Mathematics Previous Year Questions 2024 (2024–2024)

240 Mathematics previous-year questions spanning 2024–2024.

Mathematics 2024 · Application of Integrals

The area enclosed by the curves $xy+4y=16$ and $x+y=6$ is equal to:

Mathematics 2024 · Relations and Functions

Let $f:R\rightarrow R$ and $g:R\rightarrow R$ be defined as $$f(x)=\begin{cases}\log_{e}x & , & x>0\\ e^{-x} & , & x\le0\end{cases}$$ and $$g(x)=\begin{cases}x & , & x\ge0\\ e^{x} & , & x<0\end{cases}$$ Then, $g \circ f: R\rightarrow R$ is:

Mathematics 2024 · Complex Numbers

Let $P=\{z\in\mathbb{C}:|z+2-3i|\le1\}$ and $Q=\{z\in\mathbb{C}:z(1+i)+\overline{z}(1-i)\le-8\}$. Let in $P \cap Q, |z-3+2i|$ be maximum and minimum at $z_{1}$ and $z_{2}$ respectively. If $|z_{1}|^{2}+2|z_{2}|^{2}=\alpha+\beta\sqrt{2}$, where $\alpha, \beta$ are integers, then $\alpha+\beta$ equals

Mathematics 2024 · Probability

A bag contains $8$ balls, whose colours are either white or black. $4$ balls are drawn at random without replacement and it was found that $2$ balls are white and the other $2$ balls are black. The probability that the bag contains an equal number of white and black balls is:

Mathematics 2024 · Definite Integrals

The value of the integral $$\int_{0}^{\frac{\pi}{4}}\frac{x \, dx}{\sin^{4}(2x)+\cos^{4}(2x)}$$ equals:

Mathematics 2024 · Matrices and Determinants

If $A=\begin{bmatrix}\sqrt{2} & 1 \\ -1 & \sqrt{2}\end{bmatrix}$, $B=\begin{bmatrix}1 & 0 \\ 1 & 1\end{bmatrix}$, $C=ABA^{T}$ and $X=A^{T}C^{2}A$, then $\det X$ is equal to:

Mathematics 2024 · Trigonometric Functions

If $\tan A=\frac{1}{\sqrt{x(x^{2}+x+1)}}$, $\tan B=\frac{\sqrt{x}}{\sqrt{x^{2}+x+1}}$ and $\tan C=(x^{-3}+x^{-2}+x^{-1})^{\frac{1}{2}}, 0<A,B,C<\frac{\pi}{2}$, then $A+B$ is equal to:

Mathematics 2024 · Permutations and Combinations

If $n$ is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then $n$ is equal to:

Mathematics 2024 · Complex Numbers

Let $S=\{z\in C:|z-1|=1 \text{ and } (\sqrt{2}-1)(z+\overline{z})-i(z-\overline{z})=2\sqrt{2}\}$. Let $z_{1}, z_{2}\in S$ be such that $|z_{1}|=\max_{z\in S}|z|$ and $|z_{2}|=\min_{z\in S}|z|$. Then $|\sqrt{2}z_{1}-z_{2}|^{2}$ equals:

Mathematics 2024 · Statistics

Let the median and the mean deviation about the median of $7$ observations $170, 125, 230, 190, 210, a, b$ be $170$ and $\frac{205}{7}$ respectively. Then the mean deviation about the mean of these $7$ observations is:

Mathematics 2024 · Vector Algebra

Let $\vec{a}=-5\hat{i}+\hat{j}-3\hat{k}$, $\vec{b}=\hat{i}+2\hat{j}-4\hat{k}$ and $\vec{c}=(((\vec{a}\times\vec{b})\times\hat{i})\times\hat{i})\times\hat{i}.$ Then $\vec{c}\cdot(-\hat{i}+\hat{j}+\hat{k})$ is equal to:

Mathematics 2024 · Quadratic Equations

Let $S=\{x\in R:(\sqrt{3}+\sqrt{2})^{x}+(\sqrt{3}-\sqrt{2})^{x}=10\}$. Then the number of elements in S is:

Mathematics 2024 · Matrices and Determinants

If the system of equations $2x+3y-z=5$ $$x+\alpha y+3z=-4$$ $3x-y+\beta z=7$ has infinitely many solutions, then $13 \alpha \beta$ is equal to:

Mathematics 2024 · Conic Sections

For $0<\theta<\pi/2$, if the eccentricity of the hyperbola $x^{2}-y^{2}\csc^{2}\theta=5$ is $\sqrt{7}$ times the eccentricity of the ellipse $x^{2}\csc^{2}\theta+y^{2}=5$, then the value of $\theta$ is:

Mathematics 2024 · Differential Equations

Let $y = y(x)$ be the solution of the differential equation $\frac{dy}{dx} = 2x(x+y)^{3} - x(x+y) - 1$, with $y(0) = 1$. Then, $\left( \frac{1}{\sqrt{2}} + y\left(\frac{1}{\sqrt{2}}\right) \right)^{2}$ equals:

Mathematics 2024 · Limits, Continuity and Differentiability

Let $f:R\rightarrow R$ be defined as $$f(x)=\begin{cases}\frac{a-b \cos 2x}{x^2} & , & x<0\\ x^{2}+cx+2 & , & 0\le x\le1\\ 2x+1 & , & x>1\end{cases}$$ If $f$ is continuous everywhere in $R$ and $m$ is the number of points where $f$ is NOT differentiable, then $m+a+b+c$ equals:

Mathematics 2024 · Conic Sections

Let $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1, a>b$ be an ellipse, whose eccentricity is $\frac{1}{\sqrt{2}}$ and the length of the latus rectum is $\sqrt{14}$. Then the square of the eccentricity of $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ is:

Mathematics 2024 · Sequences and Series

Let $3, a, b, c$ be in A.P. and $3, a-1, b+1, c+9$ be in G.P. Then, the arithmetic mean of $a, b$ and $c$ is:

Mathematics 2024 · Conic Sections

Let $C:x^{2}+y^{2}=4$ and $C^{\prime}:x^{2}+y^{2}-4\lambda x+9=0$ be two circles. If the set of all values of $\lambda$ so that the circles C and C' intersect at two distinct points, is $R - [a, b]$, then the point $(8a+12,16b-20)$ lies on the curve:

Mathematics 2024 · Application of Derivatives

If $5f(x)+4f\left(\frac{1}{x}\right)=x^{2}-2, \forall x\ne0$ and $y=9x^{2}f(x),$ then $y$ is strictly increasing in:
Rankbit System
JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%) | JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%)

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