Question 1 :
The A.M. of a set of $50$ numbers is $38$. If two numbers of the set, namely $55$ and $45$ are discarded, the A.M. of the remaining set of numbers is :
Question 3 :
The heights of $6$ boys in a group are $142$ cm, $154 $ cm, $146$ cm, $145$ cm, $151$ cm and $150$ cm. Find the mean height per boy<br/>
Question 4 :
The arithmetic mean of the cubes of first four natural numbers is
Question 6 :
The arithmetic mean of the squares of first $n$ natural numbers is :
Question 7 :
The difference between the greatest and least value of the observations is known as
Question 8 :
The mean of $8, 7, 9, 10, 12, x$ and $14$ is $12$, then find the value of $x$.<br/>
Question 9 :
The mean of a set of seven numbers is $81$. If one of the number is discarded, then the mean of the remaining numbers is $78$. The value of discarded number is?
Question 10 :
Three friends went to a hotel and had breakfast to their taste, paying Rs 16, Rs 17 and Rs 21 respectively <br/>(i) Find their mean expenditure.<br/>(ii) If they have spent 3 times the amount that they have already spent, what would their mean expenditure be? <br/>(iii) If the hotel manager offers 50% discount, what would their mean expenditure be? <br/>
Question 12 :
The arithmetic mean of the set of observations $1, 2, 3, ..., n$ is
Question 13 :
The average of $5, 0, 6,$ <br> $\displaystyle \frac{1}{4}$ and $\displaystyle 8\frac{3}{4}$ is
Question 14 :
For which state the average number of candidates selected over the years is the maximum?<br>
Question 15 :
The average of $33.5, 30.4, 25.6, 31.5\ and \ 29$ is:
Question 17 :
The mean of $a, b, c, d$ and $e$ is $28$. If the mean of $a, c$, and $e$ is $24$, what is the mean of b and d?
Question 18 :
Mean of $25$ observations was given as $78.4$. Later it was found out that $96$ was misread as $69$. Find the correct mean.
Question 19 :
The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
Question 20 :
The mean of the distribution, in which the values of $X$ are $1,2,...,n$ the frequency of each being unity is:
Question 21 :
The range of observations 2, 3, 5, 9, 8, 7, 6, 5, 7, 4, 3 is
Question 23 :
Mean of $14, 17, 11, 13, 26, 21, 31$, and $19 $
Question 24 :
$2, 10, m, 12, 4$<br/>A group of $5$ integers is shown above. If the average (arithmetic mean) of the numbers is equal to $m$, find the value of $m$.<br/>
Question 26 :
If the average of $3, 4$, and $x$ is $2$, then find $x$.
Question 27 :
Three years ago the average age of the family of 5 members was 17 years A baby having been born the average age of the family is the same today What is the baby today?
Question 28 :
The arithmetic mean of $^nC_0,\space ^nC_1,\space ^nC_2, ... , \space ^nC_n$ is
Question 29 : <div><span>The marks of $20$ students in a test were as follows:</span><br/><span>$5, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19, 20.$</span><br/></div>The mean is
Question 30 :
Mean of $41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 49, 42, 52, 60 \ is\ 54.8$
Question 31 :
In an examination, $40\%$ of the candidates wrote their answer in Hindi and the others in English. The average marks of the candidates written in Hindi is $74$ and the average marks of the candidates written in English is $77$. What is the average marks of all the candidates?
Question 32 :
Find the mean of the following data: $18, 33, 30, 21$ and $13$.<br/>
Question 35 :
Tara's three bowling scores in a tournament were $167, 178$, and $186$. What was her average score for the tournament?
Question 38 :
If the mean of x and 1/x is M, then the mean of $\displaystyle x^{3}$ and $\displaystyle 1/x^{3}$ is
Question 39 :
The weights of 9 apples are 50,60,65,62,67,70,64,45,48 grams Their mean weight is
Question 40 :
If the average marks of three batches of $55, 60$ and $45$ students respectively is $50, 55$ and $60$, then what are the average marks of all the students?
Question 41 :
The runs scored by Sachin in $5$ test matches are $140$, $153$, $148$, $150$ and $154$ respectively. Find his mean<br/>
Question 42 :
What is the average of squares of consecutive odd numbers between $1$ and $13 $?
