Applied-Mathematics PYQ — Page 2

The effective rate equivalent to a nominal rate of 8% per annum compounded semi annually is :

Two positive numbers $x$ and $y$ such that $x + y = 60$ and $xy^3$ is maximum are :

The present value of a perpetuity of Rs 1,200 payable at the beginning of each year, if the money is worth 5% effective, is:

Let $f : R \to R$ be a function defined as $f(x) = 2x^3 - 21x^2 + 36x - 20$, then : (A) maximum value of $f(x)$ is $-3$ (B) minimum value of $f(x)$ is $-128$ (C) maximum value exists at $x = 6$ (D) minimum value exists at $x = 1$ Choose the **correct** answer from the options given below :

Which of the following is false about the central limit theorem

If $x = 2t^2 + 3, y = 3t^2 + 6t + 5$, then the value of $\frac{d^2y}{dx^2}$ is :

A swimmer's speed in swimming pool is 6 km/hr. He swims between two points in a river and returns back to the starting point. He took 24 minutes more to cover the distance upstream than downstream. If the speed of the stream is 4 km/hr, then the distance between two points is:

A discrete random variable X has the following probability distribution : | X: | 0 | 1 | 2 | 3 | 4 | 5 | |----|----|----|----|----|----|----| | P(X): | b | 3b | 5b | 3b | 4b | 6b | The value of b is :

The value of the integral $I = \int_{-1}^{1} (x + x^3 + x^5) dx$ 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 $ax + by$, where $xy = c^2$ and a, b, c are positive, is :

Pipe A can independently empty a half-filled tank in 3 hours whereas pipe B can alone fill the same tank in 4 hours, when the tank is completely empty. In how much time will the empty tank be completely filled, if both the pipes are opened together?

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

The investment ratio of P, Q and R if their profit ratio is 3 : 5 : 7 respectively and their investment time period ratio is 4 : 5 : 6 respectively is :

Match **List - I** with **List - II**. | | List - I | | List - II | |---|---|---|---| | (A) | If $y = x^2 - 8$ and $\frac{dy}{dx} = 0$, then $x = ?$ | (I) | 1 | | (B) | If $p(x) = 3x + 1$, then $R(x)$ at $x = 2$ | (II) | 0 | | (C) | If $y = x^3$, then $\frac{dy}{dx}$ at $x = -1$ | (III) | 14 | | (D) | If $C(x) = 100 + 5x$, $R(x) = 102 + 3x$, then break-even point | (IV) | 3 | Choose the **correct** answer from the options given below :

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 :

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 $x_1 > x_2$

If $y = \log\left(\frac{x^5}{e^5}\right)$, then $\frac{d^2y}{dx^2}$ is,

Match List I with List II | LIST I | LIST II | |---|---| | A. A solution that does not satisfy all the constraints is called | I. Linear | | B. The objective function in an LPP is | II. Convex polygon | | C. Linear inequalities or equations on the variables of LPP are called | III. Infeasible solution | | D. The feasible region in an LPP, formed by the convex combinations of the corner points, is called | IV. Constraints | Choose the correct answer from the options given below:

The maximum value of $Z = 3x + y$ subject to the constraints $x + y \leq 30, 2x + y \leq 40, x, y \geq 0$ is

In an LPP if the objective function $z = ax + by$ has same maximum value on two corner points of the feasible region, then the number of points at which maximum value of $z$ occurs is :

If the probability distribution of X is : | X | 2 | 3 | 4 | 5 | 6 | |---|---|---|---|---|---| | P(X) | 1/15 | 2/15 | 3/15 | 4/15 | 5/15 | Then variance is equal to :

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 :

Which of the following statements are true ? (A) Central limit theorem states that the sampling distribution of the mean $(\bar{x})$ approaches a normal distribution as the sample size increases. (B) As per Central Limit Theorem, when the sample size increases, the mean $(\bar{x})$ for the data becomes closer to the mean of overall population. (C) The shape of t-distribution does not depend on degree of freedom. Choose the correct answer from the options given below :