Practice/Question bank/JEE Main

JEE Main practice questions

NTA-style Physics, Chemistry and Maths MCQs with solutions. 2,688 questions in the bank.

1. 1Area of the region bounded by points (x,y) satisfying x^2 + y^2 ≤ |x| + |y| is x^2 + y^2 ≤ |x| + |y|Mathematics· Circles· Easy· figure
2. 2If tangents drawn from each point on the line 3x + 4y - 11 = 0 upon a parabola are at right angle and chords joining points of contact on…Mathematics· Conic Sections· Moderate
3. 3The base of a triangle passes through a fixed point (f, g) and its sides are bisected at right angles by the lines y^2 - 8xy - 9x^2 = 0.…Mathematics· Circles· Moderate· figure
4. 4If the line segment joining the foci of the ellipse$\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}$ = 1(a > b) does not subtend a right angle at…Mathematics· Conic Sections· Moderate
5. 5Let $0 < \theta < \frac{\pi}{2}$. If the eccentricity of the hyperbola$\frac{x^{2}}{\cos^{2}\theta} - \frac{y^{2}}{\sin^{2}\theta} = 1\ $is…Mathematics· Conic Sections· Moderate
6. 65 students of a class have an average height 150 cm and variance 18cm^2. A new student, whose height is 156cm, joined them. the variance…Mathematics· Statistics· Easy
7. 7If $A = \begin{bmatrix} cos\theta & - sin\theta \\ sin\theta & cos\theta \end{bmatrix}$ then the matrix A^-50 when $\theta =…Mathematics· Matrix and determinant· Moderate
8. 8The length of the perpendicular drawn from the point (2,1,4) to the plane containing the lines $\overset{\rightarrow}{r} =…Mathematics· Vectors· Tough
9. 9The area (in sq. units) bounded by the parabola y = x^2 -1, the tangent at the point (2, 3) to it and the y axis isMathematics· Definite Integration· Moderate· figure
10. 10$\lim_{y \rightarrow 0}\mspace{2mu}\frac{\sqrt{1 + \sqrt{1 + y^{4}}} - \sqrt{2}}{y^{4}}$Mathematics· Limits· Moderate
11. 11The maximum volume (in cu. m ) of the right circular cone having slant height 3m isMathematics· Application of derivative· Easy
12. 12If [x] denotes the greatest integer [IMAGE] x, then the system of linear equationsMathematics· Functions· Tough· figure
13. 13The equation of the line passing through (-4, 3, 1), parallel to the plane x+2y-z-5=0 and intersecting the line$\frac{x + 1}{- 3} = \frac{y…Mathematics· 3D· Moderate
14. 14A plane which bisects the angle between the two given planes 2x - y + 2z - 4 = 0 and x+2y+2z-2=0, passes through the pointMathematics· 3D· Moderate
15. 15Equation of a common tangent to the circle, $x^{2} + y^{2} - 6x = 0\ $and the parabola, y^2=4 x, isMathematics· Conic Sections· Moderate
16. 16The system of linear equations x+y+z=2 2 x+3y+2z=5 2x+3y+ (a^2 + 1)z = a+1Mathematics· Matrix and determinants· Moderate
17. 17The general solution of the differential equation $\left( y^{2} - x^{3} \right)dx - xydy = 0(x \neq 0)$ is:(where c is a constant of…Mathematics· Differential equation· Easy
18. 18For $x^{2} \neq n\pi + 1,n \in N$(the set of natural numbers), theintegral$\int x\sqrt{\frac{2sin\left( x^{2} - 1 \right) - sin2\left(…Mathematics· Indefinite integration· Moderate
19. 19For any $\theta \in \left( \frac{\pi}{4},\frac{\pi}{2} \right)$, the expression $3(sin\theta - cos\theta)^{4} + 6(sin\theta +…Mathematics· Trigonometry· Easy
20. 20Let f: R→ R be a function defined as $f(x) = \left\{ \begin{matrix} 5, & \ if\ & x \leq 1 \\ a + bx, & \ if\ & 1 < x < 3 \\ b + 5x, & \ if\…Mathematics· Continuity and derivability· Moderate
21. 21If y=y(x) is the solution of the differential equation, $x\frac{dy}{dx} + 2y = x^{2}$ satisfying yMathematics· Differential equation· Moderate
22. 22Let $A = \left\{ \theta \in \left( - \frac{\pi}{2},\pi \right):\frac{3 + 2isin\theta}{1 - 2isin\theta}\ ispurely\ imaginary\ \right\}$.…Mathematics· Complex Numbers· Moderate
23. 23If two sides of a square are$3x - 4y + n = 0,(n > 0),4x + 3y + m = 0,(m > 0)$, having (1,1) as center and 16 as area then the smallest…Mathematics· Theory of Equations· Tough· figure
24. 24If a circle passes through the point (1,2) and cuts the circle$x^{2} + y^{2} = 4\ $orthogonally is S=0 and locus of centre of circle $S =…Mathematics· Circles· Moderate