Question 43 :
The mean monthly salary of the $12$ employees of a firm is Rs. $1450$. If one more person joins the firm who gets Rs. $1645$ per month, what will be the mean monthly salary of $13$ employees?<br/>
Question 44 :
Mean of 10 values is 32.6. If another values is included the mean becomes 31. The included value is
Question 45 :
The mean of first 726 natural numbers is 363.5. If true then enter $1$ and if false then enter $0$.<br/>
Question 47 :
$12-n, 12, 12+n$<br/>What is the average (arithmetic mean) of the $3$ quantities in the list above? <br/>
Question 49 :
In a bundle of $20$ sticks, there are $4$ sticks each of length $1\ m \ 50 \ cm$, $10$ sticks each of length $2$ m and each of the rest of length $ 1$ m. What is the average length of the sticks in the bundle?
Question 50 : <div><span>Find the mean of the observations $8, 12, 16, 22, 10$ and $4$.</span></div>
Question 51 :
A man bought $5$ shirts at Rs. $450$ each, $4$ trousers at Rs. $750$ each and $12$ pairs of shoes at Rs. $750$ each. What is the average expenditure per article?<br>
Question 52 :
The mean of five numbers is $27$. If one of the numbers is excluded, the mean gets reduced by $2.$ Find the excluded number.
Question 53 :
Average of $8$ numbers is $20$, that of the first two is $15.5$ and that of the next three is $21\dfrac {1}{3}$, the $6^{th}$ is less than the $7^{th}$ by $4$ and $7$ less than the $8^{th}$. The last number is:
Question 54 :
The Arithmetic mean of $10$ number is $-7$. If $5$ is added to every number, then the new Arithmetic mean is
Question 55 :
The arithmetic mean of the numbers $1,3,3^3, ... , 3^{n-1}$ is
Question 56 :
The weights of 9 apples are 50, 60, 65, 62, 67, 70, 64, 45, 48 grams. Their mean weight is
Question 57 :
The heights (in $cm$) of $8$ girls of a class are $140, 142, 135, 133, 137, 150, 148$ and $138$ respectively. Find the mean height of these girls.<br/>
Question 59 :
The mean of $20$ observations is $12.5$ by error one observation was noted $-15$ instead then the correct mean is
Question 61 :
The mean of $100$ items was found to be $30$. If two observation were wrongly taken as $32$ and $12$ instead of $23$ and $11$, find the correct mean.
Question 62 :
There are $50$ numbers. Each number is subtracted from $53$ and the mean of the numbers so obtained is found to be $3.5$. The mean of the given numbers is:<br/>
Question 63 :
The average of three numbers is 60. The first is 1/4th of the sum of the other two. The first number is
Question 65 :
If the range of $14, 12, 17, 18, 16, x$ is $20$ and $x>0$, the value of $x$ is<br>
Question 66 :
In a class of $100$ students there are $70$ boys whose average marks in a subject are $75$. If the average marks of the complete class is $72$, then what is the average of the girls?
Question 67 :
$20$ years ago, when my parents got married, their average age was $23$ years, now the average age of my family, consisting of myself and my parents only is $34$ years. My present age is
Question 68 :
The mean of 96, 104, 121, 134, 142, 149, 153 and 161 is 132.5<br>If true then enter $1$ and if false then enter $0$<br>
Question 69 :
Of the three numbers, the first is twice the second and the second is twice the third. The average of the reciprocal of the number is $\displaystyle \frac{7}{72}$. The numbers are
Question 70 :
The mean of the series $a, \space a+d, \space a+2d, ..., \space a+2nd$ is
Question 71 :
If $6$, $p$, $12$, $8$ and $9$ mean of the data is $9$ then $p=$ ?<br/>
Question 72 :
The mean of the following natural numbers $1, 2,3 ...... 10$ is
Question 73 :
The average of $20$ numbers is zero. Of them, at the most, how many may be greater than zero?
