Recent questions and answers in Model Papers

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

1 answer

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

1 answer

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

1 answer

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

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

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

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

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 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

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

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

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

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

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

Let * be a binary operation on set Q of rational numbers defined as ab = $ \large\frac{3ab}{7} $. Write the identity for , if any.

answered Mar 11, 2019 by goguramchoudhary

1 answer

(a)Draw a circuit diagram of an n-p-n transmitter with its emitter base function forward biased and base collector junction reverse biased. Describe briefly its properties (b) Explain how a transistor in active state exhibits a low resistance at its emitter base junction and high resistance at its base collector junction .

answered Mar 5, 2019 by ujjawalkthakur

1 answer

A matrix A, of order 3 x 3, has determinant 4 find the value of |3A|.

answered Feb 24, 2019 by hargunnsingh633

1 answer

Find the equation of the plane passing through the points ( 1, 2, 3 ) and (0, -1, 0 ) and parrallel to the line, $ \large\frac{x-1}{2} = \frac{y+2}{3} = \frac{z}{-3} $.

answered Feb 21, 2019 by ayankumarroy7

1 answer

In a metre bridge experiment a student observed a balance point at the point J, where AJ = l. Draw the equivalent Wheatstone Bridge circuit diagram for this setup The values of R and X are both doubles and then interchanged. What would be the new position of the balance point? If in this set up, the galvanometer and battery are interchanged at the balance position, how will the balance point get affected?

answered Feb 11, 2019 by riyamalik2001oct

1 answer

Let N be the set of all natural numbers and R be the relation on N x N defined by (a, b) R (c, d) if ad = bc. Show that R is an equivalence relation.

answered Feb 10, 2019 by gopalkryadavsbg

1 answer

Two bags A and B contain 4 white and 3 black balls and 2 white,2 black balls respectively. From bag A, two balls are transferred to bag B. Find the probability of drawing (a) 2 white balls from Bag B? (b) 2 black balls from bag B? (c) 1 white and 1 black ball from bag B?

answered Jan 28, 2019 by cherub2001dec

1 answer

Find the equation of a line passing through the point (2,1,3) and perpendicular to the lines $ \large\frac{x-1}{1} = \frac{y-2}{2} = \frac{z-3}{3}$ and $\large\frac{x}{-3}=\frac{y}{2}=\frac{z}{5} $.

answered Jan 26, 2019 by abinshaji47

1 answer

Relation R in the set of Z of all integers defined as R = {(x, y) : x-y is an integer }.

answered Jan 26, 2019 by gunjankumarshahi9199

1 answer

Let X denote the number of hours you study during a randomly selected school day. The probability that X can take the values X has the following form, where k is some unknown constant. \[ p(X=x) = \left\{ \begin{array}{l l}0.1, & \quad if{ x = 0}\\ kx, & \quad if{ x = 1 \: or\: 2} \\ k(5-x), & \quad if{ x = 3 \: or\: 5} \\ 0, & \quad \: otherwise \end{array}. \right. \] (i) Find the value of K (ii) What is the probability that you study atleast two hours? Exactly two hours? Atmost two hours?

answered Jan 22, 2019 by pulkityadav56

1 answer

Write the number of all one-one functions from the set A = { a, b, c} to itself.

answered Jan 12, 2019 by singhankush1356

1 answer

A and B throws a pair of die turn by turn. The first to throw 9 is awarded by a prize. If A starts the game, show that the probability of A getting the prize is $\large \frac{9}{17} $.

answered Jan 12, 2019 by ankitgupta1301789

1 answer

Find the area of circle $ x^2+y^2=16$ which is exterior of the parabola $ y^2=6x$.

answered Jan 10, 2019 by www.rahimlaskar786

1 answer

The probability that student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university: • None will graduate, • Only one will graduate, • All will graduate.

answered Jan 8, 2019 by subasri.arasu

1 answer

Let N be the set of natural numbers and R be the relation in N defined as $R = {(a, b) : a = b – 2, b > 6}$. Then \[ \begin{array} ((A)\: (2, 4) ∈ R \quad & (B)\: (3, 8) ∈ R \\ (C) \: (6, 8) ∈ R \quad & (D)\: (8, 7) ∈ R. \end{array} \]

answered Jan 3, 2019 by valasenthil

1 answer

Find the direction cosines of a line, passing through origin and lying in the first octant, making equal angles with the three coordinates axes.

