Question 2 : Assertion: $\displaystyle \frac{13}{3125}$ is a terminating decimal fraction. Reason: If $q=2^n \cdot 5^m$ where $n, m$ are non-negative integers, then $\displaystyle \frac{p}{q}$ is a terminating decimal fraction.

Question 3 : A number $x$ when divided by $7$  leaves a remainder $1$ and another number $y$ when divided by $7$  leaves the remainder $2$. What will be the remainder if $x+y$ is divided by $7$?

Question 6 : $2\times 2\times 2\times 3\times 3\times 13 = 2^{3} \times 3^{2} \times 13$ is equal to

Question 8 : To get the terminating decimal expansion of a rational number $\dfrac{p}{q}$. if $q = 2^m 5^n$ then m and n must belong to .................

Question 9 : State whether the following statement is true or not:$\left( 3+\sqrt { 5 }  \right) $ is an irrational number. 

Question 10 : The greatest number that will divided $398, 436$ and $542$ leaving $7,11$ and $14$ remainders, respectively, is

Question 12 : Let $x=\dfrac { p }{ q } $ be a rational number, such that the prime factorization of $q$ is of the form $2^n 5^m$, where $n, m$ are non-negative integers. Then $x$ has a decimal expansion which terminates.

Question 14 : State whether the following statement is true or false.The following number is irrational<br/>$7\sqrt {5}$

Question 15 : If $a=\sqrt{11}+\sqrt{3}, b =\sqrt{12}+\sqrt{2}, c=\sqrt{6}+\sqrt{4}$, then which of the following holds true ?<br/>

Question 16 : Use Euclid's division algorithm to find the HCF of :$196$ and $38220$

Question 17 : The number of possible pairs of number, whose product is 5400 and the HCF is 30 is<br>

Question 19 : State whether the following statement is True or False.<br/>3.54672 is an irrational number.

Question 20 : For three irrational numbers $p,q$ and $r$ then $p.(q+r)$ can be

Question 21 : Find HCF of $70$ and $245$ using Fundamental Theorem of Arithmetic.&#160;

Question 22 : Assuming&#160; that x,y,z&#160; are positive real numbers,simplify the following :<br/>$ (\sqrt{x})^{-2/3}\sqrt{y^{4}}\div \sqrt{xy^{-1/2}} $<br/>

Question 25 : According to Euclid's division algorithm, using Euclid's division lemma for any two positive integers $a$ and $b$ with $a &gt; b$ enables us to find the<br/>

Question 28 : If we apply Euclid&#34;s division algorithm for $20, 8,$ then the correct answer will be

Question 31 : If a polynomial $p(x)$ is divided by $x - a$ then remainder is<br/>

Question 32 : State whether True or False.Divide : $a^2 +7a + 12 $ by $&#160; a + 4 $, then the answer is&#160;$a+3$.<br/>

Question 33 : Work out the following divisions.<br/>$96abc(3a -12) (5b +30)\div&#160; 144(a-&#160; 4) (b+&#160; 6)$<br/>

Question 34 : Work out the following divisions.$10y(6y + 21) \div 5(2y + 7)$<br/>

Question 35 : What must be subtracted from $4x^4 - 2x^3 - 6x^2 + x - 5$, so that the result is exactly divisible by $2x^2 + x - 1$?

Question 36 : Find the value of a &amp; b, if&#160; $8{x^4} + 14{x^3} - 2{x^2} + ax + b$ is divisible by $4{x^2} + 3x - 2$

Question 37 : If&#160;$\alpha , \beta$ are the roots of equation&#160;$x^2 \, - \, px \, + \, q \, = \, 0,$ then find the equation the roots of which are&#160;$\left ( \alpha ^2&#160; \, \beta ^2 \right )&#160; \,&#160; and&#160; \,&#160; \,&#160; \alpha \, + \,\beta $.

Question 38 : Is $(3x^{2} + 5xy + 4y^{2})$ a factor of $ 9x^{4} + 3x^{3}y + 16x^{2} y^{2} + 24xy^{3}&#160; + 32y^{4}$?<br/>

Question 40 : Simplify:Find$\ x(x + 1) (x + 2) (x + 3) \div&#160; x(x + 1)$<br/>

Question 41 : If a root of the equations${x^2} + px + 12 = 0$ is 4 ,while the roots of the equation ${x^2} + px + q = 0$ , are the same ,then the value of q will be

Question 43 : If $ \alpha, \beta $&#160;be the roots of the equation $&#160;a x^{2}+b x+c=0, $&#160;then value of $\dfrac{ \left(a \alpha^{2}+c\right) }{(a \alpha+b)}+\dfrac{\left(a \beta^{2}+c\right)}{ (a \beta+b)} $&#160;is

Question 45 : The sum and product of zeros of the quadratic polynomial are - 5 and 3 respectively the quadratic polynomial is equal to<br>

Question 46 : State true or false.If $a &lt; b &lt; c &lt; d$, then the roots of equation $ (x - a) (x - c) +2 (x -b) (x - d) = 0$ are real and distinct.&#160; &#160; &#160; &#160; &#160;&#160;

Question 47 : State whether True or False.Divide: $16 + 8x + x^6-8x^3 -2x^4+ x2 $ by $ x+ 4-x^3$, then the answer is&#160;$-x^3+x+4$.<br/>

Question 49 : Workout the following divisions<br/>$54lmn (l + m) (m + n) (n + 1) \div 81mn (l + m) (n + l)$

Question 50 : Find all values of a for which the equation&#160;$x^4+(a&#8722;1)x^3+x^2+(a&#8722;1)x+1=0$&#160;possesses at least two distinct negative roots.