Question 74 :
<span>The average of four consecutive even numbers is $15$. The $2$nd highest number is</span>
Question 75 :
Let $\bar{x}$ be the mean of $x_1, x_2 , ... , x_n$ and $\bar{y}$ the mean of $y_1, y_2, ... , y_n$. If $\bar{z}$ is the mean of $x_1, x_2, ... , x_n$, $y_1, y_2, ... , y_n$, then <span>$\bar{z}$</span> is equal to<br/>
Question 76 :
The mean of the numbers $\displaystyle \frac { _{ }^{ 50 }{ { C }_{ 0 }^{ } } }{ 1 } ,\frac { _{ }^{ 50 }{ { C }_{ 2 }^{ } } }{ 3 } ,\frac { _{ }^{ 50 }{ { C }_{ 4 }^{ } } }{ 5 } ,...,\frac { _{ }^{ 50 }{ { C }_{ 50 }^{ } } }{ 51 } $ equals :
Question 77 :
The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:
Question 78 :
The average of 11, 12, 13, 14, and x is 13. The value of x is
Question 79 :
M=$\left \{1, 2, 3, 4, 5, 6, 7\right \}$<br/>Each number in set $N$ is generated by dividing each number in set $M$ by $2$. Calculate the arithmetic mean of numbers in $N$.<br/>
Question 80 :
The mean of $13$ observations is $14$. If the mean of the first $7$ observations is $12$ and that of the last $7$ observations is $16$, then the $7^{th}$ observation is ___________.
Question 81 :
Find the mean of the data $x, x + a, x + 2a, x + 3a, ...$<br/>$\left[(2n+1)\: \text{terms}\right]$
Question 82 :
Find the output of the program given below<br>10 REM Average of ten numbers<br>20 READ $\displaystyle n_{1},n_{2},n_{3},n_{4}$............$\displaystyle n_{10}$<br>30 DATA 2, 4, 14, 8, 22, 32, 44, 58, 74, 92<br>40 Let Average =<br>$\displaystyle \left ( n_{1}+n_{2}+n_{3}+n_{4}+n_{5}+n_{6}+n_{7}+n_{8}+n_{9}+n_{10} \right )/10$<br>50 PRINT "Average = "; Average<br>60 END
Question 83 :
The ages of $5$ children are $13, 15, 11, 9$ and $8$ years respectively. The average age is<br/>
Question 84 :
Find the mean of the observations $425, 430, 435, 440, 445, ........... 495.$
Question 85 :
Brian got grades of $92,89$ and $86$ on his first three math tests. What grade must he get on his final test to have an overall average of $90$?
Question 86 :
The mean of the data set comprising go 16 obser vations is 16.If one of and three new observations valued 3,4 and 5 are added to the data, then
Question 87 :
In a data the number $i$ is repeated $i$ times for $i=1,2,.....,\ n$. Then the mean of the data is
Question 89 :
The sum of five numbers is $555$. The average of first two numbers is $75$ and the third number is $115$. What is the average of the last two numbers?
Question 91 :
In a Zonal athletic long jump meet the distances jumped by $10$ atheletes are: $205\:cm, 200\:cm, 275\:cm, 260\:cm, 259\:cm, 199\:cm, 252\:cm, 239\:cm, 228\:cm$ and $281\:cm$. Find the arithmetic mean of the jumps.<br/>
Question 92 :
The average of $100$ numbers is $44$. The average of these $100$ numbers and four other numbers is $50$. What is the average of the four new numbers?
Question 93 :
Rahul's mean score in $5$ tests was $84$. His mean score in the first $4$ of these tests was $87$. Calculate his score in the fifth test.
Question 94 :
A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
Question 96 :
The mean of $\displaystyle x_{1}$ and $\displaystyle x_{2}$ is $\displaystyle M_{1},$ and that of $\displaystyle x_{1},x_{2},x_{3}$...$\displaystyle x_{4}$ is $\displaystyle M_{2},$ then the mean of $\displaystyle ax_{1},ax_{2},x_{3}/a,x_{4}/a$ is
Question 97 :
The arithinetic mean of $5, 6, 8, 9, 12, 13, 17$ is<br/>
Question 100 :
If the range of $15,14,x,25,30,35$ is $23$, then the least possible value of $x$ is<br>
Question 101 :
The mean number of tickets sold daily by a comedy show over a seven-day period was $52$. The show sold $46$ tickets on the last day of that period. Find the mean number of tickets that were sold daily over the first six days.
Question 102 :
What is the average (arithmetic mean) of all numbers multiples of $6$ from $6$ to $510$ inclusive?
