Question 1 : <span>Write each of the following equations in the form ax + by + c = 0 and indicate the values of a, b and c in each case.</span><div>2x + 3y = 9.35</div>
Question 2 :
<span>If we write $\displaystyle 3x-7y=10$ in form of $\displaystyle ax+by+c=0,$ then $a+b+c=$</span><span>?</span>
Question 3 :
A train 110 metres long is running with a speed of 60 km/hr. In what time it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Question 4 :
A train travelling with constant speed crosses a 96 metres long platform in 12 seconds and another 141 metres long platform in 15 seconds. The length of the train and its speed are
Question 5 : <span>Write the following equation in the form of ax + by + c = 0 </span><div>2x = y</div>
Question 6 : <div><span>Father's age is $10$ more than twice age of his son. </span><span>What is the number of variables if the statement is written in the form of linear equation?</span></div>
Question 8 :
<span>Cost of one apple is 3 times the cost of an orange. </span>This is an example of linear equation in ..... variables.
Question 9 :
The value of $x$ and $y$ respectively in the simultaneous equations<br>$2x - \frac{3}{y} = 12$ and $5x + \frac{7}{y} = 1, y \neq 0$ is<br>
Question 10 : <span>Consider the equation:</span><br/><span>$\displaystyle y+7x=3x-2y+28$</span><div>If the equation is written in the form of <span>$\displaystyle ax+by=c$, then what is the value of a?<br/></span><br/></div>
Question 12 :
The equation representing the relation between the amount $y$ that is left of her budget after buying drinks for $x$ days in a month. $7x+y=133$ for Arzoo. What is resemblence of $(19,0)$ being the solution of the equation? <br/>
Question 13 :
At a Petrol Station regular unleaded gas is being sold for $ $3.49$ a gallon and premium gas for $ $3.79$ a gallon. If a car wash is purchased, then a discount of $ $0.10$ per gallon is applied. During one morning, a total of $850$ gallons of gas was sold, and $100$ gallons were sold at the discounted rate. The total amount collected in sales was $ $3,016.50$. Find the appropriate mathematical expressions which yield the number of regular unleaded gallons of gas, $u$, and the number of premium gallons of gas, $p$, that were sold during that morning?
Question 14 : <div>Ross is hosting a lunch party. The catering company charge<span> flat fee for serving the food plus a per person rate for the meals. If the total cost of lunch party is represented by the equation $y = 11x+300$, then the number of people attending the party is</span></div>
Question 15 :
If Arshad earns $Rs. x$ per day and spends $Rs. y$ per day, then his saving for the month of
Question 16 : <div> Find the expression of ${ T }_{ w }$ in terms of ${ T }_{ a }$, ${ T }_{ d }$, $V, E$ and $h$ if the<span> expression for evaporation rate of water $E$ is given by $E=\dfrac { \frac { { T }_{ a }-{ T }_{ d } }{ 700 } -\frac { V }{ { T }_{ w } } }{ { h }^{ 4 } } $</span><span> </span></div>
Question 17 :
Solve the following equations:<br>$x^{2} + xy + y^{2} = 84$,<br>$x - \sqrt {xy} + y = 6$.
Question 19 :
Let $m$ and $n$ be positive integers such that one-third of $m$ is $n$ less than one-half of $m$. Mark the possible value of $m$.
Question 21 :
One-fifth of a number is equal to $\dfrac{5}{8}$ of another number. If <b>35</b> is added to the first number, it becomes four times of the second number. The second number is :
Question 23 :
A man buys $m$ articles at Rs. $x$ each and another $n$ articles for Rs. $y$. If he sells all the articles at Rs. $z$ per article. Frame an equation to find his profit.
Question 24 :
<span>When a die is thrown, list the outcomes of an event of getting: </span><span>a prime number.</span>
Question 25 :
Which of the following is an example of a random experiment?
Question 26 :
Arman scored $32$ marks out of $50$ marks in Social Studies. He scored $25$ marks out of the $40$ marks in English. In which subject did he perform better?
Question 27 :
What is the sample space for choosing an odd number from $2$ to $10$ at random?<br/>
Question 28 :
A coin is tossed two times. The number of possible outcomes is
Question 30 :
Which one of the following cannot be the <span>probability of an event </span><br>
Question 31 : <span>A coin is tossed 100 times with following frequency.</span><br/><span>Head : 25, Tail : 75</span><div>How many outcomes are possible here?</div>
Question 32 :
Cards marked with the numbers $2$ to $101$ are put in a box and mixed thoroughly. One card is drawn from this box. Find the probability that the number on the card is a perfect square.
Question 34 :
A card is drawn at random from a pack of 52 cards, find the probability of getting a club or a queen is _____.
Question 35 :
How many sample points are in the sample space when a coin is flipped $4$ times?
Question 36 :
Two different digits are chosen at random from the set $1, 2, 3, 4, 5, 6, 7, 8.$ Then the probability that their sum will exceed $13$ is
Question 37 :
Four die are thrown simultaneously. The probability that $4$ and $3$ appear on two of the die given that $5$ and $6$ have appeared on other two die is?
