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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. 1The distance of point of intersection of lines represented by the equation $2x^{2} - 10xy + 12y^{2} + 5x - 16y - 3 = 0$ from origin isMathematics· Straight Lines· Moderate
  2. 2$\lim_{x \rightarrow 0}\mspace{2mu}\frac{\sqrt{1 - cos2x}}{x} =$Mathematics· Limits· Easy
  3. 3If $f(x) = \frac{x - e^{x} + cos2x}{x^{2}},x \neq$ is continuous at x=0 (where denotes greatest integer function and denotes fractional…Mathematics· Limit· Moderate
  4. 4The values of for which roots of the equation $(a - 2)x^{2} - (a - 4)x - 2 = 0$ are real and distinct and their difference is greater than…Mathematics· Quadratic Equations· Tough
  5. 5n, G.M.'s are inserted between two numbers 2 and 162. If the product of the n G.M.'s is 5832 then n isMathematics· Sequences and Series· Moderate
  6. 6The H. M. of two positive numbers is 4. If their AM, A and GM, G satisfy the relation 2A + G^2 = 27 then the numbers are.Mathematics· Sequences and Series· Moderate
  7. 7The values of a, m and b for which Lagrange's mean value theorem is applicable to the function f(x) for x $\in$ $f(x) = \left\{…Mathematics· Functions· Moderate
  8. 8If H_1, H_2, H_3........H_2n+1 are in H.P. then $\sum_{i = 1}^{2n}\mspace{2mu}( - 1)^{i}\left( \frac{H_{i} + H_{i + 1}}{H_{i} - H_{i + 1}}…Mathematics· Sequences and Series· Moderate
  9. 9Consider the sequence 8A + 2B, 6A + B, 4A, 2A - B,......., which term of this sequence will have a coefficient of A which is twice the…Mathematics· Sequences and Series· Tough
  10. 10If a^2 + b^2 - c^2 - 2ab = 0, then the family of straight lines ax + by + c = 0 is concurrent at the pointsMathematics· Straight Lines· Moderate
  11. 11Equation of the line which is parallel to the line common to the pair of lines given by 6x^2 - xy - 12y^2 = 0 and 15x^2 + 14xy - 8y^2 = 0…Mathematics· Straight Lines· Tough
  12. 12Range of $f(x) = 4^{x} + 2^{x} + 1$ isMathematics· Functions· Tough
  13. 13The locus of the points of intersection of the lines $x\cos\alpha\ + \ y\ sin\ \alpha = a$ and ${x\ sin}\alpha\ –\ y\cos\alpha = b$ (where…Mathematics· Straight Lines· Easy
  14. 14If $\ \lim_{x \rightarrow 0}\mspace{2mu}\frac{1 - \cos^{3}x}{xsinx \cdot cosx}\ $is equal to $\lambda$ then the value of $4\lambda$ isMathematics· Limits· Moderate
  15. 15The value of $\ \lim_{x \rightarrow 0}\mspace{2mu}\frac{ln(1 + 2sin3x)}{sinx}$ is equal toMathematics· Limits· Easy
  16. 16If $g(x) = \left\{ \begin{matrix} k\sqrt{x + 1}, - \frac{1}{2} \leq x \leq 2 \\ mx + 2,2 < x \leq 5 \end{matrix}\ \ \right.\ $is continuous…Mathematics· Continuity and differentiability· Moderate
  17. 17If $y = (\mathcal{l}nx)^{x},\ then\ \frac{dy}{dx}$ at x = e is equal toMathematics· Differentiation· Moderate
  18. 18Given that: f (x) = $\left\{ \begin{matrix} \frac{1 - cos4x}{x^{2}}, & \ if\ x < 0 \\ a &,\ if\ x = 0 \\ \frac{\sqrt{x}}{\sqrt{16 +…Mathematics· Continuity and differentiability· Tough
  19. 19Value of $\lambda$ so that point $\left( \lambda,\lambda^{2} \right)$ lies between the lines $|x + 2y| = 3$ isMathematics· Straight Lines· Moderate· figure
  20. 20$\lim_{x \rightarrow 0}\mspace{2mu}\frac{ln\left( tan\left( \frac{\pi}{4} + ax \right) \right)}{sinbx},b \neq 0$ is equal toMathematics· Limits· Moderate
  21. 21$\lim_{x \rightarrow \infty}\mspace{2mu}\frac{\sqrt{x^{2} + 1} - \sqrt[3]{x^{3} + 1}}{\sqrt[4]{x^{4} + 1} - \sqrt[5]{x^{4} + 1}}$ equalsMathematics· Limits· Easy
  22. 22The line L has intercepts $a$ and $b$ on the coordinate axes. The coordinate axes are rotated through a fixed angle, keeping the origin…Mathematics· Straight Lines· Moderate
  23. 23$\lim_{n \rightarrow \infty}\mspace{2mu}\frac{1^{2} + 2^{2} + 3^{2} + \ldots\ldots\ldots + n^{2}}{n^{3}} =$Mathematics· Limits· Easy
  24. 24If $y = \log_{\sqrt{e}}(sinx)$, then $\frac{dy}{dx}$ is.Mathematics· Differentiation· Moderate
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