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Recent questions tagged q23
Questions
If a 4 digit number > 5000 are randomly formed from digits 0,1,3,5,7. Find probability of forming a number divisible by 5 when (1) digits are repeated 2) digits are not repeated.
cbse
class12
additionalproblem
kvquestionbank2012
ch13
q23
p42
math
asked
Feb 5, 2013
by
meena.p
0
answers
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
A line makes angles $\alpha,\beta,\gamma\;and\;\delta$ with the four diagonals of a cube. Prove that $ \cos ^2 \alpha+\cos ^2\beta+\cos ^2 \gamma+\cos ^2 \delta=\Large\frac{4}{3}$
cbse
class12
additionalproblem
kvquestionbank2012
ch11
q23
p38
math
asked
Feb 5, 2013
by
meena.p
0
answers
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 matrices, solve the following system of equations: $ 4x+3y+3z=60, x+2y+3z=45 \: and \: 6x+2y+3z=70 $
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Feb 5, 2013
by
thanvigandhi_1
1
answer
The surface area of a balloon being inflated, changes at a rate proportional to time t. If initially its radius is 1 unit and after 3 seconds it is 2 units, find the radius after time 't'.
cbse
class12
additionalproblem
kvquestionbank2012
ch9
q23
p34
sec-a
math
asked
Feb 4, 2013
by
meena.p
1
answer
A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Feb 4, 2013
by
thanvigandhi_1
0
answers
Find the area of the region enclosed between the circles $ x^2+y^2=1\;and\;\bigg(x-\frac{1}{2}\bigg)^2+y^2=1$
cbse
class12
additionalproblem
kvquestionbank2012
ch8
q23
p32
math
asked
Feb 4, 2013
by
meena.p
1
answer
Using matrix method, solve the following system of equations : $\large\frac{2}{x}+\frac{3}{y}+\frac{10}{z}=4,\frac{4}{x}-\frac{6}{y}+\frac{5}{z}=1, \frac{6}{x}+\frac{9}{y}-\frac{20}{z}$$=2; x,y,z \neq 0$
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Feb 4, 2013
by
thanvigandhi_1
0
answers
Using elementary transformations, find the inverse of the matrix $\begin{bmatrix} 1 & 3 & -2 \\ -3 & 0 & -1 \\ 2 & 1 & 0 \end{bmatrix} $
cbse
class12
modelpaper
2012
sec-c
q23
ch3
medium
math
asked
Feb 4, 2013
by
thanvigandhi_1
1
answer
If a,b,c are positive and unequal, show that the following determinant is negative. $ \Delta = \begin{bmatrix} a & b & c \\ b & c & a \\ c & a & b \end{bmatrix} $
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Feb 4, 2013
by
thanvigandhi_1
1
answer
using matrices, solve the following system of equations $ x+2y-3z=-4;2x+3y+2z=2 ; 3x-3y-4z=11 $
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Feb 4, 2013
by
thanvigandhi_1
1
answer
Using matrices, solve the following system, of equations : $ \large\frac{1}{x}-\frac{1}{y}+\frac{1}{z}$$=4: \: \large\frac{2}{x}+\frac{1}{y}-\frac{3}{z}$$=0: \: \large\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$$=2 \qquad x \neq 0, y \neq 0, z \neq 0 $
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Feb 3, 2013
by
thanvigandhi_1
1
answer
Use product \( \begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \end{bmatrix} \) \( \begin{bmatrix} -2 & 0 & 1 \\ 9 & 2 & -3 \\ 6 & 1 & -2 \end{bmatrix} \) to solve the system of equations: $ x-y+2z=1, \: 2y-3z=1, \: 3x-2y+4z=2 $
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Feb 2, 2013
by
thanvigandhi_1
0
answers
If $\Large \int \frac {dx}{(x+1)(x-2)} \normalsize = A\; log(x+1)+B\; log(x-2)+c,then $\[(a)\;A+B=0 \qquad (b)\;AB=- \qquad(c)AB=\frac{1}{9}\qquad(d)\;AB=-9\]
cbse
class12
additionalproblem
kvquestionbank2012
ch7
q23
p25
math
asked
Feb 1, 2013
by
meena.p
0
answers
Let A = N x N and * be a binary operation on A defined by (a,b)*(c,d)=(ac,bd), show that : (i) (A*) is commutative. (ii) (A*) is associative (iii) Find the identity element, if any, in A.
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 31, 2013
by
thanvigandhi_1
1
answer
There are three coins. One is a two headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows head, what is the probability that it was the two headed coin?
