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Recent questions tagged difficult
Questions
Examine the consistency of the following system of equation. If it is consistent than solve the same. $4x+3y+6z=25\;,x+5y+7z=13\;,2x+9y+z=1 $
tnstate
class12
bookproblem
ch1
sec-1
exercise1-5
p45
q1
q1-1
sec-c
difficult
asked
Mar 30, 2013
by
poojasapani_1
1
answer
Solve the following non-homogeneous system of linear equation by determinant method: $\large \frac{1}{x}+\frac{2}{y}-\frac{1}{z}=1\;;\frac{2}{x}+\frac{4}{y}+\frac{1}{z}=5\;;\frac{3}{x}-\frac{2}{y}-\frac{2}{z}=0$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-4
p36
q9
jun-2008
sec-c
difficult
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Solve the following non-homogeneous system of linear equation by determinant method : $x+2y+z=6\;,3x+3y-z=3\;,2x+y-2z=-3 $
tnstate
class12
bookproblem
ch1
sec-1
exercise1-4
p35
q7
sec-c
difficult
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Solve by matrix inversion method following system of linear equation$\;x-3y-8z+10=0\;,3x+y=4\;,2x+5y+6z=13$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-2
p13
q5
sec-c
difficult
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Solve by matrix inversion method following system of linear equation $2x-y+z=7\;,3x+y-5z=13\;,x+y+z=5$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-2
p13
q4
sec-c
difficult
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Solve by matrix inversion method following system of linear equation $\;x+y+z=9\;,\;2x+5y+7z=52\;,2x+y-z=0$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-2
p13
q3
sec-c
difficult
asked
Mar 29, 2013
by
poojasapani_1
1
answer
Find the inverse of following matrix :$\begin{bmatrix} 1 & 0 & 3 \\2 & 1 & -1 \\1 & -1 & 1 \end{bmatrix}$
tnstate
class12
bookproblem
ch1
sec-1
exercise1-1
p9
q4
q4-1
mar-2007
modelpaper
sec-b
difficult
asked
Mar 28, 2013
by
poojasapani_1
1
answer
If the coordinates of the vertices of an equilateral triangle with sides of length 'a' are $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ then \[{\begin{vmatrix}x_1 & y_1 &1\\x_2 & y_2 &1\\x_3 & y_3 & 1\end{vmatrix}}^2=\frac{3a^4}{4}.\]
cbse
class12
ch4
sec-b
q11
p78
short-answer
exemplar
difficult
math
asked
Mar 15, 2013
by
sreemathi.v
1
answer
\[ \text{For the matrix A = } \begin{bmatrix} 2&-1&1 \\ -1& 2&- 1 \\ 1 &-1& 2 \end{bmatrix} \] \[ \text{Show that } A^{3} - 6A^{2} + 9A - 4I = O. \text{ Hence, find } A^{-1}\]
cbse
class12
bookproblem
ch4
sec5
q16
p132
difficult
sec-c
math
asked
Feb 26, 2013
by
sreemathi.v
1
answer
Differentiate each of the following w.r.t $x$: $tan^{-1}\large\frac{3a^2x-x^3}{a^3-3ax^2}$, $\frac{1}{\sqrt 3}< \frac{x}{a} <\frac{-1}{\sqrt 3}$
cbse
class12
ch5
q42
p110
short-answer
exemplar
sec-a
difficult
math
asked
Feb 19, 2013
by
sreemathi.v
1
answer
Show that $2tan^{-1}(-3)=\frac{-\pi}{2}+tan^{-1}\bigg(\frac{-4}{3}\bigg)$
cbse
class12
ch2
q6
p35
exemplar
difficult
sec-b
math
asked
Feb 19, 2013
by
sreemathi.v
1
answer
Find the volume of the largest cylinder that can be inscribed in a sphere of radius r.
