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. 1The area of the curve enclosed by $2|x| + 3|y| \leq 6$ is given by the value of $\left( \frac{4A + 8}{5} \right)$ equals toMathematics· Area under curve· Moderate· figure
  2. 2Consider $f(x) = |x - 1| + |2x - \pi| + |x - 3|$ and $g(x) = \sin^{- 1}x + \tan^{- 1}$ x. The value of x for which f (g(x)) is minimum is…Mathematics· Functions· Tough
  3. 3If sum of all terms of an infinite GP is $\frac{1}{5}$ times the sum of odd terms. Then, common ratio isMathematics· Sequences and Series· Moderate
  4. 4A line y = 2x - b cuts the parabola y = x^2 - 4x at points A and B such that the value of b for which $\angle$AOB is right angle is K then…Mathematics· Parabola· Moderate
  5. 5If z_1, z_2, z_3 are three points lying on the circle |z| = 2 then the minimum value of $\left| z_{1} + z_{2} \right|^{2} + \left| z_{2} +…Mathematics· Complex Numbers· Moderate· figure
  6. 6Equation of the circle which circumscribes the square formed by the lines xy - 9x - 2y + 18 = 0 and xy - 5x - 6y + 30 = 0 isMathematics· Circles· Tough· figure
  7. 7n is selected from the set and the number 2^n + 3^n + 5^n is formed. Total number of ways of selecting n so that the formed number is…Mathematics· Permutations and Combinations· Tough
  8. 8If $\alpha$, $\beta$ and $\gamma$are the roots of the equation x^3 - 6x^2 + 11x - 6 = 0. Then, HM of the roots isMathematics· Theory of Equations· Easy
  9. 9The standard deviations of two sets containing 10 and 20 members are 2 and 3, respectively measured from their common mean 5. The SD for…Mathematics· Statistics· Moderate
  10. 10Greatest term in the expansion of (1 + t)^2n has greatest coefficient if and only if $t \in \left( \frac{9}{10},\frac{10}{9} \right)$. The…Mathematics· Binomial Theorem· Tough
  11. 11Which of the following statement is correct?Mathematics· Easy
  12. 12If $\Delta$ = a^2 - (b-c)^2, then tan A isMathematics· Moderate
  13. 13Let B and C be two points on a circle with center A. Let P be a point on radius AB such that BC = AP & AB. BP = (AP)^2 and $\angle CAB =…Mathematics· Moderate· figure
  14. 14In a $\bigtriangleup ABC,\ if\ \frac{s - a}{11} = \frac{s - b}{12} = \frac{s - c}{13}$, then $\tan^{2}\frac{A}{2}$ is equal toMathematics· Easy
  15. 15Angles A, B and C of a triangle ABC are in A.P. With the usual notations if $\frac{b}{c} = \frac{\sqrt{3}}{\sqrt{2}}$ and $\angle C =…Mathematics· Easy
  16. 16Consider a $\Delta$ABC and let a, b and c denote the lengths of the sides opposite to vertices A, B and C respectively AD be a median of…Mathematics· Moderate· figure
  17. 17Let ABC be a triangle with $\angle BAC = \frac{2\pi}{3}$ and AB = x such that (AB) (AC) = 1. If x varies then the longest possible length…Mathematics· Tough· figure
  18. 18In a ΔABC, if b=2,c=$\sqrt{3}$ and $\angle A = \frac{\pi}{6}$, then the value of R isMathematics· Moderate
  19. 19In $\Delta$ABC with usual notation, let $\angle A = 36^{\circ},\angle B = 54^{\circ}\ $and $\angle C = 90^{\circ}$. If r is the inradius…Mathematics· Easy
  20. 20In $\Delta$ABC (with usual notations); a = 2b and |A - B| = $\frac{\pi}{3}$ then which of the following doesn't hold good?Mathematics· Moderate
  21. 21In a $\Delta$ABC (with usual notations) if ex-radii r_1, r_2, r_3 are in H.P then $\frac{a + c}{b}$ isMathematics· Moderate
  22. 22Which of the following statement is correct?Mathematics· Easy
  23. 23In $\Delta$ABC, If $\angle$B = 90° thenMathematics· Tough
  24. 24In a $\Delta$ABC, if cos A cos B + sin A sin B sin C = 1, then (where a,b,c denotes usual notation)Mathematics· Moderate
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