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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 value of b for which the equation $2\log_{1/25}(bx + 28) = - \log_{5}(12 - 4x - x^{2})$ has coincident real roots ifMathematics· Quadratic Equations· Tough
  2. 2If $cot\theta,cosec\theta$ are the roots of the equation $ax^{2} + bx + c = 0$ and $\Delta = b^{2} - 4ac$, then $a^{4}$equalsMathematics· Quadratic Equations· Easy
  3. 3If $\frac{1}{6}sin\theta,cos\theta,tan\theta$ are in G.P. then $\theta$ is equal to $(n \in Z)$Mathematics· Sequences and Series· Moderate
  4. 4If $\alpha,\beta$ are the roots of $9x^{2} + 6x + 1 = 0$, then the equation with roots $\frac{1}{\alpha},\frac{1}{\beta}$ isMathematics· Quadratic Equations· Tough
  5. 5Given that $ax^{2} + bx + c = 0,(a,b,c \in R)$ has no real root and a + b + c < 0 thenMathematics· Quadratic Equations· Moderate
  6. 6The values of p, for which 6 lie between the roots of the equation $x^{2} + 2(p - 3)x + 9 = 0$, isMathematics· Quadratic Equations· Easy
  7. 77^th term of an AP is 40, then the sum of first 13 terms isMathematics· Sequences and Series· Moderate
  8. 8The sum $\left( 1^{2} \right) + \left( 1^{2} + 2^{2} \right) + \left( 1^{2} + 2^{2} + 3^{2} \right)$. Up to 10^th bracket isMathematics· Sequences and Series· Moderate
  9. 9In a G.P., if $(2p)^{th}$ term is $q^{2}$ and $(2q)^{th}$ term is $p^{2}$ where $p\ and\ q \in N$, then its $(p + q)^{th}$ term isMathematics· Sequences and Series· Moderate
  10. 10The equation $x^{\frac{3}{4}{(\log_{2}x)}^{2} + \log_{2}x - \frac{5}{4}} = \sqrt{2}$ hasMathematics· Logarithm· Moderate
  11. 11The sum of values of x satisfying equation $2{(x + \frac{1}{x})}^{2} = {(x - \frac{1}{x})}^{2} + 8$ isMathematics· Quadratic Equations· Moderate
  12. 12A geometric progression (G.P.) consists of even number of terms. If the sum of all terms is times the sum of terms occupying odd places.…Mathematics· Sequences and Series· Moderate
  13. 13In a decreasing G.P. with common ratio such that $|x| < 1,x \neq 0$, the ratio of fourth term to second term is $1/16$ & ratio of 3^rd term…Mathematics· Sequences and Series· Easy
  14. 14If $S_{n} = 1 + \frac{1}{2} + \frac{1}{4} + \ldots\frac{1}{2^{n - 1}}\& 2 - S_{n} < \frac{1}{100}$ then the least value of n isMathematics· Sequences and Series· Tough
  15. 15If both roots of $x^{2} - 2011x + k = 0$ be prime numbers, then find the number of real values of k.Mathematics· Quadratic Equations· Tough
  16. 16$\frac{21}{20}(\frac{1}{r(2r + 1)} + \frac{1}{r(2r - 1)})$ is equal toMathematics· Sequences and Series· Moderate· figure
  17. 17Equation $\log_{4}(2x^{2} + x + 1) - \log_{2}(2x - 1) = 1$ hasMathematics· Logarithm· Tough
  18. 18If $\frac{logx}{2} = \frac{logy}{3} = \frac{logz}{5},$ then $x^{2} =$Mathematics· Logarithm· Easy
  19. 19The expression $\cos^{2}(A + B) + \cos^{2}B - 2cos(A + B)cosAcosB$ isMathematics· Compound angles· Easy
  20. 20$x^{(\log_{x}a \cdot \log_{a}y \cdot \log_{y}z)}$ is equal toMathematics· Logarithm· Easy
  21. 21$\log_{0.3}(x - 1) < \log_{0.09}(x - 1)$ then x lies in the intervalMathematics· Logarithm· Tough
  22. 22The integral value of a for which the quadratic equation (x-a)(x-10)+1= 0 has integral roots areMathematics· Quadratic Equations· Easy
  23. 23If $2x^{2} + 3x + 4 = 0$ and $ax^{2} + bx + c = 0$ where $a,b,c \in N$ have a common root, then the least value of a + b + c isMathematics· Quadratic Equations· Moderate
  24. 24Let $f:R \rightarrow R$ be a function defined by $f(x) = \frac{e^{|x|} - e^{- x}}{e^{x} + e^{- x}}$. ThenMathematics· Functions· Moderate
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