answered Dec 28, 2018 by goyat78606

1 answer

The probability that a student entering an university will graduate is 0.4. Find the probability that out of 3 students of the university: (i) none will graduate (ii) only one will graduate (iii) all will graduate.

answered Dec 26, 2018 by shekhar81123987320

1 answer

What is the angle between the direction of electric field at any. (i) axial point and (ii) equatorial point due to an electrical dipole ?

answered Dec 22, 2018 by snhaich

1 answer

A company has two plants to manufacture motor cycled. 70% motor cycles are manufactured at the first plant, while 30% are manufactured at the second plant. At the first plant, 80% motor cycles are rated of the standard quality while at the second plant, 90% are rated of standard quality. A motor cycle, randomly picked up, is found to be of standard quality. Find the probability that it has come out from the second plant.

answered Dec 20, 2018 by randhirsingh6315

1 answer

The potential difference across the collector of a transistor, used in common emitter mode is $1.5\;V,$ with the collector resistance of $3\;k \Omega.$ Find 1. The emitter and 2. The base current, if the d.c. gain of the transistor is $50$

answered Dec 12, 2018 by mg.sankkar

1 answer

Ask Questions, Get Answers

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?

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

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.

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]

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.

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

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

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.

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 $

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} $

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.

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?

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 \( \bot \)

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?

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

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

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

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

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

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

Let * be a binary operation on set Q of rational numbers defined as ab = \( \large\frac{3ab}{7} \). Write the identity for , if any.

A matrix A, of order 3 x 3, has determinant 4 find the value of |3A|.

Find the equation of the plane passing through the points ( 1, 2, 3 ) and (0, -1, 0 ) and parrallel to the line, \( \large\frac{x-1}{2} = \frac{y+2}{3} = \frac{z}{-3} \).

Let N be the set of all natural numbers and R be the relation on N x N defined by (a, b) R (c, d) if ad = bc. Show that R is an equivalence relation.

Two bags A and B contain 4 white and 3 black balls and 2 white,2 black balls respectively. From bag A, two balls are transferred to bag B. Find the probability of drawing (a) 2 white balls from Bag B? (b) 2 black balls from bag B? (c) 1 white and 1 black ball from bag B?

Find the equation of a line passing through the point (2,1,3) and perpendicular to the lines $ \large\frac{x-1}{1} = \frac{y-2}{2} = \frac{z-3}{3}$ and $\large\frac{x}{-3}=\frac{y}{2}=\frac{z}{5} $.

Relation R in the set of Z of all integers defined as R = {(x, y) : x-y is an integer }.

Write the number of all one-one functions from the set A = { a, b, c} to itself.

A and B throws a pair of die turn by turn. The first to throw 9 is awarded by a prize. If A starts the game, show that the probability of A getting the prize is \(\large \frac{9}{17} \).

Find the area of circle \( x^2+y^2=16\) which is exterior of the parabola \( y^2=6x\).

The probability that student entering a university will graduate is 0.4. Find the probability that out of 3 students of the university: • None will graduate, • Only one will graduate, • All will graduate.

Let N be the set of natural numbers and R be the relation in N defined as \(R = {(a, b) : a = b – 2, b > 6}\). Then \[ \begin{array} ((A)\: (2, 4) ∈ R \quad & (B)\: (3, 8) ∈ R \\ (C) \: (6, 8) ∈ R \quad & (D)\: (8, 7) ∈ R. \end{array} \]

Find the direction cosines of a line, passing through origin and lying in the first octant, making equal angles with the three coordinates axes.

The probability that a student entering an university will graduate is 0.4. Find the probability that out of 3 students of the university: (i) none will graduate (ii) only one will graduate (iii) all will graduate.

What is the angle between the direction of electric field at any. (i) axial point and (ii) equatorial point due to an electrical dipole ?

The potential difference across the collector of a transistor, used in common emitter mode is $1.5\;V,$ with the collector resistance of $3\;k \Omega.$ Find 1. The emitter and 2. The base current, if the d.c. gain of the transistor is $50$