Question 51 : Suppose $\alpha ,\beta .\gamma $ are roots of ${ x }^{ 3 }+{ x }^{ 2 }+2x+3=0$. If $f(x)=0$ is a cubic polynomial equation whose roots are $\alpha +\beta ,\beta +\gamma ,\gamma +\alpha $ then $f(x)=$

Question 53 : Simplify: $\displaystyle \frac { 45\left( { a }^{ 4 }-3{ a }^{ 3 }-28{ a }^{ 2 } \right) &#160;}{ 9a\left( a+4 \right) &#160;}&#160;$

Question 54 : The difference of the roots of$\displaystyle 2y^{2}-ky+16=0$ is 1/3 Find k

Question 55 : The equation&#160;$\displaystyle x^{2}+Bx+C=0$ has 5 as the sum of its roots and 15 as the sum of the square of its roots. The value of C is

Question 57 : Equation of a straight line passing through the point $(2,3)$ and inclined at an angle of $\tan^{-1}\dfrac{1}{2}$ with the line $y+2x=5$, is:

Question 58 : Two perpendicular lines are intersecting at $(4,3)$. One meeting coordinate axis at $(4,0)$, find the coordinates of the intersection of other line with the cordinate axes.

Question 61 : The value of $k$ for which the system of equations $3x + 5y= 0$ and $kx + 10y = 0$&#160;has a non-zero solution, is ________.

Question 62 : $\dfrac{1}{3}x - \dfrac{1}{6}y = 4$<br/>$6x - ay = 8$<br/>In the system of equations above, $a$ is a constant. If the system has no solution, what is the value of $a$

Question 63 : For what value of k does the system of equations$\displaystyle 2x+ky=11\:and\:5x-7y=5$ has no solution?

Question 65 : State whether the given statement is true or false:The graph of a linear equation in two variables need not be a line.<br/>

Question 66 : If $2x + y = 5$, then $4x + 2y$ is equal to _________.

Question 67 : In a zoo there are some pigeons and some rabbits. If their heads are counted these are $300$ and if their legs are counted these are $750$ How many pigeons are there?

Question 68 : Choose the correct answer which satisfies the linear equation: $2a + 5b = 13$ and $a + 6b = 10$

Question 70 : The solution of the equation $2x - 3y = 7$ and $4x - 6y = 20$ is

Question 71 : If the equations $4x + 7y = 10 $ and $10x + ky = 25$ represent coincident lines, then the value of $k$ is

Question 72 : The linear equation $y = 2x + 3$ cuts the $y$-axis at&#160;

Question 73 : If the system of equation, ${a}^{2}x-ay=1-a$ &amp; $bx+(3-2b)y=3+a$ possesses a unique solution $x=1$, $y=1$ then:

Question 74 : The unit digit of a number is $x$ and its tenth digit is $y$ then the number will be&#160;

Question 76 : Solve the following pair of simultaneous equations:$\displaystyle\, 4x\, +\, \frac{3}{y}\, =\, 1\,; 3x\, -\, \frac{2}{y}\, =\, 5$

Question 77 : Solve : $\displaystyle \frac{9}{x}\, -\,&#160;\displaystyle \frac{4}{y}\, =\, 8$ and&#160;$\displaystyle \frac{13}{x}\, +\,&#160;\displaystyle \frac{7}{y}\, =\, 101$

Question 78 : What is the value of $a$ for the following equation: $3a + 4b = 13$ and $a + 3b = 1$?&#160;(Use cross multiplication method).<br/>

Question 79 : Solve the following pair of simultaneous equations:$\displaystyle\,3x\, +\, \frac{1}{y}\, =\, 13\, ;\, \frac{2}{y}\, -\, x\, =\, 5$

Question 81 : Solve: $4x\, +\,&#160;\displaystyle \frac{6}{y}\, =\, 15$ and $6x\, -\, &#160;\displaystyle \frac{8}{y}\, =\, 14$<br/>Hence, find 'a' if $y\, =\, ax\, -\, 2$

Question 82 : Solve each of the following system of equations by elimination method.&#160;$65x-33y=97, 33x-65y=1$

Question 83 : If $2p + 3q = 18$ and $4p^{2} + 4pq - 3q^{2} - 36 = 0$ then what is $(2p + q)$ equal to?

Question 84 : Solve the following simultaneous equations by the method of equating coefficients.$\displaystyle \frac{x}{2}+3y=11; \, \, x+5y=20$

Question 85 : From the following figure, we can say:&#160;$\displaystyle \frac{2x}{3}+\frac{3y}{2}=8\frac{1}{3}; \, \, \frac{3x}{2}+\frac{2y}{3}=13\frac{1}{3}$

Question 86 : Based on equations reducible to linear equations, solve for $x$ and $y$:<br/>$\dfrac {x-y}{xy}=9; \dfrac {x+y}{xy}=5$<br/>

Question 87 : Equations of the two straight lines passing through the point $(3, 2)$ and making an angle of $45 ^ { \circ }$ with the line $x - 2 y = 3$, are

Question 88 : A straight line L through the point $(3, - 2)$ is inclined at an angle of 60$^o$ to the line $\sqrt 3 x + y = 1$. If $L$ also intersects the $x-$axis, then the equation of $L$ is

Question 89 : A line has intercepts $a$ and $b$ on the coordinate axes. When the axes are rotated through an angle $\alpha $, keeping the origin fixed, the line makes equal intercepts on the coordinate axes, then $\tan$ <br> $\alpha $=<br/>

Question 90 : The equation of the line passing through the point $P(1, 2)$ and cutting the lines $x + y - 5 = 0$ and $2x - y = 7$ at $A$ and $B$ respectively such that the harmonic mean of $PA$ and $PB$ is $10$, is

Question 92 : Equation of straight line $ax + by + c= 0$, where $3a + 4b + c = 0$, which is at maximum distance from $(1, -2)$,is

Question 93 : Based on equations reducible to linear equations<br/>Solve for x and y:&#160;$\dfrac {16}{x+3}+\dfrac {3}{y-2}=5; \dfrac {8}{x+3}-\dfrac {1}{y-2}=0$<br/>

Question 94 : If the equations $y = mx + c$ and $x &#160;\cos &#160;\alpha + y \sin &#160;\alpha = p$ represent the same straight line, then

Question 95 : The equation of the straight line which passes through $(1, 1)$ and making angle $60^o$ with the line&#160;$x+ \sqrt 3y +2 \sqrt 3=0$ is/are.

