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. 1$f(x) = \left\{ \begin{matrix} x + 1, & x < 0 \\ 1, & x = 0, \\ 2x^{2} + 1, & x > 0 \end{matrix} \right.\ $ thenMathematics· Limits, continuity and differentiability· Moderate
  2. 2A point on the parabola $y^{2} = 18x$at which the ordinate increases at twice the rate of abscissa isMathematics· Application of derivatives· Moderate
  3. 3If the function $f(x) = (1 - x)tan\frac{\pi x}{2}$ is continuous at x = 1, then fMathematics· Continuity and differentiability· Moderate
  4. 4If f(x) is derivable at x = 1, then $\lim_{x \rightarrow a}\frac{xf(a) - af(x)}{x - a}$Mathematics· Continuity and differentiability· Moderate
  5. 5The value of c in Lagrange's mean value theorem for the function $f(x) = |x|$ in the interval $\lbrack - 1,1\rbrack$ isMathematics· Continuity and differentiability· Easy
  6. 6If $y = \sin^{- 1}(3x - 4x^{3})$, then the number of points in, where y is not differentiable isMathematics· Continuity and differentiability· Tough· figure
  7. 7$\int{(\sqrt[3]{x} + \frac{1}{\sqrt[3]{x}})}^{3}dx$ equalsMathematics· Integrals· Easy
  8. 8$\int\frac{a^{\sqrt{x}}}{\sqrt{x}}dx$ equalsMathematics· Integrals· Moderate
  9. 9The principal value of $\sin^{- 1}(\frac{1}{2})$ isMathematics· ITF· Easy
  10. 10If $\sin^{- 1}(\frac{3}{x}) + \sin^{- 1}(\frac{4}{x}) = \frac{\pi}{2}$ then x equalsMathematics· ITF· Moderate
  11. 11If $\int\frac{x^{4} + 1}{x\left( x^{2} + 1 \right)^{2}}dx = A\ In|x| + \frac{B}{1 + x^{2}} + C$ thenMathematics· Integrals· Moderate
  12. 12If $B = \{ x:x = \frac{2n - 1}{n + 2},n \in W$ and $n < 4\}$ then B can be written asMathematics· Sets· Easy
  13. 13The expansion [IMAGE] is valid when n isMathematics· Binomial Theorem· Easy· figure
  14. 14$\int\tan^{- 1}(\sqrt{}\frac{1 - x}{1 + x})dx$ equalsMathematics· Integrals· Moderate
  15. 15Consider the function $f(x) = x + \frac{1}{x},x \in (\frac{1}{2},\frac{9}{2})$. If $\alpha$ is the length of interval of decrease and…Mathematics· Application of derivatives· Moderate
  16. 16If the coefficient of $x^{3}$ is 1140 in the expansion of ${(1 + 2x + kx^{2})}^{10}$, then the value of k is _____.Mathematics· Binomial Theorem· Moderate
  17. 17If the right hand derivative of $h(x) = \{ x\}$ ( is fractional part of x) exists at x = 1 and it is equal to _____.Mathematics· Continuity and differentiability· Easy
  18. 18The number of value(s) of k, for which both the roots of the equation $x^{2} - 6kx + 9(k^{2} - k + 1) = 0$are real, distinct and have…Mathematics· Quadratic Equations· Tough
  19. 19If $\tan^{- 1}(2\cos^{2}\theta + 4cos\theta + 3) + \cot^{- 1}(6^{cosec^{2}\phi} + 3) = \frac{\pi}{2}$ has solution for some $\theta$ and…Mathematics· ITF· Tough
  20. 20The interval on which f(x) = 2x^3 + 9x^2 + 12x - 1 is decreasing inMathematics· Application of derivatives· Moderate
  21. 21Let $\beta$ and $\alpha$ be the roots of $x^{2} - 6x - 2 = 0$, with $\alpha > \beta$, If $a_{n} = \alpha^{n} - \beta^{n}$ for $n \geq 1$,…Mathematics· Quadratic Equations· Tough
  22. 22A value of b for which the equations $x^{2} + bx - 1 = 0$ $x^{2} + x + b = 0$ have one root in common isMathematics· Quadratic Equations· Moderate
  23. 23Point lies on the curve $y = e^{- x^{2}}$ and has the coordinate $(x,e^{- x^{2}})$ where x > 0. Point B has the coordinates (x, 0). If the…Mathematics· Application of derivatives· Moderate· figure
  24. 24The value of [IMAGE] is equal toMathematics· Binomial Theorem· Moderate· figure
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