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Recent questions tagged sec5
Questions
Show that the differential equation is homogeneous and solve\[y'=\frac{x+y}{x}\]
cbse
class12
bookproblem
ch9
sec5
q2
p406
easy
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Show that the differential equation is homogeneous and solve\[(x-y)\;dy-(x+y)\;dx=0\]
cbse
class12
bookproblem
ch9
sec5
q3
p406
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Show that the differential equation is homogeneous and solve $(x^2-y^2)dx+2xy\;dy=0$
cbse
class12
bookproblem
ch9
sec5
q4
p406
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Show that the differential equation is homogeneous and solve $x^2\large\frac{dy}{dx}$$=x^2-2y^2+xy$
cbse
class12
bookproblem
ch9
sec5
q5
p406
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Show that the differential equation is homogeneous and solve $x\;dy-y\;dx=\sqrt{x^2+y^2}dx$
cbse
class12
bookproblem
ch9
sec5
q6
p406
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Show that the differential equation is homogeneous and solve $\left\{x\cos\bigg(\large\frac{y}{x}\bigg)\normalsize+y\sin\bigg(\large\frac{y}{x}\bigg)\right\}ydx=\left\{y\sin\bigg(\large\frac{y}{x}\bigg)-\normalsize x\cos\bigg(\large\frac{y}{x}\bigg)\right\}\normalsize xdy$
cbse
class12
bookproblem
ch9
sec5
q7
p406
difficult
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Show that the differential equation is homogeneous and solve $x\large\frac{dy}{dx}$$-y+x\sin\bigg(\large\frac{y}{x}\bigg)=$$0$
cbse
class12
bookproblem
ch9
sec5
q8
p406
medium
math
sec-b
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Show that the differential equation is homogeneous and solve $y\: dx+x\log\bigg(\large\frac{y}{x}\bigg)$$dy-2x\;dy=0$
cbse
class12
bookproblem
ch9
sec5
q9
p406
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the particular solution satisfying the given condition $(x+y)dy+(x-y)dx=0;\;y=1;\;when\;x=\;1$
cbse
class12
bookproblem
ch9
sec5
q11
p406
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the particular solution satisfying the given condition $x^2dy+(xy+y^2)\;dx=0;y=\;1;\;when\;x=\;1$
cbse
class12
bookproblem
ch9
sec5
q12
p406
difficult
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the particular solution satisfying the given condition $\large\frac{dy}{dx}-\large\frac{y}{x}$$+cosec\bigg(\large\frac{y}{x}\bigg)$$=0;\;y=\;0\;when\;x=\;1$
cbse
class12
bookproblem
ch9
sec5
q14
p406
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the particular solution satisfying the given condition $2xy+y^2-2x^2\large\frac{dy}{dx}$$=0;\;y=\;2\;when\;x=\;1$
cbse
class12
bookproblem
ch9
sec5
q15
p406
medium
modelpaper
2012
q19
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
A homogeneous differential equation of the form $\frac{\large dx}{\large dy}=h\bigg(\frac{\large x}{\large y}\bigg)$ can be solved by making the substitution
cbse
class12
bookproblem
ch9
sec5
q16
p406
easy
sec-a
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Which of the following is a homogeneous differential equation?
cbse
class12
bookproblem
ch9
sec5
q17
p407
sec-a
easy
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
If A is an invertible matrix of order 2, then det$(A^{-1})\;$ is equal to: $ (A)\; det\;(A) \quad (B)\; \frac{1}{det\;(A)} \quad (C)\; 1 \quad (D)\; 0 $
cbse
class12
bookproblem
ch4
sec5
q18
p132
easy
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Let $A$ be a nonsingular square matrix of order $3 \times 3.$ Then $| adj \;A| $ is equal to:
cbse
class12
bookproblem
ch4
sec5
q17
p132
easy
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
\[ \text{For the matrix A = } \begin{bmatrix} 1&1&1 \\ 1& 2&- 3 \\ 2 &-1& 3 \end{bmatrix} \] \[ \text{Show that } A^{3} - 6A^{2} + 5A + 11I = O. \text{ Hence, find } A^{-1}\]
cbse
class12
bookproblem
ch4
sec5
q15
p132
difficult
sec-c
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
\[ \text{For the matrix A = } \begin{bmatrix} 3 & 2 \\ 1 & 1 \end{bmatrix}, \text{ find the numbers a and b such that } A^{2} + aA + bI = O \]
cbse
class12
bookproblem
ch4
sec5
q14
p132
medium
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
\[ \text{If A = } \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}, \text{show that } A^{2} -5A +7I = 0. \text{ Hence find } A^{-1}\]
cbse
class12
bookproblem
ch4
sec5
q13
p132
medium
sec-c
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
\[ \text{Let A = } \begin{bmatrix} 3 & 7 \\ 2 & 5 \end{bmatrix} \text{and B = } \begin{bmatrix} 6 & 8 \\ 7 & 9 \end{bmatrix}. \text{Verify that } (AB^{-1}) = B^{-1}A^{-1}\]
cbse
class12
bookproblem
ch4
sec5
q12
p132
medium
sec-c
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Find the inverse of the matrix (if it exists): \[ \begin{bmatrix} 1&0&0 \\ 0&cos\alpha&sin\alpha \\ 0&sin\alpha&-cos\alpha \\ \end{bmatrix} \]
cbse
class12
bookproblem
ch4
sec5
q11
p132
easy
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Find the inverse of the matrix (if it exists): $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \\ \end{bmatrix} $
cbse
class12
bookproblem
ch4
sec5
q10
p132
medium
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Find the inverse of the matrix (if it exists): $ \begin{bmatrix} 2 & 1& 3 \\ 4 &- 1 & 0 \\ -7 & 2 & 1 \\ \end{bmatrix} $
cbse