Question 96 : If the two legs of a right angled triangle are equal and the square of the hypotenuse is $100cm^2$, then the length of each leg is _________.

Question 97 : A right-angles triangle has hypotenuse $13$ cm, one side is $12$ cm, then the third side is _________.

Question 98 : If the lengths of the sides of a triangle does not satisfy the rule of $\displaystyle { a }^{ 2 }+{ b }^{ 2 }={ c }^{ 2 }$, then that triangle does not contain a

Question 99 : If the hypotenuse of a right angled triangle is 15 cm and one side of it 6cm&#160;less than the hypotenuse, the other side b is equal to.

Question 100 : Which of the following cannot be the sides a right angle triangle?<br>

Question 101 : Given the measures of the sides of the triangle , identify which measures are in the ratio 3 : 4 : 5

Question 102 : In $\Delta ABC,$ if $AB =6\sqrt{3}$ cm, $AC=12$ cm and $BC=6$ cm, then angle B is equal to:<br/>

Question 103 : <p>&#160;In a right angle triangle, the hypotenuse is the&#160;greatest side. <br/></p><b>State whether the above statement is true or false.</b><br/>

Question 104 : A man goes 40 m due north and then 50 m due west. Find his distance from the starting point.

Question 105 : A ladder $13m$ long rests against a vertical wall. If the foot of the ladder is $5m$ from the foot of the wall, find the distance of the other end of the ladder from the ground.

Question 107 : The sides of a triangle are given below.&#160;Check whether or not the sides form a right-angled triangle.$3cm, 8cm, 6cm$

Question 108 : The hypotenuse of a grassy land in the shape of a right triangle is $1$ meter more than twice the shortest side. If the third side is $7$ meters more than the shortest side, find the sides of the grassy land.

Question 109 : In $\Delta$ ABC, angle C is a right angle, then the value<br>of tan $A + tan B $is<br><br>

Question 110 : Which of the following numbers form pythagorean triplet?&#160;<br/>i) $2, 3, 4$<br/>ii) $6, 8, 10$<br/>iii) $9, 10, 11$<br/>iv) $8, 15, 17$

Question 111 : Which of the following could be the side lengths of a right triangle?

Question 112 : Triangle ABC is right -angled at C. Find&#160;BC,&#160;If AB = 9 cm and AC = 1 cm.<br/>In each case, answer correct to two place of decimal.&#160;

Question 113 : The hypotenuse 'c' and one arm 'a' of a right triangle are consecutive integers. The square of the second arm is:

Question 114 : There is a Pythagorean triplet whose one member is $6$ and other member is $10$

Question 115 : In$ \displaystyle \bigtriangleup $ ABC , angle C is a right angle, then the value of$ \displaystyle \tan A+ \tan B is $

Question 116 : The sides of a triangle are given below.&#160;Check whether or not the sides form a right-angled triangle.$13cm, 12cm, 5cm$

Question 117 : In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find $b$ when $c=13 \ cm$ and $a=5 \ cm$.

Question 118 : In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find&#160;$a$ when $c=25 \ cm$ and $b=7 \ cm$.

Question 119 : The sides of a triangle are given below. Check whether or not the sides form a right angled triangle.$50cm, 80cm, 100cm$

Question 120 : $4\, RN^{2}\, =\, PQ^{2}\, +\, 4\, PR^{2}$<br/><b>State whether the above statement is true or false.</b><br/>

Question 121 : If $\triangle ABC\sim \triangle &#160;PQR,$ &#160;$ \cfrac{ar(ABC)}{ar(PQR)}=\cfrac{9}{4}$, &#160;$AB=18$ $cm$ and $BC=15$ $cm$, then $QR$ is equal to:

Question 122 : <p>Which among the following is/are correct?<br/>(I) If the altitudes of two similar triangles are in the ratio $2:1$, then the ratio of their areas is $4 : 1$.<br/>(II)&#160;$PQ \parallel BC$ and $AP : PB=1:2$. Then, $\dfrac{A(\triangle APQ)}{A(\triangle ABC)}=\dfrac{1}{4}$</p>

Question 123 : $\Delta ABC&#160;\sim &#160;\Delta PQR$ and $\displaystyle\frac{A(&#160;\Delta ABC)}{A(&#160;\Delta PQR)}=\dfrac{16}{9}$. If $PQ=18$ cm&#160;and $BC=12$ cm, then $AB$ and $QR$ are respectively:

Question 124 : State true or false:<br/>In parallelogram&#160;$&#160;ABCD&#160;$.&#160;$ E&#160;$&#160;is the mid-point of&#160;$&#160;AB&#160;$&#160;and&#160;$&#160;AP&#160;$&#160;is&#160;parallel to $&#160;EC&#160;$<b>&#160;</b>which meets&#160;$&#160;DC&#160;$&#160;at point&#160;$&#160;O&#160;$&#160;and&#160;$&#160;BC&#160;$&#160;produced at&#160;$&#160;P&#160;$. Hence$ BP= 2AD $<br/><br/><br/>

Question 125 : If $\triangle ABC$ is similar to $\triangle DEF$ such that BC=3 cm, EF=4 cm and area of $\triangle ABC=54 {cm}^{2}$. Determine the area of $\triangle DEF$.

Question 126 : The area of two similar triangles are in ratio 16:81. Find the ratio of its sides.

Question 127 : The hypotenuse of a right-angled triangle is $25 cm$. The other two sides are such that one side is $5 cm$ longer than the other side. Their lengths, in $cm$, are:

Question 128 : If $\triangle ABC\sim \triangle QRP,\dfrac{Ar(ABC)}{Ar(QRP)}=\dfrac{9}{4}$,$AB=18\&#160;cm$&#160;and $BC=15\ cm$; then $PR$&#160;is equal to:<br/>

Question 129 : D and F are mid-points of sides AB and AC of a triangle ABC. A line through F and parallel to AB meets BC at point E. Find AB (in cm), if EF = 4.8 cm.

