CUET UG Mathematics — Applied-Mathematics previous year questions with solutions.
Match List - I with List - II. Given that $\Sigma p_0 q_0 = 150$, $\Sigma p_0 q_1 = 80$, $\Sigma p_1 q_0 = 240$, $\Sigma p_1 q_1 = 200$. | List - I | List - II | |---|---| | (A) Laspeyre's index | (I) 160 | | (B) Paasche's index | (II) 200 | | (C) Fesher's index | (III) 205 | | (D) Dorbish and Bowley's | (IV) 250 | Choose the correct answer from the options given below :
Let A be a square matrix. Then, (A) $A + A^T$ is a symmetric matrix (B) $A - A^T$ is a skew-symmetric matrix (C) $AA^T$ is a skew-symmetric matrix (D) $A^T A$ is a symmetric matrix Choose the correct answer from the options given below :
Let $f : R \to R$ be defined such that $f(x) = 16x^2 - 16x + 12$ (A) Maximum value of $f(x)$ is 8 (B) Minimum value of $f(x)$ is 8 (C) Minimum value of $f(x)$ is 16 (D) No maximum value of $f(x)$ Choose the correct answer from the options given below :
If $C(x) = ax^2 - bx - c$ represents the total cost function then the slope of the tangent to the marginal cost curve at the point $(x, y)$ is :
The demand function of a monopolist is given by $p = 1500 - 2x - x^2$, then value of marginal revenue when $x = 20$ is :
The EMI (in Rs.) under the flat rate on a loan of Rs. 6,00,000 with 20% annual interest for 5 years is :
Corner points of the feasible region for an LPP are : (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let $z = 4x + 6y$ be the objective function. Then, Max z $-$ Min z is equal to :
Match List - I with List - II. | List - I (Functions) | List - II (Maximum value) | |---|---| | (A) $f(x) = -x^2, x \in (-\infty, \infty)$ | (I) 8 | | (B) $f(x) = -x^2 + 1, x \in (-\infty, \infty)$ | (II) 7 | | (C) $f(x) = x + 1, x \in [0, 6]$ | (III) 1 | | (D) $f(x) = x^3, x \in [0, 2]$ | (IV) 0 | Choose the correct answer from the options given below :
The present value of a perpetuity of Rs. 6,240 payable at the beginning of each year, if money is worth 10% effective, is :
The effective rate that is equivalent to a nominal rate of 12% compounded quarterly is :
The objective function $z = 4x + 3y$ can be maximised subject to the constraints $3x + 4y \leq 24$, $8x + 6y \leq 48$, $x \leq 5$, $y \leq 6$, $x \geq 0$, $y \geq 0$ :
Pipes A and B can fill a tank in 5 hours and 6 hours respectively. Another Pipe can empty the full tank in 30 hours. If all three pipes are opened together, then the tank will be filled in :
If $x^3 + y^3 = xy$, then $\frac{dy}{dx}$ is equal to :
The set of positive integers less than 50 forming the equivalence class of 6 modulo 9 is given by :
A company has issued a bond having a face value of Rs. 10,000 paying annual dividends at 8.5%. The bond will be redeemed at par at the end of 10 years, then the purchase price of this bond if the investor wishes a yield rate of 8% is : [Given $(1.08)^{-10} = 0.46319349$]
A container contains 50 litres of milk. From this container 10 litres of milk was taken out and replaced by water. This process is repeated two more times. How much milk is now left in the container ?
Mr. Ram took a loan of Rs. 4,00,000 at 10% annual interest rate and paid Rs. 20,000 as monthly instalment under flat rate system. What is the term of the loan ?
If $-\frac{1}{3x - 5} \leq 0$, then :
Which of the following statements are correct ? (A) $\text{var}(aX + b) = a^2 \text{var}(X)$ (B) $\text{var}(X) = E(X^2) - \{E(X)\}^2$ (C) $E(aX + b) = aE(X) + b$ (D) $E(X) = \sum_{i=1}^{n} p_i x_i^2$ Choose the correct answer from the options given below :
In binomial distribution with $n = 10$ and $P = \frac{1}{3}$, the probability of the event that unequal number of failures and successes occur is :
The standard deviation of a sampling distribution of a statistic is also known as :
The probability distribution of a random variable X is given below : | X | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | P(X) | 0.1 | 0.25 | 0.3 | 0.2 | 0.15 | Then, $\text{Var}\left(\frac{X}{2}\right)$ is :
A motor boat goes 20 km downstream and comes back to the starting point in 6 hours. If the speed of the boat in still water is 12 km/h, then the speed of the stream is :
If X has a Poisson distribution such that $P(X = 1) = P(X = 2)$ then $P(X = 3)$ is :