CUET Mathematics 2023 7 June Shift 1 PYQs

The value of the integral $\int e^x \left(\frac{1}{x} - \frac{1}{x^2}\right) dx$ is :

Area of the region bounded by the curve $x^2 = 4y$, $x$ - axis and $x = 3$ is

The value of the integral $I = \int_{-1}^{1} (x + x^3 + x^5) dx$ is :

If A and B are events such that $P(A/B) = P(B/A)$, then :

A die is thrown. If A is the event 'the number appearing is a multiple of 3 and B is the event 'the number appearing is even', then A and B are

Which constraints correctly represent the situation 'mixture of x and y must be at least 8 units' ?

The sum of the minor and the cofactor of the element 6 in the determinant $\begin{vmatrix} 2 & 3 & 1 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{vmatrix}$ is :

If $(x+ 1) e^y = 1$ , then :

Match List - I with list- II | List-I Equation of curves | List - II Slope of tangent at x = 2 | |---|---| | A. $Y = x^3 - x$ | 8 | | B. $Y = (x-2)^2$ | 2/3 | | C. $Y = 2x^2 + 3$ | 11 | | D. $Y = \sqrt{4x + 1} - 7$ | 0 | Choose the correct option below :

If $\begin{vmatrix} 2 & 4 \\ 5 & 1 \end{vmatrix} = \begin{vmatrix} 2x & 4 \\ 6 & x \end{vmatrix}$, then x is equal to :

The value of a for which the function $f(x) = a^x$ is increasing on R are given by :

The feasible reason for the constraints $x \geq 0$, $x + y \leq 1$ and $x - y \leq 1$, is situated in : (A) I and II quadrant only (B) I Quadrant (C) II and IV Quadrant (D) IV Quadrant (E) I , II , III and IV Quadrant Choose the correct answer from the option given below :

A matrix has 24 elements , which of the following cannot be the possible order of the matrix

Match List - I with list- II | List-I , Differential equation | List - II , Degree | |---|---| | A. $\left(\frac{dy}{dx}\right)^3 + yx = 0$ | 2 | | B. $e^{\frac{dy}{dx}} + y^2 + y'' = 0$ | 1 | | C. $Xyy'' + x(y')^2 - yy' = 0$ | Not defined | | D. $(Y'')^2 + y = 0$ | 3 | Choose the correct option below :

Any function f(x) is an increasing function in [a,b] if : (A) $x_1, x_2 \in [a, b], f(x_1) \geq f(x_2)$ if $x_1 < x_2$ (B) $x_1, x_2 \in [a, b], f(x_1) \geq f(x_2)$ if $x_1 > x_2$ (C) (A) $x_1, x_2 \in [a, b], f(x_1) \leq f(x_2)$ if $x_1 < x_2$ (D) (A) $x_1, x_2 \in [a, b], f(x_1) < f(x_2)$ if $x_1 > x_2$

Match List - I with list- II | List-I | List - II | |---|---| | A. the probability distribution is applied for discrete random variable | normal distribution | | B. A normal distribution is symmetric about | standard deviation | | C. this probability distribution is applied for continuous random variable | mean | | D. the shape of normal curve depend upon | Poisson distribution | Choose the correct option below :

A sum of Rs 60,000 invested at r percent compounded quarterly will provide payment at rupees 600 each at the end of every three months , then the value of r is :

A die is rolled thrice. What is the probability of getting a number greater than 4 in the first and the second throw of dice and a number less than 4 in the third throw?

Which of the following is false about the central limit theorem

Value of Z equals to 40x + 50y subject to constraints $3x + y \leq 9$, $x + 2y \leq 8$, $x, y \geq 0$ occurs at

Which of the following is not true

Evaluate $3^{15} \mod(7)$

The corner point of the feasible region determined by a set of linear constraints are : (0,0) , (0,4), (2,5) , (6,3) and (6,0) then which of the following point lie in the feasible region ?

Out of 1000 employees, 100 have to be selected for a survey . After being arranged in the alphabetical order each one is assigned a number from 1 to 1000. A number 4 is selected and then every 10th person is selected (i.e 4 , 14, 24 ... ) . Which form of sampling is this an example of ?