Question 104 :
The mean age of a group of persons is 40. Another group has mean age 48. If the ratio of number of persons in two groups is 5 : 3, then mean age of all the persons in two groups is
Question 106 :
Two triangles are ....... if two sides and included angle of one triangle are equal to two sides and included angle of the other triangle.
Question 107 :
If $\angle LMN \cong $ $\angle ABC$ and $\angle ABC \cong \angle XYZ$ then $\angle LMN \cong $ ......
Question 108 :
Which of the following statements is true when $\displaystyle \Delta ABC\cong \Delta DEF.$
Question 109 :
State True or False. If false, give reasons for that.<br/>A $1$-rupee and a $5$-rupee coins are congruent.
Question 110 :
If the areas of two rectangles are same, they are congruent.
Question 111 : <span>State true or false:</span><div>Any two circles of radii $4\ cm$ each are congruent.</div>
Question 112 :
If $\angle{A} \cong \angle {D}$, then $\angle {D} \cong \angle {A}$ is a ___________ property of congruence.<br/>
Question 114 :
In $\Delta ABC, AB=AC$ and $AD$ is perpendicular bisector of $BC$. The property by which $\Delta ADB$ is not congruent to $\Delta ADC$ is ______________.
Question 115 :
Two triangles are congruent, if two angles and the side included between them in one triangle is equal to the two angles and the side included between them of the other triangle.This is known as
Question 117 :
If $\displaystyle AC=PR,BC=QR$, and $\displaystyle \angle C=\angle R$ in $\displaystyle \Delta ABC$ and $\displaystyle \Delta PQR$, then
Question 118 : Consider following statements<div>I: If three angles of a $\bigtriangleup$ are equal to three angles of another $\bigtriangleup$ then the two $\bigtriangleup$ s are congruent.</div><div>II : If areas of two similar $\bigtriangleup$ s are equal, then the $\bigtriangleup'$s are congruent. Which of above 2 statements is/are correct.</div>
Question 119 :
If $\displaystyle \Delta ABC$ and $\displaystyle \Delta XYZ$ are congruent, then $\displaystyle \Delta ABC ....... \Delta XYZ.$
Question 121 :
Which of the following statements is CORRECT?<br>Statement-1 : Two triangles are said to be congruent if two sides and an angle of one triangle are respectively equal to the two sides and an angle of the other.<br>Statement-2 : Two triangles are congruent if two sides and the included angle of the one must be equal to the corresponding two sides and included angle of the other.
Question 124 :
Three students Pia, Sia and Tia wrote a statement on a blackboard.<br>Pia wrote, "All rectangles are congruent".<br>Sia wrote, "All equilateral triangles are congruent".<br>Tia wrote, "All right angled triangles are <span>congruent".<br>Who wore the INCORRECT statement?</span>
Question 125 :
If the areas of two similar triangles are equal, then they are<br/>
Question 126 :
If $AB=DE, BC=EF$ and $AC=DF,$ then $\displaystyle \Delta ABC$ _____$\Delta DEF$.
Question 127 :
If the corresponding angles of two triangles are equal then they are always congruent. The given statement
Question 128 :
Two plane figures are said to be congruent if they have_____.
Question 129 :
In a triangle $ABC$, $\angle A={ 40 }^{ o }$ and $AB=AC$, then $ABC$ is ............ triangle.
Question 130 :
The same ratio of corresponding sides is referred to as the ____ factor for polygons.
Question 132 :
<span>State the following statement is True or False</span><br/>Two equilateral triangles with their sides equal are always congruent
Question 133 :
If $\Delta ABC \cong \Delta DEF,\ \angle A=47^{\circ},\ \angle E=83^{\circ},$ then the value of $\angle C$ is:<br/>
Question 134 :
Which of the following statements is incorrect when $\displaystyle \Delta PQR\cong \Delta LMN$?<br/>
Question 136 :
Write True / False for the following statements<br>Any two congruent figure are similar.
Question 137 :
If in two triangles $ABC$ and $DEF$, $AB=\,DF$, $BC=\,DE$ and $\angle B=\angle D$, then $\triangle ABC\cong $ $\triangle $____.
Question 138 :
Given $\angle ABC$ is congruent to $\angle PQR$. Then which of the following statements is true?