Question 130 : ABC is a triangle with AB = $13$ cm, BC =$14$ cm and CA=$15$ cm. AD and BE are the altitudes from A to B to BC and AC respectively. H is the point of intersection of the AD and BE. Then the ratio of $\frac { HD }{ HB } =$

Question 131 : In $\triangle ABC \sim \triangle DEF$ such that $AB = 1.2\ cm$ and $DE = 1.4\ cm$. Find the ratio of areas of $\triangle ABC$ and $\triangle DEF$.

Question 132 : Aline segment DE is drawn parallel to base BC of $\Delta\,ABC$ which cuts ABat point D and AC at point E. If AB = 5 BD and EC = 3.2 cm. Find the length ofAE.

Question 133 : If $\Delta ABC \sim \Delta QRP, \displaystyle \frac{ar (ABC)}{ar (PQR)} = \frac{9}{4}, AB = 18 cm$ and $BC=15 cm$; then PR is equal to <br>

Question 134 : If in $\triangle $s $ABC$ and $DEF,$ $\angle A=\angle E=37^{\circ}, AB:ED=AC:EF$ and $\angle F=69^{\circ},$ then what is the value of $\angle B\: ?$<br>

Question 135 : If all the three altitudes of a triangle are equal, the triangle is equilateral.<br/><b>State whether the above statement is true or false.</b><br/>

Question 136 : The areas of two similar triangles are $121$ cm$^{2}$ and $64$ cm$^{2}$, respectively. If the median of the first triangle is $12.1$ cm, then the corresponding median of the other is:<br/>

Question 137 : If the sides of two similar triangles are in the ratio $1:7$, find the ratio of their areas.<br/>

Question 138 : $\Delta ABC$ and $\Delta DEF$ are similar and $\angle A=40^\mathring \ ,\angle E+\angle F=$

Question 139 : The perimeter of two similar triangles $\triangle ABC$ and $\triangle DEF$ are $36$ cm and $24$ cm respectively. If $DE=10 $ cm, then $AB$ is :

Question 140 : Two equilateral triangles with side $4 \ cm$ and $6 \ cm$ are _____ triangles.

Question 141 : Match the column.<br/><table class="wysiwyg-table"><tbody><tr><td>1. In&#160;$\displaystyle \Delta ABC$ and&#160;$\displaystyle \Delta PQR$,<br/>$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR},\angle A=\angle P$<br/></td><td>(a) AA similarity criterion&#160;</td></tr><tr><td>2.&#160;In&#160;$\displaystyle \Delta ABC$ and&#160;$\displaystyle \Delta PQR$,<br/>$\displaystyle \angle A=\angle P,\angle B=\angle Q$<br/><br/></td><td>(b) SAS similarity criterion&#160;</td></tr><tr><td>3.&#160;In&#160;$\displaystyle \Delta ABC$ and&#160;$\displaystyle \Delta PQR$,<br/>$\displaystyle \frac{AB}{PQ}=\frac{AC}{PR}=\frac{BC}{QR}$<br/>$\angle A=\angle P$<br/></td><td>(c) SSS similarity criterion&#160;</td></tr><tr><td>4. In&#160;$\displaystyle \Delta ACB,DE||BC$<br/>$\displaystyle \Rightarrow \frac{AD}{BD}=\frac{AE}{CE}$<br/></td><td>(d) BPT</td></tr></tbody></table>

Question 142 : Let&#160;$\displaystyle \Delta XYZ$ be right angle triangle with right angle at Z. Let&#160;$\displaystyle A_{X}$ denotes the area of the circle with diameter YZ. Let&#160;$\displaystyle A_{Y}$ denote the area of the circle with diameter XZ and let&#160;$\displaystyle A_{Z}$ denotes the area of the circle diameter XY. Which of the following relations is true?

Question 143 : $\frac{a}{r}$, a, ar are the sides of a triangle. If the triangle is a right angled triangle, then $r^2$ is given by

Question 144 : If $ \alpha \epsilon \left[ \frac { \pi&#160; }{ 2 } ,\pi&#160; \right]&#160;$ then the value of $\sqrt { 1+sin\alpha&#160; } -\sqrt { 1-sin\alpha&#160; }&#160;$ is equal to

Question 147 : The expression$ \displaystyle \left (\tan \Theta +sec\Theta \right )^{2} $ is equal to

Question 148 : The solution of $(2 cosx-1)(3+2 cosx)=0$ in the interval $0 \leq \theta \leq 2\pi$ is-

Question 150 : Maximum value of the expression $\begin{vmatrix} 1+{\sin}^{2}x &amp; {\cos}^{2}x &amp; 4\sin2x \\ {\sin}^{2}x &amp; 1+{\cos}^{2}x &amp; 4\sin2x \\ {\sin}^{2}x &amp; {\cos}^{2}x &amp; 1+4\sin2x \end{vmatrix}=$

Question 151 : IF&#160;$ \displaystyle \tan \theta =\sqrt{2} &#160; &#160;$ , then the value of&#160;$ \displaystyle \theta &#160; &#160; $ is&#160;

Question 153 : Choose the correct option. Justify your choice.<br/>$\displaystyle 9{ \sec }^{ 2 }A-9{ \tan }^{ 2 }A=$<br/>

Question 154 : The value of $\sqrt { 3 } \sin { x } +\cos { x } $ is max. when $x$ is equal to

Question 155 : Choose and write the correct alternative.<br>If $3 \sin \theta = 4 \cos \theta$ then $\cot \theta = ?$<br>

Question 156 : The given expression is $\displaystyle \sin { \theta &#160;} \cos { \left( { 90 }^{ o }-\theta &#160;\right) &#160;} +\cos { \theta &#160;} \sin { \left( { 90 }^{ o }-\theta &#160;\right) &#160;} +4 $ equal to :<br/>

Question 158 : Solve:$\displaystyle \sin ^{4}\theta +2\cos ^{2}\theta \left ( 1-\frac{1}{\sec ^{2}\theta } \right )+\cos ^{4}\theta $

Question 160 : If $sec\theta -tan\theta =\dfrac{a}{b},$ then the value of $tan\theta $ is