Question 38 :
An elevator contains $5$ passengers and stops at $10$ floors. The probability that no two passengers get down at the same floor is
Question 39 :
Choose the correct alternative answer for the following question. If $ \mathrm{n}(\mathrm{A})=2, \mathrm{P}(\mathrm{A})=\dfrac{1}{5}, $ then $ \mathrm{n}(\mathrm{S})=? $
Question 40 :
$5$ telegrams are to be distributed at random over $10$ communication channels. The probability that not more than one telegram will be sent over each channel is :
Question 41 :
A box contains $20$ identical balls of which $10$ are blue and $10$ are green. The balls are drawn at random from the box one at a time with replacement. The probability that a blue ball is drawn $4th$ time on the $7th$ draw is
Question 42 :
From $7$ gentlemen and $4$ ladies, a committee of $5$ is to be formed. The probability that this can be one so as to include at least one lady is
Question 43 :
If A is an event of a random experiment, then $A^C$ or $A^-$ or A' is called the compliment of the event.<br/>If true then enter $1$ and if false then enter $0$.<br/>
Question 44 :
The odds against A solving a problem are $8$ to $6$ and the odds in favour of B solving the same problem $14$ to $12$. The probability of solving the problem if they both try independently is
Question 45 :
$n$ different books $(n\ge 3)$ are put at random in a shelf. Among these books there is a particular book. '$A$' and a particular book $B$. The probability that there are exactly '$r$' books between $A$ and $B$ is-
Question 46 :
The odds that a book will be reviewed favourably by three independent critics are 5 to 2, 4 to 3 and 3 to 4 respectively. The probability that of the three reviewers a majority will be favourable
Question 47 : <p>A committee of five is to be chosen from a group of $8$ people which include a married couple. The probability for the selected committee which may or may not have the married couple is.</p>
Question 48 :
If $\theta$ increases from $0^0$ to $90^o$, then the value of $\cos\theta$: <br/>
Question 49 :
A ladder 20 m long is placed against a vertical wall of height 10 m, determine the distance between foot of the ladder and the wall and also the inclination of the ladder with the horizontal.
Question 50 :
If $\displaystyle \cot A=\frac{12}{5}$ then the value of $\displaystyle \left ( \sin A+\cos A \right )$ $\displaystyle \times cosec$ $\displaystyle A$ is
Question 53 :
If $cosec\,\theta=\dfrac{29}{21}$ where $0 < \theta < 90^0$, then what is the value of $4\sec\theta+4\tan\theta$ ?
Question 54 :
If $\displaystyle \sin \theta +\sin ^{2}\theta =1$ then the value of $\displaystyle \left ( \cos ^{2}\theta +\cos ^{4}\theta \right )$ is
Question 55 : <div>Solve:</div>$\displaystyle \sin ^{4}\theta +2\cos ^{2}\theta \left ( 1-\frac{1}{\sec ^{2}\theta } \right )+\cos ^{4}\theta $
Question 59 :
What is the value of sin( $ 1920^o $ ) ?
Question 60 :
If <br>$\displaystyle 16 cos \left ( \dfrac{2\pi}{15} \right ) cos\left ( \dfrac{4\pi}{15} \right ) cos\left ( \dfrac{8\pi}{15} \right ) cos\left ( \dfrac{16\pi}{15} \right ) = n$ , The value of $n$ is....
Question 61 :
If $\displaystyle 7\sin ^{2}\theta +3\cos ^{2}\theta =4$ then the value of $\displaystyle \tan \theta $ is
Question 62 :
In a $\triangle ABC,\ I$ is the incentre. The ratio $IA :IB:IC$ is equal to
Question 63 :
If $\cot\theta + \cos\theta = p$ and $\cot\theta - \cos\theta = q$, then the value of $p^2 - q^2$ is
Question 65 :
${ \sec }^{ 2 }\theta =\dfrac { 4xy }{ { \left( x+y \right) }^{ 2 } } $ is true if and only if
Question 66 :
<span>Say true or false:</span><br/>The value of $\tan\theta\space (\theta < 90^{\small\circ})$ increases as $\theta$ increases.
