Recent questions and answers in Math

Prove that every real valued function which is derivable at a point of its domain is also continuous at that point. Is the converse true?

answered May 18, 2023 by sbi071403

1 answer

Show that the function $f : Z \rightarrow Z$ defined by $f(x)=x^2$ is neither one-one nor onto.

answered Sep 9, 2022 by hackerboyqwerty123

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A calculator manufacturing company finds that the daily cost of producing calculators is given by C(x) = 200x + 7500. • If each calculator is sold for Rs. 350, find the minimum number of calculators that must be produced daily and sold to ensure no loss. • If the selling price is increased by Rs. 150, what would be the break-even point?

answered Jun 20, 2022 by thor69565

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Let * be a binary operation on the set of real numbers. If a * b = a+b-ab, 2 * ( 3 * x ) = -7, find the value of x.

answered Apr 26, 2021 by kuppurajanbharathi

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A, B and C are engaged in a printing business. A being the working partner, receives 10% of the net profit as salary. The remaining profit is divided among themselves in the ratio 4:5:9. If A gets in total Rs. 3,00,000, find the total profit in the business and the shares of B and C in it.

answered Dec 22, 2020 by makumarsahu2004

1 answer

A furniture firm manufactures chairs and tables, each requiring the use of three machines A, B and C. Production of each chair requires 2 hours on machine A, 1 hour on machine B and 1 hour on machine C. Each table requires 1 hour each on machine A and B and 3 hours on machine C. The profit obtained by selling one chair is Rs. 30 while by selling one table the profit is Rs. 60. The total time available per week on machine A is 70 hours, on machine B is 40 hours and on machine C is 90 hours. How many chairs and tables should be made per week so as to maximise profit? Formulate the problem as LPP and solve it graphically.

answered Dec 11, 2020 by ms21012003

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Find the present worth of an ordinary annuity of Rs. 1,200 per annum for 10 years at 12% per annum, compounded annually. [Use (1.12) -10 =0.3221]

answered Oct 31, 2020 by sarikabora999

1 answer

There are two families P and Q. There are 3 men, 3 women and 12 children in family P and 2 men, 2 women and 4 children in family Q. The recommended daily allowance for calories is : Man : 2400, woman : 2000, child: 1400 and man : 60 g for proteins is : woman: 40 g and child: 35 g. (i) Represent the above information by matrices. Using matrix multiplication, calculate the total requirement of calories and proteins of each of the two families.

answered Oct 25, 2020 by sharmaaseem2406

1 answer

Solve the following LPP graphically. Maximize or minimize Z = 3x+5y subject to $3x-4y\geq-12$ $2x-y+2\geq0$ $2x+3y-12\geq0$ $0\leq x\leq4$ $y\geq2$

answered Oct 19, 2020 by rvandana115

1 answer

A pure inductor is connected across an a.c. source. Show mathematically that the current in it lags behind the applied e.m.f by a phase angle of $\large\frac{\pi}{2}$ What is its inductive reactance? Draw a graph showing variation of inductive reactance with the frequency of the a.c. source.

answered Oct 17, 2020 by badalbhardwaj2

1 answer

A toy company manufactures two types of dolls, A and B. Each doll of type B takes twice as long as to produce as one of type A. If the company produces only type A. It can make a maximum of 2000 dolls per day. The supply of plastic is sufficient to produce 1500 dolls per day. Type B requires a fancy dress which cannot be available for more than 600 per day. If the company makes profit of Rs.3 and Rs.5 per doll respectively on doll A and doll B, how many of each should be produced per day in order to maximise the profit?

answered Oct 5, 2020 by rise.sparkle13

1 answer

Solve: $ydx-(x+2y)^2dy=0$

answered Oct 1, 2020 by gilledobaleros

1 answer

Using matrices, solve the following : $2x+y-3z=13; x+y-z=6 ;2x-y+4z = -12$

answered Jul 9, 2020 by hjaspinder

1 answer

Use definite integration, find the area of triangle whose vertices are (-1,6),(1,2) and (5,4).

answered May 21, 2020 by sreejaunnikrishnan161

1 answer

An AC voltage of peak $20\;V$ is connected in series with a silicon diode and a load resistance of $500 \Omega$ . The forward resistance of the diode is $10 \Omega$ and the barrier voltage is $0.7\;V$ . Find the peak current through diode and the peak voltage across the load. What will happen to these values if the diode is assumed to be ideal?

