 17Area bounded by $y = x^{2}\ and\ y = \frac{2}{1 + x^{2}}$ is.Mathematics· Definite Integration· Tough· figure
  18. 18The solution of differential equation (ex + 1) y dy = (y + 1) e^x dx is.Mathematics· Differential Equation· Easy
  19. 19If $f(x) = \int_{0}^{x}\mspace{2mu} 2|t|dt$, then the tangent to f(x) which are parallel to the angle bisector of the axes, in the first…Mathematics· Definite Integration· Tough
  20. 20The area bounded by the curves y = 6x - x^2 and y = x^2 - 2x isMathematics· Definite Integration· Easy
  21. 21The equation of the common tangent to the circle [IMAGE] and the parabola [IMAGE] above the x-axis isMathematics· Parabola· Moderate· figure
  22. 22A tangent drawn to hyperbola [IMAGE] at [IMAGE] forms a triangle of area [IMAGE] sq. units, with coordinate axes. Its eccentricity is equal…Mathematics· Hyperbola· Moderate· figure
  23. 23If [IMAGE] and [IMAGE] are the roots of the equation [IMAGE] where [IMAGE] and [IMAGE] eccentricities of an ellipse and hyperbola…Mathematics· Ellipse· Moderate· figure
  24. 24Distance between the parallel tangents having slopes [IMAGE] to the ellipse [IMAGE] isMathematics· Ellipse· Easy· figure
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