cbse
class12
modelpaper
2012
sec-c
q23
difficult
math
asked
Feb 15, 2013
by
thanvigandhi_1
1
answer
If $ f(x)=\sqrt{\large\frac{\sec x-1}{\sec x+1}}$$\: find\: f'(x). $ Also find $( f' \bigg( \large\frac{\pi}{2}\bigg).)$
cbse
class12
modelpaper
2012
sec-b
q15
difficult
math
asked
Feb 15, 2013
by
thanvigandhi_1
1
answer
Show that $ \int_0^{\large\frac{\pi}{2}} \sqrt{\tan\: x}+\sqrt{\cot x}=\sqrt {2\pi} $
cbse
class12
modelpaper
2012
sec-b
q16
difficult
math
asked
Feb 15, 2013
by
thanvigandhi_1
1
answer
Evaluate : $ \int \large\frac{8\: dx}{(x+2)(x^2+4)}$
cbse
class12
modelpaper
2012
sec-b
q19
difficult
math
asked
Feb 15, 2013
by
thanvigandhi_1
1
answer
A and B throw a pair of die turn by turn. The first to throw 9 is awarded a prize. If A starts the game, What is the probability of A getting the prize?
cbse
class12
modelpaper
2012
sec-b
q22
difficult
jeemain
probability
math
asked
Feb 11, 2013
by
thanvigandhi_1
1
answer
Find the maximum area of the isosceles triangle inscribed in the ellipse $ \large\frac{x^2}{a^2}+\frac{y^2}{b^2}$$=1$ with its vertex at one end of major axis.
class12
modelpaper
2012
sec-c
q23
difficult
asked
Feb 11, 2013
by
thanvigandhi_1
1
answer
Find the length of the perpendicular and the co-ordinates of the foot of the perpendicular from the point (2,-1,5) to the line \( \large\frac{x-11}{10}=\frac{y+2}{-4}=\frac{z+8}{-11} \).
cbse
class12
modelpaper
2012
sec-c
q27
difficult
math
asked
Feb 11, 2013
by
thanvigandhi_1
1
answer
An aerolpane can carry a maximum of 200 passengers. A profit of Rs. 400 is made on each first class ticket and a profit of Rs. 300 is made on each second class ticket. The airline reserves atleast 20 seats for the first class. However, at least 4 times as many passengers prefer to travel by second class, than by the first class. Determine how many tickets of each type must be sold, inorder to maximise the profit for the airline. What is the maximum profit? Make an L.P.P. and solve it graphically.
cbse
class12
modelpaper
2012
sec-c
q28
difficult
math
asked
Feb 11, 2013
by
thanvigandhi_1
1
answer
Solve the following differential equation : \(\large \frac{dy}{dx}=\frac{x(2y-x)}{x(2y+x)},\) if y = 1 when x = 1.
cbse
class12
modelpaper
2012
sec-b
q18
difficult
math
asked
Feb 11, 2013
by
thanvigandhi_1
1
answer
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of number of successes.
cbse
class12
modelpaper
2012
sec-b
q22
difficult
math
asked
Feb 11, 2013
by
thanvigandhi_1
1
answer
A dealer wishes to purchase a number of fans and sewing machines. He has only Rs. 5760 to invest and has space for at most 20 items. A fan costs Rs. 360 and a sewing machine cost Rs. 240. He can sell a fan at a profit of Rs. 18. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximise the profit? Translate the problem as an LPP and solve it graphically.
cbse
class12
modelpaper
2012
sec-c
q28
difficult
math
asked
Feb 10, 2013
by
thanvigandhi_1
1
answer
Prove that $\bigg( tan \bigg( \frac{\pi}{4}+\frac{1}{2} cos^{-1}\frac{a}{b} \bigg)+tan \bigg(\frac{\pi}{4}-\frac{1}{2} cos^{-1}\frac{a}{b} \bigg) = \frac{2b}{a} \bigg)$
cbse
class12
modelpaper
ch2
2012
sec-b
q11
difficult
math
asked
Feb 9, 2013
by
thanvigandhi_1
1
answer
Differentiate \( \tan^{-1} \{ \large\frac{\sqrt{1+x^2}-1}{x} \}\) w.r.t. \( x\).