answered Apr 2, 2020 by manishkr1456

1 answer

Show that the area enclosed by the circle $x^2+y^2=64a^2$ and the parabola $y^2=12ax$ is $a^2 \bigg(\frac{16}{\sqrt 3}+\large\frac {64\pi}{\sqrt 3}\bigg)$

answered Apr 1, 2020 by aparme03

1 answer

Let $f:R_+\rightarrow[-5,\infty)$ given by $f(x)=9x^2+6x-5.$ show that f is invertiable with $f^{-1}(y)=\frac{\sqrt{y+6}-1}{3}.$

answered Mar 21, 2020 by hk0312109

1 answer

Give an example to show that the relation R in the set of natural numbers, defined by $R = ( (x,y), x, y \in\: N, x \leq \: y^2)$ is not transitive.

answered Mar 20, 2020 by neelurani06041980

1 answer

The area of the region in the first quadrant enclosed by the x-axis,the line y=x and the circle $x^2+y^2=32$ is $\begin{array}{1 1}(A)\;16\pi\; sq.units & (B)\;4\pi \;sq.units\\(C)\;32\pi\; sq.units & (D)\;24\pi\;sq.units \end{array}$

answered Mar 17, 2020 by kharbans823

2 answers

What is the degree of the following differential equation? $y\large\frac{d^2y}{dx^2}+\bigg(\frac{dy}{dx} \bigg)^3$ $=x \bigg( \large\frac{d^3y}{dx^3} \bigg)^2$

answered Mar 17, 2020 by anilmathappsc

1 answer

Find the order and degree of the differential equation $\bigg[ 1+ \bigg(\large \frac{dy}{dx} \bigg)^2 \bigg]^{\large\frac{3}{2}} = \frac{d^2y}{dx^2}$

answered Mar 17, 2020 by anilmathappsc

1 answer

Find the area of the region enclosed between the circles $x^2+y^2=1\;and\;\bigg(x-\frac{1}{2}\bigg)^2+y^2=1$

answered Mar 16, 2020 by msq6786

1 answer

Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of X.

answered Feb 18, 2020 by surafelalemgirma91

2 answers

Find the equation of the plane passing through the intersection of planes $4x-y+z=10\: and \: x+y-z=4$ and parallel to the line with direction ratios < 2, 1, 1>. Find also the perpendicular distance of (1, 1, 1) from the plane.

answered Feb 17, 2020 by jyotiverma221997

1 answer

Find the area of the segment cut off from the parabola $y^2=2x$ by the line $y=4x-1$

answered Dec 22, 2019 by gourishanker2431

1 answer

Let A = set of boys of XII class in some school. Let a R b, if and only if a and b use unfair means in the exam, $a, b \in A$ Is R a transitive relation?

answered Oct 25, 2019 by Dadwalgaurav07

1 answer

To test the quality of electric bulbs produced in a factory, two bulbs are randomly selected from a large sample without replacement. If either bulb is defective, the entire lot is rejected. Suppose a sample of 200 bulbs contains 5 defective bulbs. Find the probability that the sample will be rejected.

answered Sep 18, 2019 by addisutheking

1 answer

find the equation of the normal to the curve y=x^3+2x^2 at x=0 find the coo

answered Jul 20, 2019 by noorlh

1 answer

From the point P(1, 2, 4 ) a perpendicular is drawn on the plane $2x+y-2z+3 = 0$ . Find the equation of the length and coordinates of the foot of the $\bot$

answered Jul 20, 2019 by vikashkumarpaswan858

1 answer

P(A speaks truth is) = 4/5 . A coin is tossed. 'A' reports that a head appears. The probability that actually there was a head is.

answered Jul 13, 2019 by fad.vhora

1 answer

A speaks truth 8 times out of 10 times. A dice is tossed. He reports that it was 5. What is the probability that it was actually 5?

answered Jul 13, 2019 by fad.vhora

1 answer

A cylindrical metallic wire is stretched to increase its length by $5\%$ . Calculate the percentage change resistance.