Question 161 : 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 164 : $\text{cosec } (75^{\circ} + \theta) - \sec (15^{\circ} - \theta) =$

Question 165 : If $\sec \theta + \tan \theta = p$ then $\sin \theta = \frac { p ^ { 2 } + 1 } { p ^ { 2 } - 1 }$&#160;

Question 166 : If arcs of same length in two circles subtend angles of $60^{\circ}$ and $75^{\circ}$ at their center, find the ratios of their radii.<br>

Question 167 : The value of&#160;$\displaystyle \sin^{3} \alpha \left ( 1+\cot \alpha &#160;\right )+\cos ^{3}\alpha \left ( 1+\tan \alpha &#160;\right )$ is equal to

Question 169 : The number of solutions of $\sin^{2}\theta + 3\cos \theta = 3$ in $[-\pi, \pi]$, is

Question 172 : The value of $\displaystyle \frac { \cos { \left( { 90 }^{ o }-A \right) &#160;} &#160;}{ \text{cosec}\left( { 90 }^{ o }-A \right) &#160;} \times \frac { \cot{ \left( { 90 }^{ o }-A \right) &#160;} }{ \sin { A } &#160;} $ is

Question 173 : Evaluate: $\sin { \left( { 50 }^{ o }+\theta &#160;\right) &#160;} -\cos { \left( { 40 }^{ o }-\theta &#160;\right) &#160;} +\tan {1}^{o} \tan {10}^{o} \tan {20}^{o} \tan {70}^{o} \tan {80}^{o} \tan {89}^{o}$

Question 174 : <br>In a triangle $ABC, 3\cos A+2=0$. Then the quadratic equation with roots are $\sin A, \cos A$ is<br>

Question 175 : $\text{cosec } 69^{\circ} + \cot 69^{\circ}$, when expressed in terms of angles between $0^{\circ}$ and $45^{\circ}$, becomes

Question 176 : If&#160;$\displaystyle \sin \theta +\sin ^{2}\theta = 1,$ then&#160;$\displaystyle \cos ^{2}\theta +\cos ^{4}\theta =$

Question 177 : The value of tan $1^o$ tan $2^o$ tan $3^o$.... tan $89^o$ is.

Question 178 : Solve: $\sec 70^{\circ} \sin 20^{\circ} + \cos 20^{\circ} \text{cosec } 70^{\circ} $

Question 181 : If $5\tan {\theta}=4$, then value of $\cfrac { 5\sin { \theta } -3\cos { \theta } }{ 5\sin { \theta } +2\cos { \theta } } $ is:

Question 182 : Find the value of ${k}$ for which $(\cos x+\sin x)^{2}+k\sin x\cos x-1=0$ is an identity.<br/>

Question 184 : Assertion: Statement 1:If $\displaystyle x+y+z= xyz,$ then at most one of the numbers can be negative. Reason: Statement 2: In a triangle ABC, $\displaystyle \tan A+\tan B+\tan C= \tan A \tan B \tan C $ ,there can be at most one obtuse angle in a triangle.

Question 185 : 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 187 : If $5\cos { A } =4\sin { A } $, then $\tan { A=\_ \_ \_ } $

Question 188 : $A$ tower of height $h$' standing at the centre of a square with sides of length $a$' makes the same angle $\alpha$ at each of the four corners then $a^{2}=$

Question 191 : If $x \cos \alpha +y \sin&#160;\alpha=x \cos\beta+y \sin\beta=2a(0 &lt;&#160;\alpha, \beta &lt; \pi /2)$, then

Question 192 : What is $\left(\dfrac{sec 18^{\circ}}{sec 144^{\circ}} + \dfrac{cosec 18^{\circ}}{cosec 144^{\circ}}\right)$ equals to?

Question 193 : The value of the expression $\displaystyle 1\, - \,\frac{{{{\sin }^2}y}}{{1\, + \cos \,y}}\, + \frac{{1\, + \cos \,y}}{{\sin \,y}}\, - \,\frac{{\sin \,y}}{{1\, - \cos \,y}}$ is equal to&#160;

Question 194 : <br/>If $a \sin^{2}\theta+b\cos^{2}\theta=a\cos^{2}\phi+b\sin^{2}\phi=1$ and $a \tan\theta=b\tan\phi$, then choose the correct option.<br/>

Question 195 : If $3 \sin\theta+ 5 \cos\theta=5$, then $5 \sin\theta-3 \cos\theta$ is equal to<br/>

Question 196 : If $\sin (\alpha+\beta)=1$ and $\sin(\alpha -\beta)=1/2$ where $\alpha, \beta \epsilon [0, \pi /2]$ then

Question 197 : Which one of the following when simplified is not equal to one?

Question 198 : If $ \cos^{-1}\left ( 4x^{3}-3x \right )= 2\pi -3\cos^{-1}x $, then $ x $ lies in interval

Question 199 : A Cartesian plane consists of two mutually _____ lines intersecting at their zeros. &#160;

Question 200 : Find the co-ordinates of the mid point of a point that divides AB in the ratio 3 : 2.

Question 202 : A point R (2,-5) divides the line segment joining the point A (-3,5) and B (4,-9) , then the ratio is

Question 203 : The ratio, in which the line segment joining (3, -4) and (-5, 6) is divided by the x-axis is

Question 204 : If $P \left( \dfrac{a}{3}, 4\right)$ is the mid-point of the line segment joining the points $Q ( 6, 5) $ &#160;and $R( 2, 3)$, then the value of $a$ is <br/>

Question 205 : Find the distance from the point (5, -3) to the line 7x - 4y - 28 = 0

Question 206 : If Q$\displaystyle \left ( \frac{a}{3},4 \right )$ is the mid-point of the line segment joining the points A(-6,5) and B(-2,3), then the value of 'a' is

Question 207 : If a point $P\left(\displaystyle\frac{23}{5}, \frac{33}{5}\right)$ divides line AB joining two points $A(3, 5)$ and $B(x, y)$ internally in ratio of $2:3$, then the values of x and y will be.