cbse
class12
modelpaper
2012
sec-b
q15
difficult
math
asked
Feb 9, 2013
by
thanvigandhi_1
1
answer
Evaluate : $ \int_{\Large\frac{\pi}{6}}^{\Large\frac{\pi}{3}}\large\frac{\sin\: x + \cos \: x}{\sqrt{\sin\: 2x}}$$ dx$
cbse
class12
modelpaper
2012
sec-b
q18
difficult
math
asked
Feb 9, 2013
by
thanvigandhi_1
1
answer
A small firm manufactures items A and B. The total number of items that it can manufacture in a day is at the most 24 items. A takes one hour to make while item B takes only half an hour. The maximum time available per dat is 16 hours. If the profit on one unit of item A be Rs. 300 and that of one unit of item B be Rs. 160, how many of each type of item should be produced to maximize the profit? Solve the problem graphically.
cbse
class12
modelpaper
2012
sec-c
q23
difficult
math
asked
Feb 9, 2013
by
thanvigandhi_1
1
answer
Prove that the area of the right-angled triangle of given hypotenuse is maximum when the triangle is isosceles.
cbse
class12
modelpaper
2012
sec-c
q26
difficult
math
asked
Feb 9, 2013
by
thanvigandhi_1
1
answer
Evaluate : $ \int \large\frac{2x+5}{\sqrt{7-6x-x^2}}$$dx$
cbse
class12
modelpaper
2012
sec-b
q17
difficult
math
asked
Feb 9, 2013
by
thanvigandhi_1
1
answer
Evaluate : \( \int_1^3 (2x^2+3)dx\) as the limit of sums.
cbse
class12
modelpaper
2012
sec-c
q25
difficult
math
asked
Feb 8, 2013
by
thanvigandhi_1
1
answer
Evaluate : $\begin{align*} \int \frac{tan \: x+tan^3x}{1+tan^3x} \end{align*}$
cbse
class12
modelpaper
2012
sec-c
q25
difficult
math
asked
Feb 8, 2013
by
thanvigandhi_1
1
answer
A manufacturer produces two types of steel trunks. He has two machines A and B. The first type of trunk requires 5 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 24 hours and 15 hours per day, respecively. He earns a profit of Rs. 30 and RS. 25 per trunk on the first type and second type, respecively. How many trunk of each type must be made each day to make the maximum profit?
cbse
class12
modelpaper
2012
sec-c
q27
difficult
math
asked
Feb 8, 2013
by
thanvigandhi_1
1
answer
Find the area of the region $ {(x,y):x^2+y^2 \leq 1 \leq x + y}.$
cbse
class12
modelpaper
2012
sec-c
q29
difficult
math
asked
Feb 8, 2013
by
thanvigandhi_1
1
answer
Find the area of a minor segment of the circle \( x^2+y^2=a^2\) cut off by the line \( x=\large \frac{a}{2}.\)
cbse
class12
modelpaper
2012
sec-c
q25
difficult
math
asked
Feb 7, 2013
by
thanvigandhi_1
1
answer
A manufacturing company makes two types of television sets, one is black and white and other is coloured. The company has resources to make at most 300 sets a weak. It takes Rs. 1800 to make a black and white set and Rs. 2700 to make a coloured set. The company can spend not more than Rs. 648000 a weak to make television sets. It makes a profit of Rs. 510 per black and white set and Rs. 675 per coloured set, how many sets of each type should be produced so that the company has maximum profit? Formulate this as LPP given that the objective is to maximise the profit.
cbse
class12
modelpaper
2012
sec-c
q28
difficult
math
asked
Feb 7, 2013
by
thanvigandhi_1
1
answer
20% of the bulbs produced by a machine are defective. Find the probability distribution of the number of defective bulbs in a sample of 4 bulbs chosen at random.
