Graphs of two function f(x)=sin x and (g)x=cos x is given below: Based on the above information, answer the following questions. 1. In (0, ), the curves f(x)=sin x and g (x)=cos x at x= 1. 2 2. 3 3. 4 4. 2. Value of _ 0 ^ 4 sin x dx is. 1. 1-1 2 2. 1+1 2 3. 2-1 2 4. 2+1 2 3. Value of _ 4 ^ 2 cos x dx is. 1. 1+1 2 2. 1-1 2 3. 2-2 4. 2+2 4. Value of _ 0 ^ sin x dx is. 1. 0 2. 1 3. 2 4. -2 5. Value of _ 0 ^ 2 sin x dx is. 1. 0 2. 1 3. 3 4. 4

1. (c) 4 Solution: for point of intersection, we have sin x=cos x sin x cos x =1 x=1 = 4 2. (a) 1-1 2 Solution: _ 0 ^ 4 sin x dx= [-cos x ]^ 4 _0=-cos 4 +cos0 =1-1 2 3. (b) 1-1 2 Solution: _ 2 ^ 4 cos x dx= [sin x ]^ 2 _ 4 =sin 2 -sin 4 =1-1 2 4. (c) 2 Solution: _ 0 ^ sin x dx= [-cos x ]^ _0= [-cos +cos0 ]=2 5. (b) 1 Solution: _ 0 ^ 2 sin x dx= [-cos x ]^ 2 _0= [-cos 2 +cos0 ] =0+1+1

Graphs of two function f(x)=sin x and (g)x=cos x is given below: …

The upward speed v(I) of a rocket at time I is approximated by $\text{v}(\text{t})=\text{at}^2+\text{bt}+\text{c},0\leq\text{t}\leq100,$ here $a, b$ and $c$ are constants. It has been found that the speed at times $t = 3, t = 6$ and $t = 9$ seconds are respectively $64, 133$ and $208$ miles per second..

If $\begin{bmatrix}9&3&1\\36&6&1\\81&9&1\end{bmatrix}^{-1}=\frac{1}{18}\begin{bmatrix}1&-2&1\\-15&24&-9\\54&-54&18\end{bmatrix},$ then answer the following questions.

The value of $b + c$ is:

$20$
$21$
$\frac{3}{4}$
$\frac{4}{3}$

The value of $a + c$ is:

$1$
$20$
$\frac{4}{3}$
None of these.

v(t) is given by:

$\text{t}^2+20\text{t}+1$
$\frac{1}{3}\text{t}^2+20\text{t}+1$
$\text{t}^2+\frac{1}{3}\text{t}+20$
$\text{t}^2+\text{t}+1$

The speed at time $1 = 15$ seconds is:

$346$ miles/ sec
$356$ miles/ sec
$366$ miles/ sec
$376$ miles/ sec

The time at which the speed of rocket is $784$ miles/ sec is:

$20$ seconds
$30$ seconds
$25$ seconds
$27$ seconds

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In a society there is a garden in the shape of rectangle inscribed in a circle of radius 10m as shown in given figure.

Based on the above information, answer the following questions.

If $2x$ and $2y$ denotes the length and breadth in metres, of the rectangular part, then the relation between the variables is.

$x^2 - y^2 = 10$
$x^2 + y^2 = 10$
$x^2 + y^2 = 100$
$x^2 - y^2 = 100$

The area $(A)$ of green grass, in terms of $x,$ is given by.

$2\text{x}\sqrt{100-\text{x}^2}$
$4\text{x}\sqrt{100-\text{x}^2}$
$2\text{x}\sqrt{100+\text{x}^2}$
$4\text{x}\sqrt{100+\text{x}^2}$

The maximum value of $A$ is.

$100\text{m}^2$
$200\text{m}^2$
$400\text{m}^2$
$1600\text{m}^2$

The value of length of rectangle, when $A$ is maximum, is.

$10\sqrt{2}\text{m}$
$20\sqrt{2}\text{m}$
$20\text{m}$
$5\sqrt{2}\text{m}$

The area of gravelling path is.

$100(\pi+2)\text{m}^2$
$100(\pi-2)\text{m}^2$
$200(\pi+2)\text{m}^2$
$200(\pi-2)\text{m}^2$

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A spherical ball of salt is dissolving in water in such a manner that the rate of decrease of the volume at any instant is propotional to the surface. Prove that the radius is decreasing at a constant rate.