answered Jul 9, 2019 by jesanivar

1 answer

Find the volume of the tetrahedron formed by the four planes $x+y=0,y+z=0,z+x=0,x+y=1$

answered Jul 9, 2019 by meena.clay6

1 answer

Given P(A) = 0.3, P(B) = 0.2, Find P(B/A) if A and B are mutually exclusive events.

answered Jul 1, 2019 by abhav31

5 answers

If $f^1(x)=g(x)\;and\;g^1(x)=-f(x)$ for all n and $f(2)=f^1(2)=4,$ find the value of $f^2(24)+g^2(24)$

answered Jun 24, 2019 by premkht

1 answer

Find the area bounded by the x-axis part of the curve $y=1+\Large\frac{8}{x^2}$ and the ordinates x = 2 and x = 4 If the ordinate at x = a divides the area into two equal parts find 'a'

answered Jun 8, 2019 by keerthanapradeeshbabu

1 answer

A company makes two kinds of belts, belt A is of pure leather and belt B is macro based. The respective profits are Rs.40 and Rs.30 per belt. Each belt of type A requires twice as much time as a belt of type B and if all the belts were of type B a company could make 1000 belts per day. The supply of leather and macro is sufficient for only 8000 belts per day (both A and B combined). Belt A requires a fancy buckle and only 4000 buckles are available. There are only 7000 buckles per day available for belt B. What should be the daily production of each belt to have maximum profit?

answered Jun 3, 2019 by sripada.teja

1 answer

In Young’s double slit experiment, the two slits $0.15\;m$ apart are illuminated by monochromatic light of wavelength 450nm. $The screen is$ 1.0\;m$ away from the slits. 1. Find the distance of the second a) bright fringe b) dark fringe from the central maximum. 2. How will the fringe pattern change, if the screen is moved away from the slits?

answered May 30, 2019 by utkarshguptamahan

1 answer

Show that the volume of the greatest cylinder that can be inscribed in a cone of height 'h' and semi-vertical angle $\alpha$ is $\large\frac{4}{27}\pi h^3\tan^2 \alpha$ .

answered Apr 15, 2019 by supriyadutta98

1 answer

Differentiate ‘Cry’ and ‘cry’

answered Apr 9, 2019 by priyanka.clay6

1 answer

If A is a square matrix of order 3 such that |adj A|=64. Find |A'|.

answered Apr 8, 2019 by rp075974

1 answer

A square matrix A, of order 3, has | A | = 5, find | A.adj.A |.

answered Apr 8, 2019 by rp075974

1 answer

If A is square matrix of order 3 such that | adj.A |=81, find | A |.

answered Apr 8, 2019 by rp075974

2 answers

If A is an invertible matrix of order 3 and |A|=5 then find [adj.A].

answered Mar 20, 2019 by vinothperiyasamy.1991

1 answer

A small manufacturer has employed 5 skilled men 10 semi - skilled men and makes an article in two qualities deluxe model and an ordinary model. The making of a deluxe model requires 2 hrs work bt skilled man and 2 hrs work by a semi skilled man. The ordinary model requires 1 hr by a skilled man and 3 hrs by a semi skilled man. By union rules no mam may work more than 8 hrs per day. The manufactures clear profit on deluxe model is Rs.15 and an orsinary model is Rs. 10. How many of each type should be made in order to maximize his total daily profit.

answered Mar 18, 2019 by neenanagpal21

1 answer

Find the equation of the plane which contains the line of intersection of the planes $\overrightarrow r. (\hat i + 2\hat j + 3\hat k ) -4 = 0 \overrightarrow r. (2\hat i + \hat j - \hat k ) + 5 = 0$ and which is perpendicular to the plane $\overrightarrow r. (5\hat i + 3\hat j - 6\hat k ) + 8 = 0$ .

answered Mar 17, 2019 by kavithakavitha1805

1 answer

Give an account of Hershey and Chase experiment. What did it conclusively prove? If both DNA and pro

asked Jul 5, 2017 by pady_1

1 answer

During reproduction, the chromosome number (2n) reduces to half (n) in the gametes and again the ori

asked Jun 14, 2017 by pady_1

1 answer

find intervals in which function given by f(x) = sin 3x where x belongs [0, pi/2] is 1 increasing 2 decreasing

asked Feb 26, 2017 by myselfdishu

1 answer

Which one of the following is a bird flu virus?

asked Jan 25, 2017 by priyanka.c

1 answer

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