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Recent questions tagged isc
Questions
A straight line is parallel to the x-axis and passes through the intersection of the lines $x+2y+1=0$ and $y=x+7$.Find the equation of the straight line.
isc
class12
modelpaper
2006
sec-a
q1
q1-2
asked
Apr 16, 2013
by
sreemathi.v
1
answer
Solve for x and y : $\begin{bmatrix}x^2\\y^2\end{bmatrix}+2\begin{bmatrix}2x\\3y\end{bmatrix}=3\begin{bmatrix}7\\-3\end{bmatrix}$
isc
class12
modelpaper
2006
sec-a
q1
q1-1
asked
Apr 16, 2013
by
sreemathi.v
0
answers
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.
isc
class12
modelpaper
2007
sec-c
q14
q14-b
asked
Apr 16, 2013
by
sreemathi.v
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.
isc
class12
modelpaper
2007
sec-c
q15
q15-b
asked
Apr 16, 2013
by
sreemathi.v
1
answer
In a binomial distribution,the sum of its mean and the variance is 1.8.Find the probability of two successes if the event was conducted 5 times.
isc
class12
modelpaper
2007
sec-c
q15
q15-a
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Mr.Mohan took a loan of Rs. 7,500 on 1st Jan.2005 and agreed to pay Rs.2,250 after 1month,Rs.2,400 after 3 months,Rs.3000 after 4 months and Rs.750 after 5 months in full redemption of his debit.Find the rate of interest charged.
isc
class12
modelpaper
2007
sec-c
q14
q14-a
asked
Apr 16, 2013
by
sreemathi.v
0
answers
A person borrowed a sum of money and paid it back in 3 equal annual installments of Rs.2,160 each.If the rate of interest charged is 20% p.a. compounded annually,calculate :(i)The sum borrowed (ii) The total interest charged.
isc
class12
modelpaper
2007
sec-c
q13
q13-b
asked
Apr 16, 2013
by
sreemathi.v
0
answers
A bill was drawn on 14th June 2006 at 8 months after date and was discounted on 24th September 2006 at 5% p.a.If the banker's gain on the basis of simple interest is Rs. 3,calculate the sum for which the bill was drawn.
isc
class12
modelpaper
2007
sec-c
q13
q13-a
asked
Apr 16, 2013
by
sreemathi.v
0
answers
The production of a soft drink company in thousands of litres during each month of a year is as follows :
isc
class12
modelpaper
2007
sec-b
q12
q12-b
asked
Apr 16, 2013
by
sreemathi.v
1
answer
Calculate the index number for 2005 with 2000 as the base year by the weighted aggregate method.
isc
class12
modelpaper
2007
sec-b
q12
q12-a
asked
Apr 16, 2013
by
sreemathi.v
1
answer
Find a unit vector perpendicular to the vectors $4i+3j+k$ and $2i-j+2k$.Determine the sine angle between these two vectors.
isc
class12
modelpaper
2007
sec-b
q11
q11-b
asked
Apr 16, 2013
by
sreemathi.v
0
answers
If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are three vectors,show that : $(\overrightarrow{a}+\overrightarrow{b}).\{(\overrightarrow{b}+\overrightarrow{c})\times (\overrightarrow{c}+\overrightarrow{a})\}=2[\overrightarrow{a}\; \overrightarrow{b}\;\overrightarrow{c}]$
isc
class12
modelpaper
2007
sec-b
q11
q11-a
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Prove that the plane $x+2y-z=4$ cuts the sphere $x^2+y^2+z^2-x+z-2=0$ in a circle whose radius is unity.
isc
class12
modelpaper
2007
sec-b
q10
q10-b
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Find the equation of the plane through the point (1,2,3) and perpendicular to the planes $x+y+2z=3$ and $3x+2y+z=4$.
isc
class12
modelpaper
2007
sec-b
q10
q10-a
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Solve the differential equation : $x\large\frac{dy}{dx}\normalsize-y=\sqrt {x^2+y^2}$.
isc
class12
modelpaper
2007
sec-a
q9
q9-b
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Prove that $(1+i\sqrt 3)^8+(1-i\sqrt 3)^8=-2^8$ by using De Moiver's Theorem.
isc
class12
modelpaper
2007
sec-a
q9
q9-a
asked
Apr 16, 2013
by
sreemathi.v
0
answers
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.
