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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 scores of a batsman in 10 innings are 70,38,34,48,55,42,63,46,54,44. The mean deviation about median isMathematics· Statistics· Moderate
  2. 2The mean of the 200 observation is 48 and their standard deviation is 3. Then sum of the squares of all the observations.Mathematics· Statistics· Easy
  3. 3The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observation…Mathematics· Statistics· Easy· figure
  4. 4Suppose that a and b (b $\neq$ a, b > a) are real positive numbers then the value of [IMAGE] has the value equals to.Mathematics· Limits, continuity and derivability· Moderate· figure
  5. 5For function f(x) = nx + n - + tan 4 greatest integer function), period will beMathematics· Functions· Tough· figure
  6. 6If f $(x) = a_{0} + a_{1}x^{2} + a_{2}x^{4} + \ldots.. + a_{n}x^{2n}$ be a polynomial where 0 < a_0 < a_1 < a_2 <......<a_n, the b f(x) has…Mathematics· Functions· Easy
  7. 7Let f (x) = - 4 $\sqrt{e^{- x}} + 1 + x + \frac{x^{2}}{2} + \frac{x^{3}}{3}$. If g(x) is inverse of f(x), then the value of…Mathematics· Functions· Moderate· figure
  8. 8If $\left( \tan^{- 1}\frac{y}{15} \right)^{2} + \left( \cot^{- 1}\frac{y}{15} \right)^{2} = \frac{5\pi^{2}}{8}$, they |y| =Mathematics· Functions· Easy· figure
  9. 9If $\lim_{n \rightarrow \infty}\mspace{2mu}\frac{\sqrt{n^{3} - 2n^{2} + 1} + \sqrt[3]{n^{4} + 1}}{\sqrt[4]{n^{6} + 6n^{5} + 2} -…Mathematics· Limit· Moderate
  10. 10A function f from integers to integers is defined as f(x) = $\left\{ \begin{matrix} n + 3 & n\ is\ odd\ \\ \frac{n}{2} &,n\ is\ even\…Mathematics· Functions· Tough
  11. 11If range of the function f(x) = sin^-1 x + 2tan^-1 x + x^2 + 4x + 1 is then (p + q) equalsMathematics· Functions· Moderate· figure
  12. 12Number of real solution of the equation $10^{|x|} = 1 + |2 - |x||$­­­­­­­­­­ is/areMathematics· Functions· Moderate· figure
  13. 13$\ $If minimum value of function $f(x) = \left( 1 + \alpha^{2} \right)x^{2} - 2\alpha x + 1\ is\ g(\alpha),$ then maximum value of…Mathematics· Functions· Moderate· figure
  14. 14Let g(x) = 1 + [IMAGE] and f(g(x)) = 3 + 2[IMAGE] + x, then f (x) can be equal toMathematics· Functions· Easy· figure
  15. 15The number of points at which the function f(x) = (x - |x|)^2 (1- x + |x|)^2 is not differentiable in the interval (-3, 4) isMathematics· Continuity and derivability· Moderate· figure
  16. 16Let $f(x) = \left\{ \begin{matrix} \int_{0}^{x}\mspace{2mu}\{ 1 + |1 - t|\} dt,\ \ \ \ x > 2 \\ 5x - 7,\ \ \ \ x \leq 2 \end{matrix}…Mathematics· Continuity and derivability· Moderate· figure
  17. 17Consider $f(x) = |1 - x|,1 \leq x \leq 2$ and $g(x) = f(x) + bsin\frac{\pi}{2}x,1 \leq x \leq 2$ the which of the following is correct?Mathematics· Limits, continuity and derivability· Moderate· figure
  18. 18The function f (x) = (x + 2)1/3 at x = -2Mathematics· Functions· Moderate
  19. 19Given that n is the odd, the number of ways in which three numbers in AP can be selected from 1, 2, 3, 4... n isMathematics· Permutations and Combinations· Tough· figure
  20. 20Let A and B are two points (1, 0) and (3, 0) and P is a variable point on y-axis then maximum value of angle APB is equal toMathematics· Straight Lines· Tough· figure
  21. 21A curve in the x-y plane is given by the parametric equation [IMAGE] where parameter t varies over all real numbers then the number of…Mathematics· Straight Lines· Tough· figure
  22. 22[IMAGE], where [IMAGE] is a non-zero finite number then value of is [IMAGE] equal toMathematics· Limits· Moderate· figure
  23. 23A train going from Delhi to Bombay stops at 5 intermediate stations. 10 passengers enter the train during the journey with 10 different…Mathematics· Permutations and Combinations· Easy
  24. 24The value of for which the lines joining the origin to the points of intersection of the line [IMAGE] and the curve [IMAGE] are…Mathematics· Straight Lines· Moderate· figure
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