class12
bookproblem
ch4
sec5
q9
p132
medium
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Find the inverse of the matrix (if it exists): $\begin{bmatrix} 1 & 0 & 0 \\ 3 & 3 & 0 \\ 5 & 2 & -1 \\ \end{bmatrix}$
cbse
class12
bookproblem
ch4
sec5
q8
p132
medium
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Find the inverse of the matrix (if it exists): $ \begin{bmatrix} 1&2&3 \\ 0&2&4 \\ 0&0&5 \\ \end{bmatrix} $
cbse
class12
bookproblem
ch4
sec5
q7
p132
medium
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Find the inverse of the matrix (if it exists): $ \begin{bmatrix} -1&5 \\ -3&2 \\ \end{bmatrix} $
cbse
class12
bookproblem
ch4
sec5
q6
p132
easy
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Find the inverse of the matrix (if it exists): $ \begin{bmatrix} 2&-2 \\ 4&3 \\ \end{bmatrix} $
cbse
class12
bookproblem
ch4
sec5
q5
p132
easy
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Verify A (adj A)= (adj A) A = | A | I: \[ \begin{bmatrix} 1&-1&2 \\ 3&0&-2 \\ 1&0&3 \\ \end{bmatrix} \]
cbse
class12
bookproblem
ch4
sec5
q4
p131
medium
sec-c
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Verify A (adj A)= (adj A) A = | A | I: \[ \begin{bmatrix} 2&3 \\ - 4&-6 \\ \end{bmatrix} \]
cbse
class12
bookproblem
ch4
sec5
q3
p131
medium
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Find the adjoint of the matrix: $\begin{bmatrix} 1&-1&2 \\ 2&3&5 \\ -2&0&1 \end{bmatrix} $
cbse
class12
bookproblem
ch4
sec5
q2
p131
medium
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Find the adjoint of the matrix: $\begin{bmatrix} 1&2 \\ 3&4 \end{bmatrix} $
cbse
class12
bookproblem
ch4
sec5
q1
p131
easy
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
The maximum value of $ [ x(x-1) +1]^{\frac{1}{3}}, 0 \leq \: x \leq$ is
cbse
class12
bookproblem
ch6
sec5
q29
p234
sec-a
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
For all real values of \(x\), the minimum value of \( \large\frac{1-x+x^2}{1+x+x^2}\) is
cbse
class12
bookproblem
ch6
sec5
q28
p234
sec-b
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in the point on the curve \( x^2 = 2y\) which is nearest to the point \((0, 5)\) is
cbse
class12
bookproblem
ch6
sec5
q27
p234
sec-b
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
The probability that a student is not a swimmer is 1 / 5. Then the probability that out of five students, four are swimmers is?
cbse
class12
bookproblem
ch13
sec5
p578
q15
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
In a box containing 100 bulbs, 10 are defective. What is the probability that out of a sample of 5 bulbs, none is defective?
cbse
class12
bookproblem
ch13
sec5
p578
q14
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective?
cbse
class12
bookproblem
ch13
sec5
p578
q13
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Find the probability of throwing at most 2 sixes in 6 throws of a single die.
cbse
class12
bookproblem
ch13
sec5
p578
q12
sec-b
medium
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Find the probability of getting 5 exactly twice in 7 throws of a die.
cbse
class12
bookproblem
ch13
sec5
p578
q11
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is $ \frac{1}{100}$. What is the probability that he will win a prize (a) at least once (b) exactly once (c) at least twice?
cbse
class12
bookproblem
ch13
sec5
p577
q10
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing ?
cbse
class12
bookproblem
ch13
sec5
p577
q9
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Suppose X has a binomial distribution \(B\: ( 6, \frac{1}{2})\) . Show that X = 3 is the most likely outcome. Hint : P(X = 3) is the maximum among all \(P(x_i),\: x_i = 0,1,2,3,4,5,6\)
cbse
class12
bookproblem
ch13
sec5
p577
q8
sec-b
medium
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
In an examination, 20 questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers TRUE; if it falls tails, he answers FALSE. Find the probability that he answers at least 12 questions correctly.
cbse
class12
bookproblem
ch13
sec5
p577
q7
sec-a
difficult
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?
cbse
class12
bookproblem
ch13
sec5
p577
q6
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs \[ \text{ (i) none (ii) not more than one (iii) more than one (iv) at least one} \] will fuse after 150 days of use.
cbse
class12
bookproblem
ch13
sec5
p577
q5
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that (i) all the five cards are spades? (ii) only 3 cards are spades? (iii) none is a spade?
cbse
class12
bookproblem
ch13
sec5
p577
q4
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?
cbse
class12
bookproblem
ch13
sec5
p577
q3
sec-b
medium
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.
cbse
class12
bookproblem
ch13
sec5
p577
q2
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A die is thrown 6 times. If getting an odd number is a success, what is the probability?
cbse
class12
bookproblem
ch13
sec5
p576
q1
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Show that semi-vertical angle of right circular cone of given surface area and maximum volume is \( \sin^{-1} \left(\frac{1}{3}\right)\)
cbse
class12
bookproblem
ch6
sec5
q26
p233
sec-c
medium
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
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