isc
class12
modelpaper
2007
sec-a
q8
q8-b
asked
Apr 16, 2013
by
sreemathi.v
1
answer
The bag 'A' contains 3 white and 2 black balls while the bag 'B' contains 2 white and 5 black balls.One of the bags is chosen at random and a ball is drawn from it.What is the probability that the balls is white.
isc
class12
modelpaper
2007
sec-a
q8
q8-a
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Given two regression lines $4x+3y+7=0$ and $3x+4y+8=0$,determine :
isc
class12
modelpaper
2007
sec-a
q7
q7-b
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Calculate the coefficient of correlation between X and Y from the following data using Karl Pearson's method :
isc
class12
modelpaper
2007
sec-a
q7
q7-a
asked
Apr 16, 2013
by
sreemathi.v
1
answer
Find the area enclosed by the curves $y^2=x$ and $y^2=4-3x$.
isc
class12
modelpaper
2007
sec-a
q6
q6-b
asked
Apr 16, 2013
by
sreemathi.v
1
answer
Evaluate : $\int_0^{\large \frac{\pi}{4}}\normalsize \log (1+\tan x)dx.$
isc
class12
modelpaper
2007
sec-a
q6
q6-a
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Show that the semi-vertical angle of a cone of maximum volume and of given slant height is $\tan^{-1}(\sqrt 2).$
isc
class12
modelpaper
2007
sec-a
q5
q5-b
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Verify Lagrange's mean value theorem for the function $f(x)=3x^2-5x+1$ defined in interval $[2,5].$
isc
class12
modelpaper
2007
sec-a
q5
q5-a
asked
Apr 16, 2013
by
sreemathi.v
0
answers
If $\sin y=x\sin (a+y),$show that $\large\frac{dy}{dx}=\large\frac{\sin^2(a+y)}{\sin a}$.
isc
class12
modelpaper
2007
sec-a
q4
q4-b
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Prove that : $2\tan^{-1}\bigg(\large\frac{1}{3}\bigg)\normalsize +\cot ^{-1}(4)=\tan^{-1}\bigg(\large\frac{16}{13}\bigg).$
isc
class12
modelpaper
2007
sec-a
q4
q4-a
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Show that the bisectors of the angles between the pair of straight lines $11x^2-16xy-y^2=0$ are parallel and perpendicular to $x+2y+5=0.$
isc
class12
modelpaper
2007
sec-a
q3
q3-b
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Find the value of 'k' so that the second degree equation $12x^2-10xy+ky^2+14x-5y+2=0$ may represent a pair of straight lines.For this value of 'k' find the angle between the lines represented by the above equation.
isc
class12
modelpaper
2007
sec-a
q3
q3-a
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Solve the following system of equations using matrices : $x+y+z=6,x-y+z=2,2x+y-z=1$.
isc
class12
modelpaper
2007
sec-a
q2
q2-b
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Using the properties of determinants ,show that $\begin{vmatrix}x-y-z & 2x & 2x\\2y & y-z-x & 2y\\2z & 2z & z-x-y\end{vmatrix}=(x+y+z)^3$
isc
class12
modelpaper
2007
sec-a
q2
q2-a
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Solve the differential equation $\tan y dx+\sec^2y\tan x dy=0$.
isc
class12
modelpaper
2007
sec-a
q1
q1-10
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Find the modulus and amplitude of the complex number $\large\frac{2+3i}{3+2i}$.
isc
class12
modelpaper
2007
sec-a
q1
q1-9
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Five students scored marks as follows : 8,10,15,20,22.
isc
class12
modelpaper
2007
sec-a
q1
q1-8
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Kamal and Monika appear for an interview for two vacancies.The probability of Kamal's selection is $\large\frac{1}{3}$ and that of Monika's selection is $\large\frac{1}{5}$.Find the probability that only one of them will be selected.
isc
class12
modelpaper
2007
sec-a
q1
q1-7
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Find the equation of the ellipse whose minor axis is 4 and which has a distance of 6 units between its foci.
isc
class12
modelpaper
2007
sec-a
q1
q1-6
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Solve $\int\large\frac{1}{x\cos^2(1+\log x)}\normalsize dx$.
