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JEE Main practice questions

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

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  1. 1If C arbitrary constant then the value of $\int\ 4sinxcos\frac{x}{2}cos\frac{3x}{2}$ dx is equal to.Mathematics· Indefinite integration· Moderate
  2. 2If c is arbitrary constant then $\int\frac{\left( x^{8} + 4 \right)dx}{x^{4} - 2x^{2} + 2} =$Mathematics· Indefinite integration· Easy
  3. 3If f(x) =a_0 + a_1 x^2 + a_2 x^4 +........+a_n x^2n be a polynomial where 0 < a_0 < a_1 < a_2 <....< a_n then f(x) hasMathematics· Monotonocity· Moderate
  4. 4Let f and g be function satisfying f(0)=1, g(0)=0 and $f^{'}(x) = g(x),g^{'}(x) = f(x)$ then fMathematics· Differentiation· Easy
  5. 5Number of point of minima of the polynomial $y = 10x^{6} - 24x^{5} + 15x^{4} - 40x^{2} + 108$ is (are) equal to ?Mathematics· Monotonocity· Moderate· figure
  6. 6If $y = 2\sin^{- 1}\sqrt{1 - x} - \sin^{- 1}(2\sqrt{x - x^{2}})$ where $x \in (0,\frac{1}{2})$ then $\frac{dy}{dx}$ is equal toMathematics· Differcntiation· Modertae
  7. 7Let f(x) and g(x) be two continuous functions defined from$\ R \rightarrow R,$ such that f (x_1 ) > f (x_2 ) and $g\left( x_{1} \right) <…Mathematics· Monotonocity· Tough
  8. 8Given $P(x) = x^{4} + ax^{3} + bx^{2} + cx + d$ such that x = 0 is the only real root of P'(x) = 0. If P (-1) < PMathematics· Monotonocity· Tough
  9. 9If the function $f(x) = \frac{t + 3x - x^{2}}{x - 4}$ where is a parameter has a local minima and a local maxima, then the range of values…Mathematics· Monotonocity· Moderate
  10. 10If the range of the function $y = \frac{x - 1}{x + 1}$ on the interval $0 \leq x \leq 4$ be then the value of 5 b - 2 a =.Mathematics· Monotonocity· Moderate
  11. 11If y = sec$\left( \tan^{- 1}x \right)$, and value of $\frac{dy}{dx}\ $at x = 1 is equal to $\frac{\lambda}{3\sqrt{2}}$ then $\lambda$ is…Mathematics· Differentiation· Easy· figure
  12. 12If a curve is represented parametrically by the equations x = 4t^3 + 3 and y = 4 + 3t^4 and $\frac{\left( \frac{d^{2}x}{dy^{2}}…Mathematics· Differentiation· Moderate
  13. 13The global maximum and minimum values of f(x) = 3x^4 - 8x^3 + 12x^2 - 48x + 25, x $\in$ are M and m respectively then value of 2M + m is…Mathematics· Monotonocity· Easy
  14. 14If x^2 + y^2 = 2 and 2y" + ay^-3 = 0, then value of $\frac{5a}{2}$ is equal toMathematics· Differentiation· Moderate
  15. 15If $y = \log_{\sqrt{e}}(sinx),$ then $\frac{dy}{dx}$ isMathematics· Differentiation· Easy
  16. 16If $f(x) = \log_{x}(lnx),$ then f' (x) at x=e is equal toMathematics· Differentiation· Moderate
  17. 17If differentiable function f(x) is inverse of g(x) then $f^{'}'(g(x))$ is equal toMathematics· Differentiation· Moderate
  18. 18If $x = a\cos^{3}t,y = b\sin^{3}t,$ then $\frac{dy}{dx} =$Mathematics· Differentiation· Easy
  19. 19If $y = \left( x^{x} \right)^{x},$ then $\frac{dy}{dx} =$Mathematics· Differentiation· Moderate
  20. 20Let $f(x) = \int\frac{x^{2}dx}{\left( 1 + x^{2} \right)\left( 1 + \sqrt{1 + x^{2}} \right)}$ and f (0) = 0, then the value of fMathematics· Indefinite integration· Moderate
  21. 21$\int\frac{x^{2} - 1}{\left( x^{2} + 1 \right)\sqrt{1 + x^{4}}}$ dx is equal toMathematics· Indefinite integration· Tough
  22. 22The Value $I = \int_{- 1}^{1}\mspace{2mu}\left( \cos^{- 1}x + \frac{x^{7} - 3x^{5} + 7x^{3} - x}{\cos^{2}x} \right)dx$ isMathematics· Definite Integration· Easy
  23. 23If integral $\int_{2}^{4}\mspace{2mu}\sqrt{\frac{x^{2} - 4}{x^{4}}}dx = ln(2 + \sqrt{3}) - \frac{\lambda\sqrt{3}}{64},$ then find the value…Mathematics· Definite Integration· Moderate
  24. 24The integral $\int_{0}^{1}\mspace{2mu}\frac{\tan^{- 1}x}{1 + x}$ dx equalsMathematics· Definite Integration· Moderate
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