Question 140 :
If two legs of a right triangle are equal to two legs of another right triangle. then the right triangles are congruent.
Question 141 :
In $\triangle$ABC, AB = AC and AD is perpendicular bisector of BC. The property by which $\triangle$ADB is not congruent to $\triangle$ADC is ______.
Question 142 :
If $\overline{AB} \cong \overline {CD}$, and $\overline {CD} \cong <br/>\overline {EF},$ then $\overline{AB}\cong \overline{EF}$ is a ___________ property of congruence.<br/>
Question 143 :
If the hypotenuse of one right triangle is equal to the hypotenuse of another right triangle, then the triangles are congruent.
Question 144 :
Consider the following statements:<br>i) If three sides of a triangle are equal to three sides of another triangle, then the triangles are congruent.<br>ii) If the three angles of a triangle are equal to three angles of another triangle respectively, then the two triangles are congruent.
Question 145 :
Two triangles are .......... if two angles and included side (common to both the angles) are equal to two angles and included side (common to both angles) of the other triangle.
Question 146 : <span>State true or false:</span><div>Any two right triangles with hypotenuse $5\ cm$, are congruent.</div>
Question 147 :
$\Delta ABC \cong \Delta PQR$. If AB $=$ 5 cm, $\angle B = 40^{\circ}$ and $\angle A = 80^{\circ},$ then which of the following is true.<br>
Question 148 :
Assertion: Two triangles are said to be congruent if two sides and an angle of one triangle are respectively equal to the two sides and an angle of the other.
Reason: Two triangles are congruent if two sides and the included angle of the one must be equal to the corresponding two sides and included angle of the other.<br>Which of the following options hold?
Question 149 :
State 'T' for true and 'F' for false.<br>1. To examine the congruency of plane figures, the superposition method is used.<br>2. If two line segments have different lengths, they are congruent.<br>3. The measure of two congruent angles is the same.<br>4. Object which are exact copies of one another are called plane objects.<br>5. If the corresponding angles of two triangles are equal, the triangles are said to be congruent.<br>1 2 3 4 5
Question 151 :
In $\triangle ABC$ and $\triangle DEF$, $\angle B=\angle E,AB=DE,BC=EF$. The two triangles are congruent under ............. axiom.
Question 152 :
If $\displaystyle \Delta ABC\cong \Delta XYZ$, which of the following statements is incorrect ?
Question 153 :
In a triangle $ABC$, $\overline{AB} \cong \overline {AB}$ is a _________ property of congruence.<br/>
Question 154 :
<span>If $\angle{D} \cong \angle {B}$ and $\angle {B} \cong \angle {Q},$ then $\angle{D}\cong \angle{Q}$ is a ________ property of congruence.</span><br/>
Question 156 :
In $\displaystyle \bigtriangleup ABC and \bigtriangleup DEF, AB=DE,BC=EF, and \angle B=\angle E,$. The triangles are congruent by SSS test.<br/>
Question 157 :
If $\triangle ABC\cong \triangle PQR $, then which of the following is not true?
Question 158 :
If a line through one vertex of a triangle divides the opposite sides in the ratio of other two sides, then the line bisects the angle at the vertex.<br/><br/>
Question 159 :
For $\displaystyle \Delta ABC$ and $\displaystyle \Delta DEF,$ $AB=FE, BC=ED$ and $\displaystyle \angle B=\angle E$. Therefore ............
Question 160 :
In $\triangle ABC$ and $\triangle PQR$, $ \angle A = \angle Q$ and $\angle B = \angle R.$ Which side of $\triangle PQR$ should be equal to side $BC$ of $\triangle ABC$ so that the two triangles are congruent?<br/>
Question 161 :
In $ \bigtriangleup ABC\: and\: \bigtriangleup DEF, \angle B=\angle E =90^{\circ};AC=DF\: and\: BC=EF.$ <br/>Then,<br/>triangles are congruent.<br/><br/><br/>
Question 162 :
Which of the following is not a criterion for congruence of triangles?<br/>
Question 163 : <p></p><p>Two line segments are congruent if they have the same length.<br/></p><p></p>
Question 164 :
Which of the following condition even if satisfied, does not make the two triangles congruent?