cbse
class12
modelpaper
2012
sec-c
q29
difficult
math
asked
Feb 7, 2013
by
thanvigandhi_1
1
answer
Differentiate the following function w.r.t.\( x\) $(x)^{\Large\cos x}+(\sin x)^{\Large\tan \: x} $
cbse
class12
modelpaper
2012
sec-b
q14
difficult
math
asked
Feb 6, 2013
by
thanvigandhi_1
1
answer
A given quantity of metal is to be cast into a solid half cicular cylinder (i.e., with rectangular base and semicircular ends). Show that in order that the total surface area may be minimum, the ratio of the length of the cylinder to the diameter of its circular ends is \( \pi : ( \pi + 2). \)
cbse
class12
modelpaper
2012
sec-c
q24
difficult
math
asked
Feb 6, 2013
by
thanvigandhi_1
1
answer
Find all the local maximum values and local minimum values of the function \( f(x)=\sin 2x-x, -\large\frac{\pi}{2} < x < \large\frac{\pi}{2} \)
cbse
class12
modelpaper
2012
sec-c
q24
difficult
math
asked
Feb 6, 2013
by
thanvigandhi_1
1
answer
Evaluate : $ \int \large\frac{x^4dx}{(x-1)(x^2+1)} $
cbse
class12
modelpaper
2012
sec-c
q27
difficult
math
asked
Feb 6, 2013
by
thanvigandhi_1
1
answer
Prove the following : $\large\frac{9\pi}{8}-\frac{9}{4}sin^{-1}\bigg(\large\frac{1}{3} \bigg) = \frac{9}{4}sin^{-1}\bigg(\large \frac{2\sqrt 2}{3} \bigg) $
cbse
class12
modelpaper
ch2
2012
sec-b
q12
difficult
math
asked
Feb 6, 2013
by
thanvigandhi_1
1
answer
Prove that : $\large \frac{d}{dx} \bigg[ \frac{x}{2} \sqrt{a^2-x^2} + \frac{a^2}{2} \sin^{-1}\bigg( \frac{x}{a} \bigg) \bigg] = \sqrt{a^2-x^2} $
cbse
class12
modelpaper
2012
sec-b
q16
difficult
math
asked
Feb 6, 2013
by
thanvigandhi_1
1
answer
Evaluate : $\int e^{2x}\sin\: x\: dx$
cbse
class12
modelpaper
2012
sec-b
q17
difficult
math
asked
Feb 6, 2013
by
thanvigandhi_1
1
answer
Evaluate : $ \int \large\frac{3x+5}{\sqrt{x^2-8x+7}}$$dx $
cbse
class12
modelpaper
2012
sec-b
q17
difficult
math
asked
Feb 6, 2013
by
thanvigandhi_1
1
answer
Using matrices, solve the following system of equations : $x+2y-3z=-4, 2x+3y+2z=2 \: and \: 3x-3y-4z=11 $
cbse
class12
modelpaper
2012
sec-c
q23
difficult
math
asked
Feb 5, 2013
by
thanvigandhi_1
1
answer
If a, b & c are the lengths of the sides of a triangle, using vector method, show that its area is $\sqrt {s(s-a)(s-b)(s-c)}$ where $2s=a+b+c$
cbse
class12
kvquestionbank2012
ch10
q27
p36
difficult
sec-c
math
asked
Feb 5, 2013
by
meena.p
1
answer
Using vector method, show that the diagonals of a Rhombus bisect each other at right angles.
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q23
p36
difficult
sec-b
math
asked
Feb 5, 2013
by
meena.p
1
answer
Using vector method, prove that if two medians of a triangle are equal, then it is an isosceles.
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q22
p36
difficult
sec-b
math
asked
Feb 5, 2013
by
meena.p
1
answer
Using vector method, prove that if the diagonals of a parallelogram are equal in length, then it is a rectangle.
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q21
p36
difficult
sec-b
math
asked
Feb 5, 2013
by
meena.p
1
answer
Prove that the perpendicular bisectors of a triangle are concurrent.
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q20
p36
difficult
sec-b
math
asked
Feb 5, 2013
by
meena.p
1
answer
Prove that the altitudes of a triangle are concurrent.
cbse
class12
additionalproblem
kvquestionbank2012
ch10
q19
p36
difficult
sec-b
math
asked
Feb 5, 2013
by
meena.p
1
answer
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