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Three friends A, Band Care playing a dice game. The numbers rolled up by them in their first three chances were noted and given by A= {1, 5}, B = {2, 4, 5} and C = {1, 2, 5} as A reaches the cell 'SKIP YOUR NEXT TURN' in second throw.

Based on the above information, answer the following questions.

P(A | B) =

$\frac{1}{6}$
$\frac{1}{3}$
$\frac{1}{2}$
$\frac{2}{3}$

P(B | C) =

$\frac{2}{3}$
$\frac{1}{12}$
$\frac{1}{9}$
$0$

$\text{P}(\text{A}\cap\text{B}|\text{C})=$

$\frac{1}{6}$
$\frac{1}{2}$
$\frac{1}{12}$
$\frac{1}{3}$

P(A | C)

$\frac{1}{4}$
$1$
$\frac{2}{3}$
None of these.

$\text{P}(\text{A}\cup\text{B}|\text{C})=$

0
$\frac{1}{2}$
$\frac{2}{3}$
1

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Read the following text carefully and answer the questions that follow:
A building contractor undertakes a job to construct 4 flats on a plot along with parking area. Due to strike the probability of many construction workers not being present for the job is 0.65 . The probability that many are not present and still the work gets completed on time is 0.35 . The probability that work will be completed on time when all workers are present is 0.80 .
Let: $E _1$ : represent the event when many workers were not present for the job;
$E _2$ : represent the event when all workers were present; and
E: represent completing the construction work on time.
i. What is the probability that all the workers are present for the job? (1)
ii. What is the probability that construction will be completed on time? (1)
iii. What is the probability that many workers are not present given that the construction work is completed on time? (2)
OR
What is the probability that all workers were present given that the construction job was completed on time?(2)

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A plane started from airport situated at O with a velocity of 120m/s towards east. Air is blowing at a velocity of 50m/ s towards the north as shown in the figure.
The plane travelled 1hr in OP direction with the resultant velocity. From P to R the plane travelled 1hr keeping velocity of 120m/s and finally landed at R.

Based on the above information, answer the following questions.

What is the resultant velocity from O to P?

100m/ s
130m/ s
126m/ s
180m/ s

What is the direction of travel of plane from O to P with East?

$\tan^{-1}\Big(\frac{5}{12}\Big)$
$\tan^{-1}\Big(\frac{12}{3}\Big)$
50
80

What is the displacement from O to P?

600km
468km
532km
500km

What is the resultant velocity from P to R?

120m/ s
70m/ s
170m/ s
200m/ s

What is the displacement from P to R?

450km
532km
610km
612km

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The nut and bolt manufacturing business has gained popularity due to the rapid Industrialization and introduction of the Capital-Intensive Techniques in the Industries that are used as the Industrial fasteners to connect various machines and structures. Mr. Suresh is in Manufacturing business of Nuts and bolts. He produces three types of bolts, $\mathrm{x}, \mathrm{y}$, and $\mathrm{z}$ which he sells in two markets. Annual sales (in ₹) indicated below:

(i) If unit sales prices of $x, y$ and $z$ are $₹ 2.50$, ₹ 1.50 and $₹ 1.00$ respectively, then find the total revenue collected from Market-I \&II.

(ii) If the unit costs of the above three commodities are ₹2.00, ₹ 1.00 and 50 paise respectively, then find the cost price in Market I and Market II.

(iii) If the unit costs of the above three commodities are ₹2.00, ₹1.00 and 50 paise respectively, then find gross profit from both the markets.

OR

If matrix $\mathrm{A}=\left[a_{i j}\right]_{2 \times 2}$ where $\mathrm{a}_{\mathrm{ij}}=1$, if $\mathrm{i} \neq \mathrm{j}$ and $\mathrm{a}_{\mathrm{ij}}=0$, if $\mathrm{i}=\mathrm{j}$ then find $\mathrm{A}^2$.

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If the equation is of the form $\frac{\text{dy}}{\text{dx}}=\text{py}=\text{Q},$ where P, Q are functions of x, then the solution of the differential equation is given by $\text{ye}^{\int\text{pdx}}=\int\text{Q e}^{\int\text{pdx}}\text{dx}+\text{c},$ where $\text{e}^{\int\text{pdx}}$ is called the integrating factor (I.F.).
Based on the above information, answer the following questions.