If $A = \begin{bmatrix} -2 & 1 \\ 3 & 2 \end{bmatrix}$ and $B' = \begin{bmatrix} -1 & 1 \\ 0 & 2 \end{bmatrix}$, then $(A+2B)' =$

For a given data of 5 observation $\sum y = 311$, $\sum x^2 = 10$ and $\sum xy = 90$. The equation of the trend line is :

If the cost function and the profit function for a company is given by $C = 10 - 0.3x^2$ and $P = 0.3x^2 + 2x - 10$ respectively , where X represent units of output, then the revenue function is given by :

A company produces two types of belts A & B with a profit of Rs 2 and Rs 1.50 respectively. Belt of type A needs twice as much time to make as belt type B . The company can produce at the most 1000 belts of type B per day . Material for 800 belts is available per day . At the most , 400 buckles for belt type A and 700 for belts type B are available . Then the appropriate LPP is :

The corner points of the feasible region determined by $x + y \leq 8$, $2x + y \geq 8$, $x \geq 0$, $y \geq 0$, are A(0, 8), B(4, 0) and C(8, 0). If the objective function Z = ax + by has its maximum value on the line segment AB, then the relation between a and b is :

A monopolist's Demand function is $x = 70 - \frac{P}{2}$, the revenue at $x = 5$ will be :

If $y = \log_3(\log_3 x)$, then $\frac{dy}{dx}$

Matrix $A = \begin{bmatrix} 0 & a & 5 \\ 4 & b & -1 \\ c & 1 & 0 \end{bmatrix}$ is skew - symmetric, then the values of a, b c are :

The Solution set of the inequality three $3x + 4y \leq 12$ is :

The increase in the sale of shawls during winters is an example of :

Which of the following is not a statistic ?

Match list I with list II. 4 defective pens are mixed with 10 normal pens. 3 pens are drawn one by one with replacement , then the probability distribution of the number of defective pens is : | List-I | List - II | |---|---| | A. P(X=0) | 8/343 | | B. P(X=1) | 60/343 | | C. P(X=2) | 125/343 | | D. P(X=3) | 150/343 | Choose the correct option below :

T- test : A t- test is a test of difference for parameter data $t = \frac{\overline{x1} - \overline{x2}}{s\sqrt{\frac{1}{n1} + \frac{1}{n2}}}$ Then read the following statements and choose the correct statements (A) the null hypothesis and the alternative hypothesis have the same viewpoint (B) In t- test testing the significance of mean value is done, when sample size is small (C) T - test for two independent groups when variance is equal (D) Testing is a process used by statisticians to accept or reject the hypothesis (E) if the value of test statistics is greater than the table values, we do not reject the null hypothesis Choose the correct answer from the options given below :

If $t = e^{2x}$ and $\log_e t^2$, then $\frac{d^2y}{dx^2}$ is :

Let $P = \begin{bmatrix} 5 & 2 \\ 7 & 4 \end{bmatrix}$, $Q = \begin{bmatrix} 2 & 5 \\ 3 & 8 \end{bmatrix}$, $R = \begin{bmatrix} 2 & -1 \\ 3 & 4 \end{bmatrix}$, then the matrix S such that QS - RP = 0 will be :

The cost of type A cement is Rs 100 per kg and that of type B cement is Rs 120 per kg. If both are mixed in the ratio of 2:3, the price of the cement mixer per kg will be

Two inlet pipes can fill a tank in 20 minutes and 24 minutes respectively . An outlet pipe can empty 30 liters of water per minute. If all three pipes working together can fill the tank in 15 minutes. The capacity of the tank is :

Mr. Jain takes a personal loan of rupees 10,00,000 at 12% rate of interest per annum for three years. His EMI by flat rate method is :

Jeep A and Jeep b are competing in a motor race. After starting together, Jeep B covers the target of 30 kilometer in 30 minutes 4 seconds. Jeep A covers the target in 30 minutes one second. By what distance will Jeep A beat Jeep B ?

If $x = at^2$ and $y = a^3 t^3$, then $\frac{d^2 y}{dx^2}$ will be :

If a square matrix B satisfies $B^2 = I - B$ and $B^n = 5I - 8B$, then the value of n is :

A motor boat can row at the speed of 12 kilometres per hour in Still water . if the river is flowing at 4 kilometer per hour and it takes 12 hours for a round trip , then the distance between the two places is

The minimum value of $f(x) = 4x^3 - 48x + 105$ in the interval [1,3] is :

If the mean of a binomial distribution is 24 and its standard deviation is 4 , then the probability of getting success is :

Consider the following hypothesis test : $H_0 : \mu \leq 24$, $H_a : \mu > 24$ A sample of 64 provided a sample mean of 24.3 . The population standard deviation is 2. The value of the test statistic is :

A vehicle has a scrap value of Rs 7,50,000 after 6 years of its purchase . If the annual depreciation charge is Rs 55,000, then the original cost of the vehicle is :