Recent questions and answers in Model Papers

A television manufacturer finds that the total cost for the production and marketing of $x$ number of television sets is : $c(x)=300x^2+4200x+13,500.$Each product is sold for Rs.8,400.Determine the break-even points.

answered Jul 31, 2022 by avnis3021

2 answers

An examination of 8 applicants for a clerical post was taken by a firm.The marks obtained by the applicants in the Reasoning and Aptitude tests are given below :

answered Feb 17, 2022 by dhananjanisandamali9

2 answers

Using matrices,solve the following system of equations : $x+2y=5,y+2z=8,2x+z=5$.

answered Sep 11, 2021 by baldeepsamra4

2 answers

The production of a soft drink company in thousands of litres during each month of a year is as follows :

answered Mar 27, 2021 by nafishaali678

1 answer

The following results were obtained with respect to two variable x and y :$\sum x=30,\sum y=42,\sum xy=199,\sum x^2=184,\sum y^2=318,n=6.$

answered Jan 7, 2021 by trishagon2003

1 answer

One set of 100 observations has the mean as 15 and another set of 150 observations has the mean as 16.Find the mean of 250 observations by combining the two sets of given observations.

answered Jan 5, 2021 by vihaan.toprani

1 answer

An insurance company insured 1500 scooter drivers,2500 car drivers and 4500 truck drivers.The probability of a scooter ,a car and a truck meeting with an accident is 0.01,0.02 and 0.04 respectively.If one of the insured persons meets with an accident,find the probability that he is a scooter driver.

answered Dec 1, 2020 by smileastha010

1 answer

Calculate the index number for 2005 with 2000 as the base year by the weighted aggregate method.

answered Nov 2, 2020 by sugandhasharma555

1 answer

Given that the total cost function for x units of a commodity is : $C(x)=\large \frac{x^3}{3}\normalsize +3x^2-7x+16$

answered Oct 1, 2020 by aditawesomebohra

1 answer

The fixed cost of a new product is Rs.18,000 and the variable cost is Rs.550 per unit.If the demand function $p(x)=4000-150x$,find break even points.

answered Aug 12, 2020 by priyankamahato2289

1 answer

Akhil and Vijay appear for an interview for two vacancies.The probability of Akhil's selection is $\large\frac{1}{4}$ and Vijay's selection is $\large\frac{2}{3}$.Find the probability that only one of them will be selected.

answered Jul 27, 2020 by ravigk01

1 answer

Verify Rolle's theorem for the function $f(x)=e^{2x}(\sin 2x-\cos 2x)$ defined in the interval $\begin{bmatrix}\large\frac{\pi}{8},\frac{5\pi}{8}\end{bmatrix}$

answered Jul 22, 2020 by kishorevenkatkm

1 answer

If $M(\theta)=\begin{bmatrix}\cos \theta & \sin\theta\\-\sin\theta &\cos\theta\end{bmatrix}$,show that $M(x)M(y)=M(x+y).$

answered May 20, 2020 by umeshjoshi5689

1 answer

Calculate Spearman's rank correlation coefficient between the advertisement cost and sales from the following data :

answered Apr 16, 2020 by karinashaikh49

1 answer

Find the area enclosed by the curves $y^2=x$ and $y^2=4-3x$.

answered Mar 12, 2020 by www.9ishanki9

1 answer

Five bad eggs are mixed with 10 good ones.If three eggs are drawn one by one with replacement ,find the probability distribution of the number of goods eggs drawn.

answered Mar 8, 2020 by mehmoodmudassir

1 answer

A dice is tossed three times.Getting a '3' or a '5' is considered a success.Find the probability of at least two successes.

answered Feb 8, 2020 by sdadhich.bst

1 answer

A box contains 4 red and 5 black marbles.Find the probability distribution of the red marbles in a random draw of three marbles.Also find the mean and standard deviation of the distribution.

answered Jan 24, 2020 by priyanshi.mohta11

1 answer

Assuming that on an average one telephone out of 10 is busy,seven telephone numbers are randomly selected and called.Find the probability that three of them will be busy.

answered Jan 17, 2020 by anishdey45

1 answer

Calculate the coefficient of correlation between X and Y from the following data using Karl Pearson's method :

answered Jan 9, 2020 by swayammohapatra2000

1 answer

If total cost function is given by $C=a+bx+cx^2$,where x is the quantity of output.Show that : $\frac{d}{dx}(AC)=\frac{1}{x}(MC-AC),$where $MC$ is the marginal cost and $AC$ is the average cost.

answered Dec 29, 2019 by spuaprajapati1975

1 answer

Using Rolle's theorem,find a point on the curve $y=\sin x+\cos x-1,x\in \begin{bmatrix}0,\large\frac{\pi}{2}\end{bmatrix}$ where the tangent is parallel to the x-axis.

answered Dec 23, 2019 by ishas4761

2 answers

A class consists of 50 students out of which there are 10 girls.In the class 2 girls and 5 boys are rank holders in an examination.If a student is selected at random from the class and is found to be a rank holder,what is the probability that the student selected is a girl?

answered Dec 20, 2019 by ayushsharma934516

1 answer

The following table shows the sales and advertisement expenditure of a firm :

answered Dec 11, 2019 by neeleshgour44

1 answer

A company is selling a certain product.The demand function of the product is linear.The company can sell 2000 units when the price is Rs.8 per unit and when the price is Rs.4 per unit,it can sell 3000 units,Determine :

answered Oct 22, 2019 by faizala626

1 answer

Sample of polythene bags from a manufacturer are tested by a buyer for bursting pressure with the following data :

answered Jul 15, 2019 by fjmuna7267

1 answer

If the regression equation of $x$ on $y$ is given by $mx-y+10=0$ and the equation of $y$ on $x$ is given by $-2x+5y=14$,determine the value of 'm' if the coefficient of correlation between $x$ and $y$ is $\large\frac{1}{\sqrt {10}}$.