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 31, 2013
by
thanvigandhi_1
0
answers
Suppose x has binomial distribution \( B \bigg( 4, \large\frac{1}{3} \bigg)\). Find the most likely outcome.
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 30, 2013
by
thanvigandhi_1
0
answers
Find the matrix P satisfying the matrix equation $ \begin{bmatrix} 1 & 2 \\ 2 & 3 \\ \end{bmatrix} P \begin{bmatrix} 4 & 7 \\ 3 & 5 \\ \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \\ \end{bmatrix}. $
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 30, 2013
by
thanvigandhi_1
0
answers
Solve the following system of equation by matrix method : $ u-2v+w=1, 2u+v+w=1 , u+v-2w=-2 $
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 29, 2013
by
thanvigandhi_1
1
answer
The function $ f(x)=-\Large\frac{x}{2}\normalsize+ \sin x $ is always increasing in \[(a)\;\bigg(-\frac{\pi}{2},\frac{\pi}{2}\bigg)\qquad(b)\;\bigg(0,\frac{\pi}{4}\bigg)\qquad(c)\;\bigg(\frac{\pi}{4},\frac{\pi}{2}\bigg)\qquad(d)\;\bigg(-\frac{\pi}{3},\frac{\pi}{3}\bigg)\qquad\]
cbse
class12
additionalproblem
kvquestionbank2012
ch6
q23
p17
math
asked
Jan 29, 2013
by
meena.p
0
answers
Find the co-ordinates of the foot of the perpendicular drawn from the point A(1,8,4,) to the line joining the points B(0,-1,3) and C(2,-3,-1).
cbse
class12
modelpaper
2005
sec-b
q23
math
asked
Jan 28, 2013
by
fingeazy
0
answers
For the matrix \( A= \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & -3 \\ 2 & -1 & 3 \end{bmatrix} \), show that \( A^3-6A^2+5A+11I=0.\) Hence, find \(A^{-1}.\)
cbse
class12
modelpaper
2012
sec-c
q23
ch4
bookproblem
sec5
q15
p132
math
asked
Jan 27, 2013
by
thanvigandhi_1
0
answers
If \( A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \\ \end{bmatrix} \), prove that $A^n = \begin{bmatrix} 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \\ \end{bmatrix} $, for \( n \in N.\)
cbse
class12
modelpaper
2012
sec-c
q23
ch3
medium
math
asked
Jan 27, 2013
by
thanvigandhi_1
1
answer
The sum of three numbers is -1. If we multiply second number by 2, third number by 3 and add them, we get 5. If we subtract third number from the sum of first and second number, we get -1. Represent the information by the system of equation and find the number using inverse of a matrix.
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 26, 2013
by
thanvigandhi_1
0
answers
Discuss the continuity of the following function at x = 0 $f(x)= \left\{ \begin{array}{1 1} \Large\frac{x^4+x^3+2x^2}{\tan ^{-1}x} & \quad ,\;x\neq0 \\ 10 & \quad ,\;x=0 \end{array} \right. $
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q23
p12
medium
math
sec-b
asked
Jan 25, 2013
by
meena.p
1
answer
A one hour routine check was made by security staff of MNC from \(\large \frac{1}{2} \) hour before office opening time. Total 80 cars are checked and result was 9 cars carrierd no official, 20 cars carried one official, 16 cars carried 2 officials, 20 cars carried 3 officials and 15 cars carried 4 officials. (i) Using this information, write down a row matrix and a column whose product gives us the total number of official carried by the 80 cars. (ii) What was the average number of official per car?
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 25, 2013
by
thanvigandhi_1
0
answers
Let A and B be 3 x 3 matrices such that $ A^T=-A\;and\;B^T=B.$Then the matrix $\lambda(AB+3BA)$ is skew symmetric matrix for $\lambda$.
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q23
p8
math
sec-b
asked
Jan 24, 2013
by
meena.p
0
answers
Using elementary transformations, find the inverse of the matrix : $\begin{bmatrix} 2 & -1 & 4 \\ 4 & 0 & 2 \\ 3 & -2 & 7 \end{bmatrix}$
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 24, 2013
by
thanvigandhi_1
0
answers
Using matrices, solve the following system of linear equations : $ 2x+y+z=2,x+3y-z=5, 3x+y-2z=6$
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 24, 2013
by
thanvigandhi_1
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.
cbse
class12
modelpaper
2005
sec-c
q23
math
asked
Jan 24, 2013
by
fingeazy
1
answer
A and B are partners in a business sharing profits and losses equality. They admit a new partner C and it is agreed that now the profit and losses will be shared amongst A, B and C in the ratio 9 : 8 : 7 respectively. If C paid Rs. 2.10 lakh as premium for the good will, find the shares of A and B in the premium.
cbse
class12
modelpaper
2005
sec-c
q23
math
asked
Jan 24, 2013
by
fingeazy
0
answers
Solve for x:$\tan^{-1}(x+1)+\tan^{-1}x+\tan^{-1}(x-1)=\tan^{-1}3.$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q23
p6
medium
sec-b
math
asked
Jan 24, 2013
by
meena.p
1
answer
A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a number 6. Find the probability that it is actually a number 6.
