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CBSE XII
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Math
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Model Papers
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.
cbse
class12
modelpaper
2005
sec-c
q23
math
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.
cbse
class12
modelpaper
2012
sec-c
q28
math
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]
cbse
class12
modelpaper
2005
sec-c
q24
math
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.
cbse
class12
modelpaper
2012
sec-b
q13
math
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.
cbse
class12
physics
modelpaper
mock-test-series-2015
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?
cbse
class12
modelpaper
2012
sec-c
q24
math
answered
Oct 5, 2020
by
rise.sparkle13
1
answer
Using matrices, solve the following : $2x+y-3z=13; x+y-z=6 ;2x-y+4z = -12$
cbse
class12
modelpaper
2012
sec-c
q23
math
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).
cbse
class12
modelpaper
2012
sec-c
q25
math
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?
cbse
class12
physics
modelpaper
mock-test-series-2015
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.
cbse
modelpaper
2012
sec-a
q1
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 $
cbse
class12
modelpaper
2012
sec-a
q7
math
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} $
cbse
class12
modelpaper
2012
sec-a
q7
math
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.
cbse
class12
modelpaper
2012
sec-c
q24
math
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?
cbse
class12
modelpaper
2012
sec-b
q11
math
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.
cbse
class12
modelpaper
2012
sec-b
q22
math
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 \( \bot \)
cbse
class12
modelpaper
2012
sec-c
q27
math
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?
cbse
class12
modelpaper
2012
sec-b
q22
math
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.
cbse
class12
physics
modelpaper
mock-test-series-2015
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?
cbse
class12
modelpaper
2012
sec-c
q28
math
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?
cbse
class12
physics
modelpaper
mock-test-series-2015
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 \( \large\frac{4}{27}\pi h^3\tan^2 \alpha \).
cbse
class12
modelpaper
2012
sec-c
q24
math
answered
Apr 15, 2019
by
supriyadutta98
1
answer
If A is a square matrix of order 3 such that |adj A|=64. Find |A'|.
cbse
class12
modelpaper
2012
sec-a
q4
math
answered
Apr 8, 2019
by
rp075974
1
answer
A square matrix A, of order 3, has | A | = 5, find | A.adj.A |.
cbse
modelpaper
2012
sec-a
q5
answered
Apr 8, 2019
by
rp075974
1
answer
If A is square matrix of order 3 such that | adj.A |=81, find | A |.
cbse
class12
modelpaper
2012
sec-a
q1
math
answered
Apr 8, 2019
by
rp075974
2
answers
If A is an invertible matrix of order 3 and |A|=5 then find [adj.A].
cbse
class12
modelpaper
2012
sec-a
q4
math
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.
cbse
class12
math
modelpaper
mock-test-series-2015
sec-c
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 $ .
cbse
class12
modelpaper
2012
sec-c
q27
math
answered
Mar 17, 2019
by
kavithakavitha1805
1
answer
Let * be a binary operation on set Q of rational numbers defined as a*b = \( \large\frac{3ab}{7} \). Write the identity for * , if any.
cbse
class12
modelpaper
2012
sec-a
q1
math
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 .
cbse
class12
physics
modelpaper
mock-test-series-2015
answered
Mar 5, 2019
by
ujjawalkthakur
1
answer
A matrix A, of order 3 x 3, has determinant 4 find the value of |3A|.
cbse
class12
modelpaper
2012
sec-a
q3
math
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, \( \large\frac{x-1}{2} = \frac{y+2}{3} = \frac{z}{-3} \).
cbse
class12
modelpaper
2012
sec-b
q21
math
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?
cbse
class12
physics
modelpaper
mock-test-series-2015
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.
cbse
modelpaper
2012
sec-b
q11
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?
cbse
class12
modelpaper
2012
sec-c
q28
math
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} $.
cbse
class12
modelpaper
2012
sec-b
q21
math
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 }.
cbse
class12
modelpaper
2012
sec-a
q1
math
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?
cbse
class12
modelpaper
2012
sec-c
q29
math
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.
cbse
class12
modelpaper
2011
sec-a
q1
math
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 \(\large \frac{9}{17} \).
cbse
class12
modelpaper
2012
sec-b
q22
math
answered
Jan 12, 2019
by
ankitgupta1301789
1
answer
Find the area of circle \( x^2+y^2=16\) which is exterior of the parabola \( y^2=6x\).
cbse
class12
modelpaper
2012
sec-c
q25
math
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.
cbse
class12
modelpaper
2005
sec-c
q22
math
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 \[ \begin{array} ((A)\: (2, 4) ∈ R \quad & (B)\: (3, 8) ∈ R \\ (C) \: (6, 8) ∈ R \quad & (D)\: (8, 7) ∈ R. \end{array} \]
cbse
class12
modelpaper
2012
sec-a
q1
math
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.
cbse
class12
modelpaper
2012
sec-a
q10
math
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.
cbse
class12
modelpaper
2012
sec-b
q21
math
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 ?
cbse
class12
physics
modelpaper
mock-test-series-2015
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.
cbse
class12
modelpaper
2005
sec-c
q21
math
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 $50$
cbse
class12
physics
modelpaper
mock-test-series-2015
answered
Dec 12, 2018
by
mg.sankkar
1
answer
Two bags A and B contain 2 white, 4 red and 3 white, 3 red balls respectively. One of the bags is selected at random and a ball is drawn from it. If the selected ball is of white colour, find the probability that it is drawn from bag A.
cbse
class12
modelpaper
2012
sec-b
q22
math
answered
Dec 6, 2018
by
hrithwikp
1
answer
Verify Lagrange's mean value theorem for the following function : \( f(x) = \sin \: x - \sin\: 2x \: in \: [0, \pi ] \)
cbse
class12
modelpaper
2012
sec-b
q14
math
answered
Dec 6, 2018
by
kp5018800
1
answer
A catering agency has two kitchen to prepare food at two places A and B. From these places 'Mid-day Meal' is to be supplied to three different schools situated at P, Q , R. The monthly requirement of the school are respectively 40,40 and 70 food packets. A packet contains lunch for 1000 students. The capacity of kitchen A and B are 60 and 70 packets per month respectively. The transportation cost per packets from the kitchens to school is given below : How many packets from each kitchen should be transported to school so that the cost of transportation is minimum? Also find the minimum cost.
cbse
class12
modelpaper
2012
sec-c
q29
math
answered
Nov 30, 2018
by
vanshgreat08
1
answer
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