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 $A^{3} = \lbrack\begin{matrix} 8 & - 57 \\ 0 & 27 \end{matrix}\rbrack$, where A is an upper triangular matrix with real entries, then…Mathematics· Matrix and determinants· Easy
  2. 2If x, y, z are different and [IMAGE] and $(\Delta = 0)$ then xyz is equal toMathematics· Matrix and determinants· Moderate· figure
  3. 3For 3×3 matrices A and B, which of following statement is incorrect?Mathematics· Matrix and determinants· Easy
  4. 4Which of the following is not an equivalence relation in ZMathematics· Relation· Moderate
  5. 5Let f(x)=a^(a>0) be written as $f(x) = g(x) + h(x),$ where g(x) is an even function and h(x) is an odd function then the value of the $g(x…Mathematics· Functions· Tough
  6. 6The relation $R = \{(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)\}$ on set $A = \{ 1,2,3\}$ isMathematics· Relation· Moderate
  7. 7If M is square matrix such that $M^{2} = M$, then $(I + M)^{3} - 7M$ is equal toMathematics· Matrix and determinants· Tough
  8. 8Total number of ordered pairs (x, y) satisfying $|y| = \cos x$ and $y = \sin^{- 1}(sinx)$ where $x \in \lbrack - 2,\ 3\rbrack$ is equal toMathematics· ITF· Easy
  9. 9If the adjoint of a 3×3 matrix A is [IMAGE], then the magnitude of the determinant of matrix A isMathematics· Matrix and determinants· Moderate· figure
  10. 10If the trivial solution is the only solution of the system of equations - $\begin{matrix} x - ky + z = 0 \\ kx + 3y - kz = 0 \\ 3x + y - z…Mathematics· Matrix and determinants· Tough· figure
  11. 11Sum of all real solution of equation $\{ x\} + 2x = \lbrack x\rbrack$ (where & are fractional part function and greatest integer function…Mathematics· Functions· Moderate
  12. 12If the value of $sin(2\tan^{- 1}\frac{1}{3}) + cos(\tan^{- 1}2\sqrt{2})$ is $\lambda$ then value of $\frac{15}{7}\lambda$ isMathematics· ITF· Easy
  13. 13Number of elements in the range of the function $\ f(x) = \tan^{- 1}\sqrt{\lbrack x\rbrack + \lbrack - x\rbrack} + \sqrt{2 - |x|} +…Mathematics· ITF· Moderate
  14. 14Domain of the function $f(x) = \frac{1}{x} + 2^{(\sin^{- 1}x + \cos^{- 1}x)} + \frac{1}{\sqrt{4 - x^{2}}}$ is $x \in \lbrack - a,a\rbrack -…Mathematics· ITF· Moderate
  15. 15Let $\lambda$ and $\alpha$ be real. If denote the set of all values of $\lambda$ for which the system of linear equations $\lambda x +…Mathematics· Matrix and determinants· Moderate· figure
  16. 16Let $f(x) = x^{105} + x^{53} + x^{27} + x^{13} + x^{3} + 3x + 1$. If g(x) is inverse of function f(x), then the value of $9g^{'}(1)$ isMathematics· ITF· Easy
  17. 17The number of solutions of the equation$\ \tan^{- 1}(4\{ x\}) + \cot^{- 1}(x + \lbrack x\rbrack)) = \frac{\pi}{2}$, is (where denotes…Mathematics· ITF· Tough
  18. 18The function f is not defined for x = 0, but for all non zero real numbers x, $f(x) + 2f(\frac{1}{x}) = 3x$ The equation $f(x) = f( - x)$…Mathematics· Functions· Moderate
  19. 19If $f(x) = \frac{x - 1}{x + 1}$ then f(f(a x)) is equal toMathematics· Functions· Easy
  20. 20A relation R on set of point of given plane defined as$(A,B) \in RifOA = OB$ where O is fixed point on same plane. Then relation R isMathematics· Relation· Easy
  21. 21Let $f:R \rightarrow R$ defined by $f(x) = x^{3} + x^{2} + 100x + 5sinx$ then function f(x) isMathematics· Functions· Easy
  22. 22The relation R defined on the set N of natural number by $x\ Ry \Leftrightarrow 2x^{2} - 3xy + y^{2} = 0$ isMathematics· Relation· Moderate
  23. 23If $f(x) = 5^{\sqrt{4x^{2} - 1}}$. Which of the following are true / False ? I. The domain of f(x) is $|x| \geq \frac{1}{2}$ II. The range…Mathematics· Functions· Moderate
  24. 24If log_2 (ax^2 + x + a) ≥ 1∀ x∈R, then exhaustive set of valueMathematics· Sets· Moderate· figure
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