Question 208 : The ratio in which the line segment joining (3,4) and (-2,1) is divided by the y-axis is

Question 209 : Find the ratio in which the line segment joining the points $(3,5)$ and $(-4,2)$ is divided by y-axis.<br/>

Question 210 : The point P divides the line segment joining the points&#160;$\displaystyle A\left ( 2,1 \right )$ and&#160;$\displaystyle B\left ( 5,-8\right )$ such that&#160;$ \frac{AP}{AB}=\frac{1}{3}$ If P lies on the line&#160;$\displaystyle 2x+y+k=0$<br/>then the value of k is-

Question 211 : In what ratio does the point $\begin{pmatrix} \dfrac { 1 }{ 2 },\dfrac { -3 }{ 2 } \end{pmatrix}$ divide the line segment joining the points $(3,5)$ and $(-7,9)$?<br/>

Question 212 : In how many maximum equal parts, a rectangular cake can be divided using three straight cuts?

Question 213 : State whether the following statements are true or false . Justify your answer.<br>Point $ A(-6 , 10) , B(-4 , 6) $ and $ C(3 , -8) $ are collinear such that $ AB = \dfrac{2}{9} AC $ .

Question 214 : What is the ratio in which $P(2, 5)$ divides the line joining the points $(8, 2)$ and $(-6, 9)$?

Question 215 : What will be the value of $y$ if the point $\begin{pmatrix} \dfrac { 23 }{ 5 },y \end{pmatrix}$, divides the line segment joining the points $(5,7)$ and $(4,5)$ in the ratio $2:3$ internally?<br/>

Question 216 : The coordinates of the third vertex of an equilateral triangle whose two vertices are at $(3, 4), (-2 3)$ are ______.

Question 217 : Number of points with integral co-ordinates that lie inside a triangle whose co-ordinate are (0,0), (0, 21) and (21, 0)

Question 218 : The straight line $3x+y=9$ divides the line segment joining the points $(1,\,3)$ and $(2,\,7)$ in the ratio

Question 219 : State whether the following statements are true or false . Justify your answer.<br>The points $ (0 , 5) , (0 , -9) $ and $ (3 , 6) $ are collinear .

Question 220 : The line segment joining the points $(3, -4)$ and $(1, 2) $ is trisected at the points P and Q. If the and co-ordinates of P and Q are $(p, -2)$ and $(\frac{5}{3}, q)$ respectively, find the value of p and q.

Question 221 : If $a&gt; 0$ and $P(-a, 0), Q(a, 0)$ and $R(1,1) $ are three points such that $\displaystyle \left|(PR)^{2}-(QR)^{2} \right| = 12,$ then<br/>

Question 222 : If $\displaystyle A \left(\frac{2c}{a},\frac{c}{b}\right),B\left(\frac{c}{a},0\right)$ and $\displaystyle C\left(\frac{1+c}{a},\frac{1}{b}\right) $ are three points, then<br/>

Question 223 : If two vertices of a parellelogram are $(3,2)$ and $(-1,0)$ and the diagonals intersect at $(2, -5)$, then the other two vertices are:

Question 224 : If the line $2x+y=k$ passes through the point which divides the line segment joining the points $(1, 1)$ and $(2, 4)$ in the ratio $3 : 2$ ,then $k$ equals:

Question 225 : If $P\left( x,y,z \right) $ is a point on the line segment joining $Q\left( 2,2,4 \right) $ and $R\left( 3,5,6 \right) $ such that the projections of $OP$ on the axis are $\cfrac { 13 }{ 5 } ,\cfrac { 19 }{ 5 } ,\cfrac { 26 }{ 5 } $ respectively, then $P$ divides $QR$ in the ratio

Question 226 : The points $A\left( {2a,\,4a} \right),\,B\left( {2a,\,6a} \right)\,$ and $C\left( {2a + \sqrt 3 a,\,5a} \right)$ (when $a&gt;0$) are vertices of&#160;

Question 227 : $ABC$ is an isosceles triangle. If the coordinates of the base are $B(1,3)$ and $C(-2,7)$. The vertex $A$ can be

Question 228 : The mid point of the segment joining $(2a, 4)$ and $(-2, 2b)$ is $(1, 2a+1)$, then value of b is

Question 229 : If the three distance points $\left( { t }_{ i\quad }2{ at }_{ i }+{ { at }^{ 3 }_{ i } } \right) \quad for\quad i=1,2,3$ are collinear then the sum of the abscissae of the points is

Question 230 : Consider the points $A(0,\ 1)$ and $B(2,\ 0)$, and $P$ be a point on the line $4x+3y+9=0$. The coordinates of $P$ such that $|PA-PB|$ is maximum are

Question 231 : Out of the digits $1$ to $9$, two are selected at random&#160;and one is found to be $2$, the probability that their&#160;sum is odd is

Question 232 : A biased coin with probability $p , 0 &lt; p &lt; 1 ,$ of heads is tossed until a head appears for thefirst time. If the probability that the number of tosses required is even, is $2 / 5 ,$ then $p$ equal to

Question 233 : Two dice are thrown. Find the odds in favour of getting the sum $4$.<br/>

Question 234 : If the odd in favour of an event are $4$ to $7$, find the probability of its no occurence.

Question 235 : If $P(A) = \dfrac{5}{9}$, then the odds against the event $A$ is

Question 236 : If I calculate the probability of an event and it turns out to be $7$, then I surely know that<br/>

Question 237 : The probability of an event $A$ lies between $0$ and $1$, both inclusive. Which mathematical expression best describes this statement?<br/>

Question 238 : A coin is tossed $400$ times and the data of outcomes is below:<span class="wysiwyg-font-size-medium">&#160;<span class="wysiwyg-font-size-medium"><br/><table class="wysiwyg-table"><tbody><tr><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">Outcomes&#160;</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$H$</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$T$</p></td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">Frequency</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$280$</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$120$</p></td></tr></tbody></table><p><br/></p><p>Find:</p><p>(i) $P(H)$, i.e., probability of getting head</p><p>(ii) $P (T)$, i.e., probability of getting tail.&#160;</p><p>(iii) The value of $P (H) + P (T)$.</p>

Question 239 : Ticket numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5 ?

