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. 1If $a_{n} = \sum_{r = 0}^{n}\mspace{2mu}\frac{1}{\ ^{n}C_{r}},\ then\ \sum_{r = 0}^{n}\mspace{2mu}\frac{r}{\ ^{n}C_{r}} = \frac{k}{4}n…Mathematics· Binomial Theorem· Tough
  2. 2If $\alpha = e^{\left( \frac{2\pi i}{7} \right)}\ and\ f(x) = A_{0} + \sum_{k = 1}^{20}\mspace{2mu} A_{k}x^{k}$ and the value of $f(x) +…Mathematics· Thoery of equation· Tough· figure
  3. 3If [IMAGE],then the ordered pair (A, β) is equal toMathematics· Binomial Theorem· Tough· figure
  4. 4The positive real value of k so that planes $x - y + z + 1 = 0,kx + 3y + 2z - 3 = 0,3x + \ \ \ \ \ \ \ \ \ \ \ \ \ \ ky + z - 2 = 0\ $form…Mathematics· 3D· Easy Easy· figure
  5. 5Let $f(x) = x^{3} + 6x^{2} + ax + 2\.\ If\ ( - 3, - 1)$ is the largest possible open interval in which f(x) is a decreasing function, then…Mathematics· Application of derivatives· Moderate· figure
  6. 6The number of ways in which 7 identical balls can be distributed into 3 different boxes such that no box remains empty is n and p is the…Mathematics· Permutations and Combinations· Moderate
  7. 7If number of terms in expansion of $(a + b + c)^{n} + (a + b - c)^{n}\ are\ 4$ and $\sin^{- 1}\left( \frac{\sqrt{x}}{n} \right) + \sin^{-…Mathematics· Binomial Theorem· Easy / Moderate
  8. 8A hyperbola passes through the focus of the ellipse $\frac{x^{2}}{25} + \frac{y^{2}}{4} = 1$ and its transverse and conjugate axes coincide…Mathematics· Conic Sections· / Tough
  9. 9An electric component manufactured by a company is tested for its defectiveness by a sophisticated device. Let denote the event "the device…Mathematics· Probability· Easy
  10. 10The graph of the function y=f(x) has a unique non-vertical tangent at (e^a, 0) through which the graph passes then $\lim_{x \rightarrow…Mathematics· Limits· Moderate
  11. 11If 11 A.M.s are inserted between 28 and 10, then find the number of integral A.M's.Mathematics· Sequences and Series· Moderate
  12. 12Suppose a parabola $y = x^{2} - ax - 1$ intersects the coordinate axes at three points A, B and C. The circumcircle of ∆ABC intersects the…Mathematics· Circles· Tough· figure
  13. 13If z_1, z_2, z_3, are three collinear points in the argand plane such that $\left| \left( z_{3} - z_{1} \right)\left( z_{3} - z_{2} \right)…Mathematics· Complex Numbers· Moderate
  14. 14If θ denotes the acute angle between the curves, y=10-x^2 and y=2+x^2 at a point of their intersection, then |tanθ | is equalMathematics· Application of derivatives· Easy
  15. 15If $\sin^{3}xsin3x = \sum_{r = 0}^{n}\mspace{2mu} a_{r}cosrx$ is an identity, then a_2 + a_4 =Mathematics· Trigonometry· Moderate
  16. 16Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class,…Mathematics· Permutations and Combinations· Easy
  17. 17For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can…Mathematics· Probability· Moderate· figure
  18. 18Let a_1, a_2,......... a_30, be an A.P., S = $\sum_{i = 1}^{30}\mspace{2mu} a_{i}$ and $T = \sum_{i = 1}^{15}\mspace{2mu} a_{(2i - 1)}$. If…Mathematics· Sequences and Series· Moderate· figure
  19. 19Let $\overset{\rightarrow}{a} - \overset{\hat{}}{i} - \overset{\hat{}}{j},\overset{\rightarrow}{b} = \overset{\hat{}}{i} +…Mathematics· Vectors· Moderate
  20. 20A triangle has a vertex at (1,2) and the mid points of the two sides through it are (-1,1) and (2,3). Then the centroid of this triangle isMathematics· Easy· figure
  21. 21A metal sample carrying a current along x-axis with density Jx is subjected to a magnetic field Bz (along z-axis). The electric field Ey…Physics· figure
  22. 22Two liquids of densities 1 are mixed in equal volumes. A cube of external dimension 20 cm has an inner cubical portion of side 10 cm whose…Physics· figure
  23. 23For D1 forward bias resistance is 20 Ohm and reverse bias resistance is 600 Ohm. For D2 forward bias resistance is 30 Ohm and reverse bias…Physics· figure
  24. 24A horizontal conductor is oriented north south and carries some current. A positively charged particle located vertically above it and…Physics· figure
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