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 23, 2013
by
thanvigandhi_1
0
answers
Let $f : A \rightarrow B$ be a given function. A relation R in the set A is given by $R = {(a,b) \varepsilon A \times A : f(a) = f(b)}.$ Check, if R is an equivalence relation.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q23
p4
math
sec-b
asked
Jan 23, 2013
by
meena.p
1
answer
Use product $ \begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \end{bmatrix} \begin{bmatrix} -2 & 0 & 1 \\ 9 & 2 & -3 \\ 6 & 1 & -2 \end{bmatrix} $ to solve the system of equations : $ x-y+2z=1; 2y-3z=1; 3x-2y+4z = 2$
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 22, 2013
by
thanvigandhi_1
0
answers
Given that \( A = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 1 & 2 \end{bmatrix}\) and \( B = \begin{bmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 2 -1 & 5 \end{bmatrix}\). Find AB. Hence, using this to solve the following system of linear equations. \( x-y=3;\: 2x+3y+4z=17; \: y+2z=7\)
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 21, 2013
by
thanvigandhi_1
0
answers
Solve the differential equation $(1+y^2)\tan^{-1}xdx+2y(1+x^2)dy=0$
cbse
class12
ch9
sec-b
q23
p194
short-answer
exemplar
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
Find the value of $\lambda$ such that the vectors $\overrightarrow{a}=2\hat i+\lambda\hat j+\hat k$ and $\overrightarrow{b}=\hat i+2\hat j+3\hat k$ are orthogonal
cbse
class12
ch10
q23
p217
exemplar
easy
sec-a
math
asked
Jan 17, 2013
by
sreemathi.v
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
asked
Jan 16, 2013
by
thanvigandhi_1
1
answer
Using elementary transformation, find the inverse of the following matrix \( \begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \end{bmatrix} \)
cbse
class12
modelpaper
2012
sec-c
q23
ch3
medium
math
asked
Jan 16, 2013
by
thanvigandhi_1
1
answer
Draw a rough sketch of the given curve $y=1+|x+1|,x=-3,x=3,y=0$ and find the area of the region bounded by them,using integration.
cbse
class12
ch8
q23
p177
exemplar
sec-b
medium
math
asked
Jan 16, 2013
by
sreemathi.v
1
answer
Using properties of determinants, prove the following : \( \begin{bmatrix} (b+c)^2 & ab & ca \\ ab & (a+c)^2 & bc \\ ac & bc & (a+b)^2 \end{bmatrix} = 2abc (a+b+c)^3.\)
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 16, 2013
by
thanvigandhi_1
0
answers
Evaluate the following : $\begin{align*} \int \frac{\sin^6x+\cos^6x}{\sin^2x \cos^2x}dx \end{align*}$
cbse
class12
ch7
q23
p164
short-answer
exemplar
sec-b
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Let A = R-{3} and B = R-{1}. Consider the function\( f:A \rightarrow B\) defined by \( f(x)=\large\frac{x-2}{x-3}\). Is f one-one and onto? Justify your answer.
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 11, 2013
by
thanvigandhi_1
0
answers
At what point,the slope of the curve $y=-x^3+3x^2+9x-27$ is maximum?Also find the maximum slope.
cbse
class12
ch6
q23
p137
short-answer
exemplar
easy
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Using matrix solve the following system of linear equations : $ x+y+z=4;2x-y+z=-1;2x+y-3z = -9$
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 10, 2013
by
thanvigandhi_1
0
answers
If \( A = \begin{bmatrix} 3 & 1 \\ 7 & 5 \end{bmatrix} \), find x and y that \( A^2+x1 = yA.\) Hence find \( A^{-1} \).
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 10, 2013
by
thanvigandhi_1
0
answers
If $A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{bmatrix}.$Prove that \( A^2-4A-51=0\). Hence find \( A^{-1} \)
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
Using matrix method solve the following system of linear equations : $ x+y-z=1; 3x+y-2z=3 ;x-y-z = -1$
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
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