Question 165 :
In $\triangle ABC$ and $\triangle DEF$, $AB = FD$ and $\angle A = \angle D.$ The two triangles will be congruent by $SAS$ axiom, if:<br/>
Question 166 :
The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.<br/><br/><br/><br/>
Question 168 :
For a $\displaystyle \Delta ABC,\angle A={ 90 }^{ o }$ and $\displaystyle \angle B={ 45 }^{ o }$. If $\displaystyle \Delta ABC\cong \Delta XYZ,$ then $\displaystyle \angle Z= $____.
Question 169 :
Consider the following statements relating to the congruency of two right triangles.<br/>(1) Equality of two sides of one triangle with any two sides of the second makes the triangle congruent.<br/>(2) Equality of the hypotenuse and a side of one triangle with the hypotenuse and a side of the second respectively makes the triangle congruent.<br/>(3) Equality of the hypotenuse and an acute angle of one triangle with the hypotenuse and an angle of the second respectively makes the triangle congruent.<br/>Of these statements:
Question 170 :
State whether the following statement is true or false.<br>If two rectangles have equal area, they are congruent.<br>
Question 172 : Assertion : Two $\Delta$s are said to be congruent if two sides and an angle of the one triangle are respectively equal to the two sides and an angle of the other triangle.<br/>Reason: Two $\Delta$s are congruent if two sides and the included angle of the one triangle are equal to the corresponding two sides and included angle of the other triangle.<div><br/></div><div>Two statements A and R are given above. Which of the following statements is correct?</div>
Question 173 :
State whether the following statement is true or false.<br>If two squares have equal areas, they are congruent.<br>
Question 174 :
In $\triangle ABC$ and $\triangle PQR$, $\angle A = \angle Q$ and $\angle B = \angle R.$ Which side of $\Delta$ $PQR$ should be equal to side $AB$ of $\Delta ABC$ so that the two triangles are congruent?<br/>
Question 175 :
It is given that $\triangle ABC\cong \triangle FDE$ and $AB=\,5cm$, $\angle B={ 40 }^{ 0 }$ and $\angle A={ 80 }^{ 0 }$. Then which of the following is true?
Question 177 :
If three sides of a triangle are respectively equal to three sides of another triangle, then the triangles are:
Question 178 :
In a rectangle $PQRS$, $QS$ is a diagonal. Then $\displaystyle \Delta PQS......\Delta RSQ$
Question 179 :
In $\Delta ABC, \angle A= 30^o , \angle B=40^o $ and $\angle C=110^o$ <br/>In $\Delta PQR, \angle P= 30^o , \angle Q=40^o $ and $\angle R=110^o$ <br/>Then Is $\Delta ABC \cong \Delta PQR$ by AAA ?<span><br/></span>
Question 180 :
For a $\displaystyle \Delta XYZ, ZY = 12\ m, YX = 8\ m$ and $XZ = 10\ m$. If $\displaystyle \Delta ZYX\cong \Delta ABC$, then $AC =$ _____ $m$.
Question 181 :
In $\Delta ABC$, D is a point on BC such that AB = AD = BD = DC. <b>then</b><br/>$\angle ADC\, :\, \angle C\, =\, 4\, : \, 1$<br/><b>State whether the above statement is true or false.</b><br/>
Question 183 :
For a $\displaystyle \Delta ABC,$ $AB = 4 $ mm, $BC= 5$ mm and $AC = 6 $ mm. If $\displaystyle \Delta ABC\cong \Delta DEF$, then $EF =$___.
Question 184 :
If $M$ is the mid-point of a line segment $AB$, then we can say that $AM$ and $MB$ are congruent.
Question 185 :
In $\bigtriangleup ABC and \bigtriangleup QRP, AB =QR,\angle B=\angle R\:and \: \angle C=\angle P.$ By A.S.A, $\triangle ABC$ and $\triangle QRP$ are similar
Question 186 :
If $\displaystyle x^{2}-(a+b)x+ab=0,$ then the value of $\displaystyle \left ( x-a \right )^{2}+\left ( x-b \right )^{2}$ is
Question 187 : <div>Say true or false:</div>The degree of the sum of two polynomials each of degree $5$ is always $5$.<br/>
Question 188 :
Degree of the polynomials $\dfrac{x^{23} + x^{14} - x^{16}}{x^2}$ is ______
Question 189 :
$x^{2} + y^{2} - 2z^{2} + 5x - 7$ is a _____
Question 190 :
Assertion: Degree of a zero polynomial is not defined.
