If A and B are non-singular matrix then, which of the following is incorrect?

If any three rows or columns of a determinant are identical then the value of the determinant is ________.

The term containing x³ in the expansion of (x - 2y)⁷ is _________.

If \(\frac { kx }{ (x+4)(2x-1) } =\frac { 4 }{ x+4 } +\frac { 1 }{ 2x-1 } \) then k is equal to _______.

The focus of the parabola x² = 16y is _______.

If the circle touches x axis, y axis and the line x = 6 then the length of the diameter of the circle is _______.

The value of \(\sin15^o\) is ______.

The value of \(\frac{2\tan30^o}{1+tan^230}\) is _____.

f(x) = - 5 , for all \(x\in R\), is a ________.

\(\lim _{ x\rightarrow 0 }{ \frac { { e }^{ x }-1 }{ x } } =\)________.

Profit P(x) is maximum when ________.

If R = 5000 units / year, C₁ = 20 paise , C₃ = Rs. 20 then EOQ is _______.

The present value of the perpetual annuity of Rs. 2000 paid monthly at 10 % compound interest is _______.

Example of contingent annuity is _______.

Which of the following is positional measure?

When calculating the average growth of economy, the correct mean to use is?

Example for positive correlation is______.

Scatter diagram of the variate values (X,Y) give the idea about ________.

The minimum value of the objective function Z = x + 3y subject to the constraints 2x + y ≤ 20, x + 2y ≤ 20, x > 0 and y > 0 is ______.

In critical path analysis, the word CPM mean ______.

The technology matrix of an economic system of two industries is\(\begin{bmatrix} 0.50 & 0.30 \\ 0.41 & 0.33 \end{bmatrix}\). Test whether the system is viable as per Hawkins Simon conditions.

Evaluate the following using binomial theorem:(999)⁵

Find the center and radius of the circle 5x² + 5y² + 4x - 8y - 16 = 0

Evaluate \(\cot\left(\frac{-15\pi}{4}\right)\)

Differentiate the following functions with respect to x, \(x^{\frac{3}{2}}\)

Find the maximum and minimum values of x³-6x²+7

A cash prize of Rs. 1,500 is given to the student standing first in examination of Business Mathematics by a person every year. Find out the sum that the person has to deposit to meet this expense. Rate of interest is 12% p.a

Suppose one person is selected at random from a group of 100 persons are given in the following

What is the probability that the man selected is a Psychologist?

Calculate the correlation coefficient from the following data
N = 9, ΣX = 45, ΣY = 108, ΣX² = 285, ΣY² = 1356, ΣXY = 597

A toy company manufactures two types of dolls A and B. Market tests and available resources have indicated that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B is atmost half of that for dolls of type A. Further, the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units. If the company makes profit of n2 and n6 per doll, how many of each should be produced weekly in order to maximize the profit. Formulate the above as mathematical LPP.

If A \(= \begin{bmatrix} 1 & -1 \\2 & 3 \end{bmatrix}\) show that A² - 4A + 5I₂ = 0 and also find A^-1.

Find the 5^th term in the expansion of (x - 2y)^13.

Find the equation of the parabola whose focus is (-3, 2) and the directrix is x + y = 4.

Find the values of the following  sin (-105)°

Show that \(\underset { x\rightarrow 0 }{ lim } \frac { \log { \left( 1+{ x }^{ 2 } \right) } }{ \sin ^{ 3 }{ x } } =1\)

If the demand law is given by p = 10e^{\(-\frac { x }{ 2 } \)} then find the elasticity of demand.

Find the yield on 20% stock at 80.

Calculate GM for the following table gives the weight of 31 persons in sample survey.

Compute the co-efficient of correlation batween the variates x and y from the given data:
No. of pairs of x and y series=8.x-series A.M.=74.5, x-series assumed mean =69, x-series S.D=13.07, y-series S.D=15.85, sum of products of corresponding deviations of x and y series =2176.

Solve the following LPP graphically. Maximize Z =−x₁ + 2x₂
Subject to the constraints −x₁ + 3x₂ ≤ 10, x₁ + x₂ ≤ 6,x₁ − x₂ ≤ 2 and x₁,x₂ ≥ 0

Suppose the inter-industry flow of the product of two industries are given as under.

Determine the technology matrix and test Hawkin's -Simon conditions for the viability of the system. If the domestic demand changes to 80 and 40 units respectively, what should be the gross output of each sector in order to meet the new demands.

If 22P_r+1:20P_r+2=11: 52, find r.

Resolve into partial fraction \(\frac{9}{(x-1)(x+2^2)}\)

Show that the equation 12x² - 10xy + 2y² + 14x - 5y + 2 = 0 represents a pair of straight lines and also find the separate equations of the straight lines.

Prove that \(\frac { 4tan\ x(1-{ tan }^{ 2 }x) }{ 1-6{ tan }^{ 2 } x+{ tan }^{ 4 } x } =tanx\)

If cosA = \(\frac{4}{5}\)and cosB = \(\frac{12}{13}\),\(\frac{3\pi}{3}<(A, B)<2 \pi,\) find the value of cos(A+B).

Show that \( f(x)= \begin{cases}5 x-4, & \text { if } 0< x \leq 1 \\ 4 x^3-3 x, & \text { if } 1< x< 2\end{cases}\) is continuous at x = 1

Find the absolute (global) maximum and absolute minimum of the function
 f(x) = 3x⁵ – 25x³ + 60x + 1 in the interval [–2,1]

Find the marginal productivities for Capital (K) and Labour (L) if P = 10K-K² + KL when K = 2 and L = 6.

Rani sold Rs.8000 worth 7% stock at 96 and invested the amount realised in the shares of FV Rs.100 os a 10% stock by which her income increased by Rs.80. Find the purchase price of 10% stock.

An unbiased die is thrown twice. Let the event A be odd number on the first throw and B the event odd number on the second throw. Check whether A and B events are independent.

Find out the coefficient of correlation in the following case and interpret.

Calculate the earliest start time, earliest finish time, latest start time and latest finish time of each activity of the project given below and determine the Critical path of the project and duration to complete the project.

Solve graphically: Minimize Z = 20x₁ + 40x_2.
Subject to the constraints 36x₁ + 6x₂ ≥ 108,3x₁ + 12x₂ ≥ 36,20x₁ + 10x₂ ≥ 100 and x₁,x₂≥0