isc
class12
modelpaper
2007
sec-a
q1
q1-5
asked
Apr 16, 2013
by
sreemathi.v
0
answers
If $e^{x+y}=xy,$show that $\large\frac{dy}{dx}\normalsize=\large\frac{y(1-x)}{x(y-1)}$.
isc
class12
modelpaper
2007
sec-a
q1
q1-4
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Find the equation of the parabola having focus at (3,-4) and directrix as $x+y=2.$
isc
class12
modelpaper
2007
sec-a
q1
q1-3
asked
Apr 16, 2013
by
sreemathi.v
0
answers
Find the equation of the line passing through the intersection of the straight lines $2x+3y=1$ and $3x+4y=6$ and perpendicular to the line $5x-2y=7$.
isc
class12
modelpaper
2007
sec-a
q1
q1-2
asked
Apr 16, 2013
by
sreemathi.v
0
answers
If $A\begin{bmatrix}1 & 2\\2 & 1\end{bmatrix}$,show that $A^2-3I=2A$.
isc
class12
modelpaper
2007
sec-a
q1
q1-1
asked
Apr 16, 2013
by
sreemathi.v
0
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?
isc
class12
modelpaper
2008
sec-c
q15
q15-b
asked
Apr 15, 2013
by
sreemathi.v
1
answer
Eight coins are thrown simultaneously.
isc
class12
modelpaper
2008
sec-c
q15
q15-a
asked
Apr 15, 2013
by
sreemathi.v
0
answers
The average cost function associated with producing and marketing $x$ units of an item is given by $AC=2x-11+\large\frac{50}{x}$.Find : (i) The total cost function and marginal cost function. (ii) The range of values of the output $x$ for which AC is increasing.
isc
class12
modelpaper
2008
sec-c
q14
q14-b
asked
Apr 15, 2013
by
sreemathi.v
0
answers
A manufacturer produces two types of steel trunks.He has two machines,A and B.The first type of trunk requires 3 hours on machine A and 3 hours on machine B.The second type requires 3 hours on machine A and 2 hours on machine B.Machines A and B can work at most for 18 hours and 15 hours per day respectively.He earns a profit of Rs. 30 per trunk on the first type of trunk and Rs. 25 per trunk on the second type.Formulate a Linear Programming Problem to find out how many trunks of each type he must make each day to maximise his profit.
isc
class12
modelpaper
2008
sec-c
q14
q14-a
asked
Apr 15, 2013
by
sreemathi.v
1
answer
Mr.Aggarwal buys a house at Rs. 30,00,000 for which he agrees to make equal payments at the end of each year for 10 years.If money is worth 10% p.a., find the amount of each installment.[Take $(1.1)^{-10}=0.3855]$
isc
class12
modelpaper
2008
sec-c
q13
q13-b
asked
Apr 15, 2013
by
sreemathi.v
0
answers
The banker's gain on a certain bill due 6 months hence is Rs. 100,the rate of interest being 10% per annum.Find the face value of the bill.
isc
class12
modelpaper
2008
sec-c
q13
q13-a
asked
Apr 15, 2013
by
sreemathi.v
0
answers
Given $\overrightarrow{a}=i-2j+k,\overrightarrow{b}=2i+j+k$ and $\overrightarrow{c}=i+2j-k$.Find $\overrightarrow{a}\times(\overrightarrow{b}\times \overrightarrow{c})$
isc
class12
modelpaper
2008
sec-b
q12
q12-b
asked
Apr 15, 2013
by
sreemathi.v
0
answers
Find $\overrightarrow{a}.\overrightarrow{b}$ if $ \mid\overrightarrow{a}\mid=2, \mid\overrightarrow{b}\mid=5$ and $\mid \overrightarrow{a}\times \overrightarrow{b}\mid$=8.
isc
class12
modelpaper
2008
sec-b
q12
q12-a
asked
Apr 15, 2013
by
sreemathi.v
0
answers
Coded monthly sales figures of a particular brand of T.V. for 18 months commencing January 1,2005 are as follows :
isc
class12
modelpaper
2008
sec-b
q11
q11-b
asked
Apr 15, 2013
by
sreemathi.v
0
answers
A small industrial concern used three raw materials A,B and C in its manufacturing process.The prices of the materials was as shown below :
isc
class12
modelpaper
2008
sec-b
q11
q11-a
asked
Apr 15, 2013
by
sreemathi.v
0
answers
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