answered Jun 27, 2019 by kavinilavu2812

1 answer

Using properties of determinants,show that $P\alpha^2+2q\alpha+r=0$,given that :p,q and r are not in G.P and $\begin{vmatrix}1 & \large\frac{q}{p} & \alpha+\large\frac{q}{p}\\1 & \large\frac{r}{q} & \alpha+\large\frac{r}{q}\\p\alpha+q &q\alpha+r &0\end{vmatrix}=0$.

answered Apr 28, 2019 by veerpalsidhu110

2 answers

If the two regression lines of a bivariate distribution are $4x-5y+33=0$ and $20x-9y-107=0$,

answered Apr 15, 2019 by anonymo007007007

1 answer

Compute Karl Pearson's Coefficient of correlation between sales and expenditures of a firm for six months

answered Feb 21, 2019 by himayathkhan132

1 answer

Draw a rough sketch of the curve $y=x^2-5x+6$ and find the area bounded by the curve and the $x$-axis.

answered Feb 5, 2019 by yamunabisht9458

1 answer

A closed right circular cylinder has volume $\large\frac{539}{2}$cubic units.Find the radius and the height of the cylinder so that the total surface area is minimum.

answered Jan 30, 2019 by varunsai051

1 answer

Three numbers are given whose sum is $180$ and the ratio between first two of them is $1: 2$.If the product of the number is greatest,find the numbers.

answered Jan 25, 2019 by suhitagarwal9

1 answer

show that the function $f(x)=x^2-6x+1$ satisfies the Lagrange's Mean value Theoem.Also find the co-ordinate of a point at which the tangent to the curve represented by the above function is parallel to the chord joining A(1,-4) and B(3,-8).

answered Jan 21, 2019 by ranjani.hogwarts

1 answer

Two lines of regression are given by x+2y-5=0, 2x+3y-8=0 and σ2x("sigma squared"x)=12, Calculate the mean value of x and y, variable of Y and the coefficient of correlation between x and y.

answered Jan 16, 2019 by g.cute143

2 answers

It is given that Rolle's theorem holds good for the function : $f(x)=x^3+ax^2+bx,x\in [1,2]$ at the point $x=\large\frac{4}{3}$.Find the values of a and b.

answered Jan 6, 2019 by tejasri52.prasanna

1 answer

Two horses are considered for a race.The probability of selection of the first horse is $\large\frac{1}{4}$ and that of the second is $\large\frac{1}{3}$.What is the probability that :

answered Jan 5, 2019 by ionathomas2

1 answer

Bag contains 2 white,1 black and 3 red balls,Bag B contains 3 white ,2 black and 4 red balls and Bag C contains 4 white ,3 black and 2 red balls.One Bag is chosen at random and 2 balls are drawn at random from that Bag.If the randomly drawn balls happen to be red and black,what is the probability that both balls come from Bag B?

answered Dec 6, 2018 by hrithwikp

1 answer

A company has two plants which manufacture scooters.Plant I manufactures 80% of the scooters while Plant II manufactures 20% of the scooters.At plant I ,85 out of 100 scooters are rated as being of standard quality,while at Plant II only 65 out of 100 scooters are rated as being of standard quality.If a scooter is of standard quality,what is the probability that it came from Plant I?

answered Nov 19, 2018 by dhavaltailor80

1 answer

A factory has three machines A,B and C producing 1,500,2,500 and 3,000 bulbs per day,respectively.Machine A produces 1.5% defective bulbs,machine B produces 2% defective bulbs and machine C produces 2.5% defective bulbs.At the end of the day,a bulb is drawn at random and is found to be defective.What is the probability that this defective bulb has been produced by machine B?

answered Nov 8, 2018 by gabbasarkhel123

1 answer

A closed circular cylinder has a volume of 2156c.c.What will be the radius of its base so that its total surface area is minimum.Find the height of the cylinder when its total surface area is minimum.

answered Nov 3, 2018 by alamt1785

1 answer

(i) Show that the second degree equations $x^2-5xy+4y^2+x+2y-2=0$ represents a pair of straight lines.(ii) Find the equations of the individual lines and their point of intersection.

answered Oct 23, 2018 by binod.kr.singh2106

1 answer

A fair die is thrown once.What is the probability that either an even number or a number greater than three will turn up?

answered Sep 28, 2018 by saravananmaths434

1 answer

Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random.What is the probability that the ticket has a number which is a multiple of 3 or 7.

answered Sep 26, 2018 by saravananmaths434

1 answer

In a single throw of two dice,find the probability of getting a total of at most 9.

answered Sep 26, 2018 by saravananmaths434

1 answer

Solve the following system of liner questions by matrix inverse method. 2x+2y+6z=52, 3x+2y+z=26, 2x+2y+6z=18

asked Jul 6, 2015 by sahunitinkumar68

1 answer

Using Demoivre's theorem,find the least value of n for which $\bigg(\large\frac{i+\sqrt 3 i}{\sqrt 2(1+i)}\bigg)^n$ is purely imaginary.

asked Apr 22, 2013 by sreemathi.v

0 answers

Solve : $(1+y+x^2y)dx+(x+x^3)dy=0$

asked Apr 22, 2013 by sreemathi.v

0 answers

Solve : $\large \frac{d^2y}{dx^2}\normalsize =\log x$

asked Apr 22, 2013 by sreemathi.v

0 answers

Find the real values of $x$,$y$ satisfying the equality $\large \frac{x-2+(y-3)i}{1+i}\normalsize=1-3i$

asked Apr 22, 2013 by sreemathi.v

0 answers

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