Question 240 : A pair of dice is thrown once The probability that the sum of the outcomes is less than 11 is

Question 241 : Three different numbers are selected at random from the set $A = \{1,2,3, ...... 10 \}$. The probability that the product of two of the numbers is equal to third is :<br/>

Question 242 : What are the odds in favour of throwing at least 8 in a single throw with two dice?

Question 243 : There are 5 letters and 5 different envelopes. The number of ways in which all the letters can be put in wrong envelope, is.

Question 244 : Let $A$ and $B$ be two events with $P(A) = \dfrac {1}{3}, P(B) = \dfrac {1}{6}$ and $P(A\cap B) = \dfrac {1}{12}$. What is $P(B|\overline {A})$ equal to?

Question 245 : There are three events $A$, $B$ and $C$&#160;out of which&#160;one&#160;and&#160;only one&#160;can happen. The odds are $7$ to $3$ against $A$ and $6$ to $4$ against $B$. The odds against&#160;C are

Question 246 : If the odds in favour of winning a race by three horses are $1 : 4, 1 : 5$ and $1 : 6$, find the probability that exactly one of these horses will win.

Question 247 : One of the two events, A and B must occur. If&#160;$P\left ( A \right )=\dfrac{2}{3}P\left ( B \right ),$ the odds in favour of $B$ are

Question 248 : The odds in the&#160;favour of an event are $3 : 5$.The probability of occurrence of the event is?

Question 249 : In a race, the odds in favour of horses $A, B, C, D$ are $1:3, 1:4, 1:5$ and $1:6$ respectively. Find probability that one of them wins the race.

Question 250 : The chance of an event happening is the square of the chance of a second event but the odds against the first are the cube of the odds against the second. The chance of each event is

Question 251 : An integer is chosen at random between 1 and 100. Find the probability that it is divisible by 8.<br/>

Question 253 : Results on the bar exam of Law School Graduates<br/><table class="wysiwyg-table"><tbody><tr><td></td><td>Passed bar exam</td><td>Did not pass bar exam</td></tr><tr><td>Took review course</td><td>18</td><td>82</td></tr><tr><td>Did not take review course</td><td>7</td><td>93</td></tr></tbody></table>The table above summarizes the results of $200$ law&#160;school graduates who took the bar exam. If one of&#160;the surveyed graduates who passed the bar exam is&#160;chosen at random for an interview, what is the&#160;probability that the person chosen did not take the&#160;review course?<br/>

Question 254 : A pair of dice is thrown seven times . Getting a total of numbers on the two dice to be seven is considered as a success . Find the probability of getting&#160;$7$ in exactly $2$ trials out of $7$.<br/>

Question 255 : If $E$ and $F$ are event with $P\left( E \right) \le P\left( F \right) $ and $P\left( E\cap F \right) &gt;0$, then

Question 256 : The chance of an event happening is the square of the chance of a second event but the odds against the first are the cube of the odds against the second.The chances of the events are

Question 257 : $A, B$ are two events of a simple space.Assertion (A):- $A, B$ are mutually exclusive&#160;$\Rightarrow P\left ( A \right )\leq P\left ( \bar{B} \right )$Reason (R):- $A, B$ are mutually exclusive &#160;$\Rightarrow P\left ( A \right )+ P\left ( B \right )\leq 1$

Question 258 : The $2013$ U.S. Census recorded the highest educational attainment of all adults aged $25$ years or older in country $T$, one of the most educated parts of the country. The results are given in the two-way table below.<br/><table class="wysiwyg-table"><tbody><tr><td></td><td>Men</td><td>Women</td><td>Total</td></tr><tr><td>High School Diploma</td><td>7535</td><td>7234</td><td>14769</td></tr><tr><td>Bachelor's Degree</td><td>17170</td><td>23455</td><td>40625</td></tr><tr><td>Master's Degree</td><td>45105</td><td>41078</td><td>86183</td></tr><tr><td>Professional Degree</td><td>23501</td><td>23405</td><td>46906</td></tr><tr><td>Doctoral Degree</td><td>16232</td><td>15817</td><td>32049</td></tr><tr><td>Total</td><td>10953</td><td>110989</td><td>220532</td></tr></tbody></table>According to the data presented in the table above, if one was told to choose a person at random out of the entire population aged $25$ years or older in country $T$, find the percentage probability that the person he/she chooses turns out to be a man with a doctoral degree.

Question 259 : $P(A\cap B) = \dfrac{1}{2}, P(\overline{A} \cap \overline{B})=\dfrac{1}{2}$ and $2P(A)=P(B)=p$, then the value of $p$ is equal to

Question 260 : In a box, there are $8$ red, $7$ blue and $6$ green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

Question 261 : A party of $23$ persons take their seats at a round table. The odds against two specified persons sitting together is

Question 262 : A man and his wife appear for an interview for two posts. The probability of the man's selection is $\dfrac{1}{5}$ and that of his wife selection is $\dfrac{1}{7}$. The probability that at least one of them is selected, is:

Question 263 : A fair coin is flipped $5$ times.<br/>&#160;The probability of getting more heads than tails is $\dfrac{1}{2}$<br/><br/>

Question 264 : The chance of an event happening is the square of the chance, of a second event but the odds against the first are the cubes of the odds against thefirst are the cubes of the odds against the second. Find the chance of each.

Question 265 : There are two bags $A$ and $B$. Bag A contains $3$ white and $4$ red balls whereas bag $B$ contains $4$ white and $3$ red balls. Three balls are drawn at random (without replacement) from one of the bags and are found to be two white and one red. Find the probability that these were drawn from bag $B$.

Question 266 : X and Y plays a game in which they are asked to select a number from $21-50$. If the two number match both of them wins a prize. Find the probability that they will not win a prize in the single trial.

