CUET UG Mathematics — Applied-Mathematics previous year questions with solutions.
The total cost function for $x$ units of a commodity is given by $C(x) = \frac{25x^3}{3} - 75x^2 + 48x + 34$. The output $x$ at which the marginal cost is minimum is :
The present value of a perpetual income of ₹ $x$ payable at the end of each 6 months is ₹ 1,80,000. If the money is worth 5% compounded semi-annually, then the value of $x$ is ₹ :
A person buys a flat for which he makes down payment of ₹ 7,50,000 and the balance is to be paid in 10 years by monthly instalments of ₹ 22,000 each. If the bank charges interest at the rate of 12% per annum, then the actual price of the flat using flat rate system is :
If the matrix $A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix}$ satisfies the equation $A^T A = I_3$, then $x^2 + y^2 + z^2$ is :
If $x = 6t^2$, $y = \frac{6}{t^2}$, then $\frac{d^2 y}{dx^2}$ is equal to :
The number of all possible matrices of order 3 $\times$ 3 with each entry 2 or 3 is.
If $\begin{vmatrix} -a^2 & ab & ac \\ ba & -b^2 & bc \\ ac & bc & -c^2 \end{vmatrix} = 4x$, then $x =$
If $x = 2at, y = at^2$, where 'a' is a constant, then $\frac{d^2 y}{dx^2}$ at $x = 2$ is :
The variance of the number of heads in two tosses of a coin is :
The interval in which where the function $f(x) = x^3 - 3x^2 + 4x + 1, x \in R$ is increasing in, is :
The area bounded by the curve $y = x^2$ between $x = 0$ and $x = \pi$ in the first quadrant is :
The area of the triangle with vertices $(1,4), (2,7)$ and $(4,13)$ is :
If $A = \begin{bmatrix} 1 & 0 \\ -1 & 7 \end{bmatrix}, I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ and $A^2 = 8A + kI$, the value of k is :
Let X & Y be 2 invertible square matrix, then which of the following is true (A) $(AB)^{-1} = A^{-1} B^{-1}$ (B) $(AB)^{-1} = B^{-1} A^{-1}$ (C) $(AB)' = A' B'$ (D) $(AB)' = B' A'$ Choose the answer from the options given below
The order and degree Of the differential equation $\frac{d^2 y}{dx^2} + 2 e^{-x} = 0$, respectively are
the general solution of the differential equation $(1 + y) dx - 2x dy = 0$ is :
If $v = \frac{4}{3} \pi r^3$, at what rate is cubic / unit sec is increasing when $r = 10$, and $\frac{dr}{dt} = 0.01$ ?
Objective function $Z = 200x + 500y$, subject to constraint, $x + 2y \geq 10, 3x + 4y \leq 24$, $x \geq 0, y \geq 0$ - (iii), the minimum value of Z is :
The value of the integral $\int_{-3}^{3} (x^3 - x) dx$ is :
Given a linear programming problem, Max $Z = 22x + 18y$, Subject to constraints $x + y \leq 20, 360x + 240y \leq 5760, x \geq 0, y \geq 0$. Its corner points are :
10 works hard drawn successively with replacement from a lot containing 10% defective bulb. The probability that there is at least one defective bulb is :
The corner points of feasible region determined by the following system of linear inequalities $2x + y \leq 10, x + 3y \leq 15, x \geq 0, y \geq 0$ are $(0,0), (5,0), (3,4)$ and $(0,5)$, then the relation between p and Q so that minimum of Z occurs both points $(3,4)$ and $(0,5)$ is :
$\int \frac{dx}{x^{n+1} - x}\,dx$
If $P = \begin{bmatrix} -2 & 2 & 0 \\ 3 & 1 & 4 \end{bmatrix}$ and $Q = \begin{bmatrix} 2 & 0 & -2 \\ 7 & 1 & 6 \end{bmatrix}$, If $5Q - 3P + 2R = 0$, then the matrix R is