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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. 1Number of ways 3 girls and 5 boys can be seated around a circular table such that no two girls sit together and not more than two boys sit…Mathematics· Permutations and Combinations· Moderate· figure
  2. 2Let A = set of all 3 × 3 matrices having entries +1 or -1, if a matrix B from the set A is chosen randomly, then the probability that the…Mathematics· Probability· Tough
  3. 3If a and b are any two numbers belonging to the set, then the number of pairs (a, b) such that product of a and b is divisible by 3 isMathematics· Permutations and Combinations· Tough
  4. 4The number of ways in which 15 identical toys can be distributed among 3 children so that each of them gets at least two toys is equal toMathematics· Permutations and Combinations· Moderate
  5. 5The coefficient of x^4 in the expansion of $\left( 1 + x + x^{2} + x^{3} \right)^{11}$ is (where $(n\ r\ ) = \ ^{n}C_{r})$Mathematics· Binomial Theorem· Tough
  6. 6A man wants to distribute 101 coins of a rupee each; among his three sons with the condition that no one receives more money that the…Mathematics· Permutations and Combinations· Tough
  7. 7In a workshop there are five machines and the probability of any one of them to be out of service on a day is $\frac{1}{4}$. If the…Mathematics· Probability· Moderate
  8. 8Let n be an odd integer and the number $(n\ 151\ )$ is divisible by $(n\ 150\ )$ but is not equal to it. Then the half of sum of the digits…Mathematics· Binomial Theorem· Moderate· figure
  9. 9In an box, there are 20 cards, out of which 10 are labelled as A and the remaining 10 are labelled as B. Cards are drawn at random, one…Mathematics· Probability· Easy
  10. 10If a_r denotes the coefficients of x^r in the expansion of $(1 - x)^{2n - 1}(n \in N)$ then the sum of possible values of (a_r-1 + a_2n-r)…Mathematics· Binomial Theorem· Tough· figure
  11. 11If the coefficient of $x^{12}$ in $\left( (1 + 2x)^{10} + (1 + 2x)^{11} + \ldots + (1 + 2x)^{20} \right)$ is $\ ^{n}C_{r} \cdot 2^{r}$ then…Mathematics· Binomial Theorem· Moderate· figure
  12. 12(If the ratio of co-efficient of three consecutive terms in expansion of $(1 + x)^{n}$ is $1:7:42$ then n =Mathematics· Binomial Theorem· Moderate· figure
  13. 13The chance that the vowels are separated in an arrangement of the letters of the word "HORROR" isMathematics· Probability· Moderate· figure
  14. 14If A, B and C are three events such that that P(B)Mathematics· Probability· Moderate· figure
  15. 15Total number of ways in which 15 identical blankets can be distributed among 4 persons so that each of them gets at least two blankets,…Mathematics· Permutations and Combinations· Moderate
  16. 16A missile is destroyed before hitting the target by a probability of $\frac{1}{3}$. If the missile is not destroyed probability of hitting…Mathematics· Probability· Easy· figure
  17. 17The term that is independent of x in the expansion of$\ $ is.Mathematics· Binomial Theorem· Moderate· figure
  18. 18The sum of the series $\ ^{20}C_{0} - \ ^{20}C_{1} + \ ^{20}C_{2} - \ ^{20}C_{3} + \ldots + \ ^{20}C_{10}\ is\ $Mathematics· Binomial Theorem· Moderate
  19. 19Let f (x) $= \frac{1}{\sqrt{6 - \left\lbrack x^{2} - 2 \right\rbrack}}$, is the greatest integer function, then number of positive integral…Mathematics· Functions· Easy
  20. 20denotes greatest integer function then,Mathematics· Continuity and derivability· Tough· figure
  21. 21For what triplets of real numbers (a, b, c) with a $\neq$ 0 the function $f(x) = \left\{ \begin{matrix} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \…Mathematics· Continuity and derivability· Tough
  22. 22The Rolle's theorem is applicable in the interval [IMAGE] for the functionMathematics· Continuity and derivability· Easy· figure
  23. 23If $\lim_{x \rightarrow 1}\mspace{2mu}\frac{1 - x + lnx}{1 + cos\pi x} = L$, then $|\lbrack 17L\rbrack|$ equals denotes greatest integer…Mathematics· Limits, continuity and derivability· Tough
  24. 24The least positive integral value of for which the function f (x) = 2 b x-3 sin x + c is monotonically increasing $\forall x \in$ R isMathematics· Functions· Easy· figure
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