Question 267 : If odds against solving a question by three students are $2:1, 5:2$ and $5:3$ respectively, then probability that the question is solved only by one students is

Question 268 : In a set of games it is $3$ to $5$ in favour of the winner of the previous game..&#160;Then the probability that a&#160;person who has won the first game shall win at least $2$ out of the next $5$ games is ?

Question 269 : There are two events $A$ and $B$. If odds against $A$ are as $2:1$ and those in favour of $ A \cup B$ are $3:1$ , then

Question 270 : There are four letters and four addressed envelopes. The probability that all letters are not dispatched in the right envelope is:<br/>

Question 271 : The angle of sector with area equal to one fifth of total area of whole circle&#160;

Question 272 : Lengthof an arc of a circle with radius $r$ and central angle $\theta$is(angle in radians):

Question 273 : If the area of a circle is $346.5 \displaystyle cm^{2}$. Its circumference is

Question 274 : If radius of a circle is increased to twice its original length, how much will the area of the circle increase ?

Question 275 : If the radius of a circle increased by 20% then the corresponding increase in the area of circle is ................

Question 276 : The length of minor arc $\widehat {AB}$ of a circle with radius $7$ units&#160; is $14$. Find the length of major arc $\widehat {AB}$.

Question 277 : If the radius of a circle be r cm then its area will be equal to-

Question 278 : If the circumference of a circle is reduced by 50 % then the area will be reduced by

Question 279 : If one side of a square is 2.4 m. Then what will be the area of the circle inscribed in the square?

Question 280 : The ratio of areas of square and circle is givenn : 1 where n is a natural number. If the ratio of side of square and radius of circle is k :1, where k is a natural number, then n will be multiple of

Question 281 : The perimeter of a sector of a circle is $56$ cms and the area of the circle is $64\pi$ sq. cms&#160; Find the area of sector.

Question 282 : A cord in the form of square encloses the area 'S'$ \displaystyle cm^{2} $ If the same cord is bent into the form of a circle then the area of the circle is

Question 283 : Find the circumference of the circle with the following radius : 10 cm

Question 284 : The perimeter of a sector of a circle is 37cm. If its radius is 7cm, then its arc length is

Question 285 : A roller of diameter 70 cm and length 2m is rolling on the ground What is the area covered by the roller in 50 revolutions?

Question 288 : The distance between the two parallel chords of length 8 cm and 6 cm in a circle of diameter 10 cm if the chords lic on the same side of the centre is

Question 289 : State true or false:<br/>Sector is the region between the chord and its corresponding arc.

Question 290 : The diameter of a circle is $1$. Calculate the area of the circle.

Question 292 : If the radius of a circle is $\displaystyle \frac{7}{\sqrt{\pi}}$ cm, then the area of the circle is equal to

Question 293 : The diameters of two circles are $32\:cm$ and $24\: cm$ . Find the radius of the circle having itsarea equal to sum of the areas of the twogiven circle.

Question 294 : The area of the sector of a circle, whose radius is $6$ m when the angle at the centre&#160;is $42^0$, is

Question 295 : Area of a rectangle and the area of a circle are equal. If the dimensions of the rectangle are $10\,cm \times11\, cm$, then radios of the circle is<br>

Question 297 : A sector of $120^{\circ}$ cut out from a circle has an area of $9\displaystyle \frac{3}{7}$sq cm. The radius of the circle is

Question 298 : If the difference between the circumference and radius of a circle is $37$ cm, then the area of the circle is<br/>

Question 299 : Find the area of sector whose length is $30\ \pi$ cm and angles of the sector is $40^o$.

Question 300 : There are two circular gardens A and B. The circumference of garden A is $1.760 km$ and the area of garden B is $25$ times the area of garden A. Find the circumference of garden B.

Question 301 : What is the area of a sector with an arc length of <font color="#888888">$120 cm $ and radius $4cm$</font>?<br/>

Question 302 : The radii of two circles are in the ratio $3 : 8$. If the difference between their areas is$2695\pi \: cm^{2}$ ,find the area of the smaller circle.

Question 303 : Let a and b be two positive real numbers such that a $a + 2b \leq 1$. Let $A_{1} \space and \space A_{2}$ be, respectively. the areas of circles with radii $ab^{3} \space and \space b^{2}$. Then the maximum possible value of $\dfrac{A_{1}}{A_{2}}$ is

Question 304 : The sides of a triangle are $5$, $12$ and$ 13$ units. A rectangle of width $10$ units is constructed equal in area to the area of the triangle. Then the perimeter of the rectangle is&#160;

Question 306 : In $\bigodot (P, 6)$, the length of an arc is $\pi$. Then the arc subtends an angle of measure ___at the center.

Question 307 : What is the length of an arc of a circle with a radius of $5$ if it subtends an angle of ${60}^{o}$ at the center?

Question 308 : A circular disc of radius 10 cm is divided into sectors with angles $120^{\circ}$ and $150^{\circ}$ then the ratio of the area of two sectors is<br>

Question 309 : Find the area of a sector with an arc length of $20 cm$ and a radius of $6 cm$.<br/>

Question 310 : The minute hand of a clock is $7\ cm$ long. Find the area traced by it on the clock face between $4{:}15$ p.m. and $4{:}35$ p.m.

Question 311 : The area of a sector of a circle of angle $\displaystyle 60^{\circ}$ is $\displaystyle \frac{66}{7}cm^{2}$ then the area of the corresponding major sector is<br>

Question 312 : A sphere with diameter $50$ cm intersects a plane $14$ cm from the center of the sphere. What is the number of square centimeters in the area of the circle formed?

Question 313 : If a bicycle wheel makes $5000$ revolution in moving $11$ km, then diameter of wheel is

Question 314 : The ratio of the slant height of two right cones of equal base is 3 : 2 then the ratio of their volumes is <br>

Question 315 : A wire bent in the form a square incloses an area of 484 $\displaystyle m^{2}$ but if the same wire is bent in the form of a circle the area enclosed will be <br>

Question 316 : The perimeter of a quadrant of a circle of radius $\dfrac{7}{2}$ cm is:<br/>