Practice/Question bank/JEE Main
JEE Main practice questions
NTA-style Physics, Chemistry and Maths MCQs with solutions. 2,688 questions in the bank.
- 1Let equation of two sides of a triangle are 4x + 5y = 20 and 3x - 2y + 6 = 0. If orthocentre of triangle is (1, 1) then the equation of…Mathematics· Straight Lines· Tough
- 2$\lim_{x \rightarrow - 1}\mspace{2mu}\left( \frac{1}{1 + x} - \frac{3}{1 + x^{3}} \right)$ is equal toMathematics· Limits, continuity and derivability· Moderate
- 3If $f(x) = \left\{ \begin{matrix} 3x - 1,\ \ \ \ x \geq 1 \\ 2x + 3,\ \ \ \ x < 1 \end{matrix},g(x) = \right.\ \left\{ \begin{matrix} 3 - x…Mathematics· Limits, continuity and derivability· Easy
- 4The function f(x) = maximum $\left\{ \sqrt{x(2 - x)},2 - x \right\}$ is non-differentiable at x equal toMathematics· Limits, continuity and derivability· Tough· figure
- 5The values of $\lambda$ for which equation x^2 - y^2 - x - $\lambda$y - 2 = 0 represents a pair of straight lines, areMathematics· Straight Lines· Easy
- 6Let f(x) = $\frac{1}{x - 1}$,and n be number of points of discontinuity of the function$f\left( \frac{1}{x - 1} \right)$. The value of…Mathematics· Limits, continuity and derivability· Moderate
- 7The value of $\lim_{x \rightarrow \alpha}\mspace{2mu}\frac{1 - cos\left( ax^{2} + bx + c \right)}{(x - \alpha)^{2}}$ where $\alpha,\beta$…Mathematics· Limits· Moderate
- 8If a variable line, drawn through the point of intersection of the straight lines 3x + 2y - 6 = 0 and 2x + 3y - 6 = 0, meets the x-axis and…Mathematics· Straight Lines· Tough
- 9The value of $\lim_{x \rightarrow 2}\mspace{2mu}\frac{\sqrt{1 + \sqrt{2 + x}} - \sqrt{3}}{x - 2}\ is\ \frac{1}{2\sqrt{p}}.$ Find p.Mathematics· Limits· Easy
- 10A differentiable function f is satisfying the relation f(x + y) = f(x) + f(y) + 2xy(x + y) - $\frac{1}{3}\forall x,y \in$ R and $\lim_{h…Mathematics· Limits· Moderate
- 11The area of the parallelogram contained by the lines 4y - 3x + 1 = 0, 4y - 3x - 1 = 0, 3y - 4x + 1 = 0 and 3y - 4x + 2 = 0 is…Mathematics· Straight Lines· Easy
- 12The sides of a triangle have the combined equation x^2 - 3y^2 - 2xy + 8y - 4 = 0. The third side, which is variable always passes through…Mathematics· Straight Lines· Moderate· figure
- 13Find the absolute value of $\lim_{x \rightarrow 1^{+}}\mspace{2mu}\frac{4(x - 1)}{\sin^{- 1}\left( \frac{2x}{1 + x^{2}} \right) - 2\tan^{-…Mathematics· Limits· Moderate
- 14$\ If\ \lim_{n \rightarrow \infty}\mspace{2mu}\frac{\sum_{r = 1}^{2n}\mspace{2mu}\left( \sqrt{r}\sum_{r =…Mathematics· Limits· Moderate
- 15How many five letter words are to be formed out of the letters of the word INFINITESIMALMathematics· Pemutation and combination· Moderate
- 16In a [IMAGE] ABC, angles A,B,C are in 2: 3: 4 respectively then the cosA is equal toMathematics· Limits, continuity and derivability· Easy· figure
- 17A point equidistant from the lines 4x + 3y + 10 = 0, 5x - 12y + 26 = 0 and 7x + 24y - 50 = 0 isMathematics· Straight Lines· Moderate
- 18Let $f(x) = \left\{ \begin{matrix} \int_{0}^{x}\mspace{2mu}\{ 1 + |1 - t|\} dt,\ \ \ x > 2 \\ \ \ \ \ 5x - 7,\ \ \ \ \ \ \ \ \ \ \ \ \ \ \…Mathematics· Limits, continuity and derivability· Tough
- 19The set of points where x^2 |x| is thrice differentiable isMathematics· Limits, continuity and derivability· Moderate
- 20There are 5 girls and 7 boys. A team of 3 boys and 2 girls is to be formed such that no two specific boys are in the same team. Number of…Mathematics· Pemutation and combination· Easy
- 21A spherical balloon is filled with $4500_{\pi}$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate…Mathematics· Differentiation· Moderate
- 22$\int\frac{dx}{\sqrt{(1 + x)} + \sqrt{x}} =$Mathematics· Indefinite integration· Easy
- 23If C is arbitrary constant then $\int\left\lbrack f(x)g^{''}(x) - f^{''}(x)g(x) \right\rbrack$dx is equal toMathematics· Indefinite integration· Easy
- 24If C is arbitrary constant then $\int\frac{a^{x}}{\sqrt{1 - a^{2x}}}dx =$Mathematics· Indefinite integration· Moderate