The integrating factor of the differential equation $\sin\text{x}\frac{\text{dy}}{\text{dx}}+2\text{y}\cos\text{x}=1$ is $(\sin\text{x})^\lambda,$ where $\lambda=$

0
1
2
3

Integrating factor of the differential equation $(1-\text{x}^2)\frac{\text{dy}}{\text{dx}}-\text{xy}=1$ is:

$-\text{x}$
$\frac{\text{x}}{1+\text{x}^2}$
$\sqrt{1-\text{x}^2}$
$\frac{1}{2}\log(1-\text{x}^2)$

The solution of $\frac{\text{dy}}{\text{dx}}+\text{y}=\text{e}^{-\text{x}},\text{ y}(0)=0,$ is:

$\text{y}=\text{e}^\text{x}(\text{x}-1)$
$\text{y}=\text{xe}^{-\text{x}}$
$\text{y}=\text{xe}^{-\text{x}}+1$
$\text{y}=(\text{x}+1)\text{e}^{-\text{x}}$

General solution of $\frac{\text{dy}}{\text{dx}}+\text{y}\tan\text{x}=\sec\text{x}$ is:

$\text{y}\sec\text{y}=\tan\text{x}+\text{c}$
$\text{y}\tan\text{x}=\sec\text{x}+\text{c}$
$\tan\text{x}=\text{y}\tan\text{x}+\text{c}$
$\text{x}\sec\text{x}=\tan\text{y}+\text{c}$

The integrating factor of differential equation $\frac{\text{dy}}{\text{dx}}-3\text{y}=\sin2\text{x}$ is:

$\text{e}^{3\text{x}}$
$\text{e}^{-2\text{x}}$
$\text{e}^{-3\text{x}}$
$\text{xe}^{-3\text{x}}$

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In a classroom, teacher explains the properties of a particular curve by saying that this particular curve has beautiful up and downs. It starts at 1 and heads down until $\pi$ radian, and then heads up again and closely related to sine function and both follow each other, exactly $\frac{\pi}{2}$ radians apart as shown in figure.

Based on the above information, answer the following questions.

Name the curve, about which teacher explained in the classroom.

Cosine
Sine
Tangent
Cotangent

Area of curve explained in the passage from 0 to $\frac{\pi}{2}$ is.

$\frac{1}{3}\text{ sq.unit}$
$\frac{1}{2}\text{ sq.unit}$
${1}\text{ sq.unit}$
${2}\text{ sq.units}$

Area of curve discussed in classroom from $\frac{\pi}{2}$ to $\frac{3\pi}{2}$ is.

-2 sq. units
2 sq. units
3 sq. units
-3 sq. units

Area of curve discussed in classroom from $\frac{3\pi}{2}$ to $2\pi$ is.

1 sq. unit
2 sq. units
3 sq. units
4 sq. units

Area of explained curve from 0 to $2\pi$ is.

1 sq. unit
2 sq. units
3 sq. units
4 sq. units

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Graphs of two function $\text{f}(\text{x})=\text{sin}\text{ x}$ and $\text{(g)}\text{x}=\text{cos}\text{ x}$ is given below:

Based on the above information, answer the following questions.

In $(0, \pi)$, the curves $\text{f}(\text{x})=\text{sin}\text{ x}$ and $\text{g}\text{ (x)}=\text{cos}\text{ x}$ at $\text{x}=$
1. $\frac{\pi}{2}$
2. $\frac{\pi}{3}$
3. $\frac{\pi}{4}$
4. ${\pi}$
Value of $\int\limits_{0}^{\frac{\pi}{4}}\text{sin}\text{ x}\text{ dx}$ is.
1. $1-\frac{1}{\sqrt{2}}$
2. $1+\frac{1}{\sqrt{2}}$
3. $2-\frac{1}{\sqrt{2}}$
4. $2+\frac{1}{\sqrt{2}}$

Value of $\int\limits_\frac{\pi}{4}^{\frac{\pi}{2}}\text{cos}\text{ x}\text{ dx}$ is.
1. $1+\frac{1}{\sqrt{2}}$
2. $1-\frac{1}{\sqrt{2}}$
3. $2-\sqrt{2}$
4. $2+\sqrt{2}$
Value of $\int\limits_{0}^{\pi}\text{sin}\text{ x}\text{ dx}$ is.

0
1
2
-2

Value of $\int\limits_{0}^\frac{\pi}{2}\text{sin}\text{ x}\text{ dx}$ is.

0
1
3
4

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