Question 67 :
$\cot { \dfrac { \pi }{ 20 } } \cot { \dfrac { 3\pi }{ 20 } } \cot { \dfrac { 5\pi }{ 20 } } \cot { \dfrac { 7\pi }{ 20 } } \cot { \dfrac { 9\pi }{ 20 } } \cot { \dfrac { 15\pi }{ 20 } } =$
Question 68 :
If $\displaystyle \sin^4\theta+\frac {1}{\sin^4\theta}=194$, then the value of $(2 \text{cosec}\theta-\cot\theta \cos\theta)$ can be<br/>
Question 69 :
If $\cos x + \sec x = - 2$ for a positive odd integer $n$ then $\cos^nx + \sec^nx$ is
Question 70 :
If $ \theta = \displaystyle \frac{\pi }{4n} $ , then value of $ \tan \theta \:\tan 2\theta ...\tan \left ( 2n-1 \right )\theta $ equals
Question 72 :
In a right angle triangle $\triangle ABC,\,\sin ^{ 2 }{ A } +\sin ^{ 2 }{ B } +\sin ^{ 2 }{ C } $ is
Question 73 :
<br/>If $a \sin^{2}x+b\cos^{2}x=c, b\sin^{2}y+a\cos^{2}y=d$ and $a \tan x=b\tan y,$ then $\displaystyle \frac{a^{2}}{b^{2}}$ equals to<br/>
Question 74 :
${\cos ^2}{48^ \circ } - {\sin ^2}{12^ \circ }$ is equal to -
Question 75 :
If $2 \sec 2\alpha = \tan\beta + \cot \beta$, then one of the value of $\alpha+\beta$ is-
Question 76 :
If $0\leq x, y\leq 180^o$ and $\sin (x-y)=\cos(x+y)=\dfrac 12$, then the values of $x$ and $y$ are given by
Question 78 :
<span>Check whether the given equation is a quadratic equation or not.</span><br/>$3{ x }^{ 2 }-4x+2=2{ x }^{ 2 }-2x+4$
Question 79 : <div><span>Check whether the following is a quadratic equation.</span></div><div><span>$(x - 3) (2x + 1) = x (x + 5)$</span><br/></div>
Question 82 :
If, in the expression $x^2 - 3$, x increases or decreases by a positive amount a, the expression changes by an amount
Question 83 :
Find the roots of the following quadratic equation by using the quadratic formula <br>$4{x^2} + 3x + 5 = 0$<br>
Question 84 :
Find the product of zeros of the quadratic polynomial: $x^{2} - 4x + 3$.
Question 85 :
Before Robert Norman worked on 'Dip and Field Concept', his predecessor thought that the tendency of the magnetic needle to swing towards the poles was due to a point attractive. However, Norman showed with the help of experiment that nothing like point attractive exists. Instead, he argued that magnetic power lies is lodestone. Which one of the following is the problem on which Norman and others worked?
Question 86 : <span>Is the following equation a quadratic equation?</span><div>$\displaystyle \frac{3x}{4} - \frac{5x^2}{8} = \frac{7}{8}$</div>
Question 87 :
<span>Check whether the given equation is a quadratic equation or not.</span><br/>${ x }^{ 2 }+2\sqrt { x } -3$
Question 88 :
If $\left (a + \dfrac {1}{a}\right )^{2} = 3$, then the value of $a^{6} - \dfrac {1}{a^{6}}$ will be
Question 89 :
If r,s,t are the roots of the equation ${ 8x }^{ 3 }+1001x+2008=0$ . the value of ${ \left( r+s \right) }^{ 3 }+{ \left( s+t \right) }^{ 3 }+{ \left( t+r \right) }^{ 3 }$ is
Question 90 :
If $m + n = 1$, then the value of $m^{3} + n^{3} + 3mn$ is equal to when $m=1$
Question 91 :
The product of two consecutive integers is $156$. Find the integers.<br/>
Question 92 :
Elisa is $3$ years older than her brother Joseph. If the product of their ages is $10$. Find the age of Elisa.<br/>
Question 93 :
In a square box, a glass is to be surrounded by a $2$ cm glass border. If the total area of the square is $121$ cm$^{2}$. Find the dimension of the glass box.<br/>
Question 95 :
The length of a rectangle is twice the side of a square and its width is 6 m greater than the side of the square. If the area of the rectangle is three times the area of the square; find the dimensions of each.
Question 96 :
If $x+y+z = 0$ then what is the value of<br/>$\dfrac{1}{x^2 + y^2 - z^2} + \dfrac{1}{y^2 + z^2 - x^2} + \dfrac{1}{z^2 + x^2 - y^2}$<br/>
Question 97 :
If one root of the equation $x^2-4x+k=0$ is $6$, then the value of k will be
Question 98 :
Find the term independent of x in the expansion of $\left(2x^2-\dfrac{3}{x^3}\right)^{25}$.
Question 99 :
If $\alpha, \beta$ are the roots of the equation $2x^{2} - 3x - 6 = 0$, then the equation whose roots are $\alpha^{2} + 2$ and $\beta^{2} + 2$ is
Question 100 :
For what value of $k$ is $x^2 + kx + 9=(x+3)^2$?
Question 101 :
$\alpha ,\beta $ are roots of the equation $2{x^2} - 5x - 6 = 0$ then
Question 103 :
If $|2x + 3|\le 9$ and $2x + 3 < 0$, then
Question 104 :
The difference between two positive integers is $13$ and their product is $140$. Find the two integers.<br/>
Question 106 :
If $x = 3t, y = 1/ 2(t + 1)$, then the value of $t$ for which $x = 2y$ is
Question 107 :
All the values of '$a$' for which the quadratic expression $ax^2+(a-2)x-2$ is negative for exactly two integral values of $x$ may lie in