Reason: Degree of a non-zero constant polynomial is $0$
Question 191 :
The degree of polynomial $(x +1)(x^2 - x - x^4 + 1)$ is .................
Question 193 :
State whether true or false :<br>$ x^3 - 5xy + 6x + 7 $ is a polynomial
Question 197 : <div><span>In case of a polynomial in one variable, the highest power of the variable is called the degree of the polynomial.</span><br/><span>In case of polynomials in more than one variable, the sum of the powers of the variables in each term is taken up and the highest sum so obtained is called the degree of the polynomial.</span><br/></div><div><br/></div>Find the polynomial with degree $6$.
Question 199 :
If $x+y+z=0,$ what will be the value of $\dfrac { { x }^{ 2 }+{ y }^{ 2 }+{ z }^{ 2 } }{-(xy+yz+zx) } ?$
Question 201 : <span>Write down the degree of the following polynomial:</span><div>$6a^{4} - a^{4}b^{3} + ab^{3} + b^{4}$<br/></div>
Question 205 :
$\left( 14{ x }^{ 2 }yz-28{ x }^{ 2 }{ y }^{ 2 }{ z }^{ 3 }+32{ y }^{ 2 }{ z }^{ 2 } \right) \div \left( -4xy \right) $ is equal to
Question 206 :
The difference of the degrees of the polynomials $3x^2y^3+5xy^7-x^6$ and $3x^5-4x^3+2$ is
Question 207 :
The degree of the polynomials $p(y) = y^{3}, q(y) = (1-y^{4})$ are<br/>
Question 213 :
If the quotient of $x^4-11x^3+44x^2-76x+48$. When divided by $(x^2-7x+12)$ is $Ax^2+Bx+C$, then the descending order of A, B, C is :
Question 214 :
Degree of the polynomials $\left( {x + 2} \right)\left( {{x^2} - 2x + 4} \right)$ is
Question 217 :
The degree of the polynomial $x^{2} - 5x^{4} +\dfrac {3}{4}x^{7} - 73x + 5$ is ____
Question 220 :
The degree of a polynomial $7x^{4} + 6x^{2} + x$ is
Question 221 :
Find the value of $\displaystyle a+{ a }^{ 2 }-{ a }^{ 3 }+{ a }^{ 4 }-{ a }^{ 5 }$ if <span>$\displaystyle a=-2$.</span>
Question 224 : <div>What is the degree of the following polynomial expression:</div><span></span>$9x^{\frac{2}{3}} - 3x + 4$<br/>
Question 226 : <div>What is the degree of the following polynomial expression:</div><span></span>$\dfrac{4}{3}x^{7} - 3x^{5} + 2x^{3} + 1$<br/>
Question 228 :
The degree of the polynomial $2x^{4} - 3x^{2} + 9$ is
Question 231 :
If $x = 2, y = 3$, then $x^{2} + y^{3}$ is equal to<br>
Question 232 : <div>State whether following statement is true or false.</div>The degree of the sum of two polynomials each of degree $5$ is always $5.$<br/>
Question 233 :
The degree of the polynomial $\left ( x+1 \right )\left (x ^{2} -x-x^{4}+1\right )$ is:<br/>
Question 234 :
The letters with respect to which there exists symmetry for the expression<br>$2x^{3}+3y^{3}+2z^{3}+7x^{2}z+7xz^{2}+xyz$ is:<br>
Question 236 :
The expression $ \displaystyle 3(\sin x-cos x)^{4}+6(sinx+cosx)^{2} +4(sin^{6}x+cos^{6}x) $ is equal to
Question 237 : <div>What is the degree of the following polynomial expression:</div><span></span>$ u^{\frac{-1}{2}} + 3u +2$<br/>
Question 239 :
If the degree of the polynomial $\displaystyle \left ( p^{6}+\frac{3}{7} \right )\left ( p^{n}+3p \right )$ is $9$ then the value of $n$ is
Question 240 :
State whether the statement is true (T) or false (F).<br>$(9x - 51) \div 9$ is $x - 51$.<br>
Question 241 :
$p(y) = 5y^3 - 2y^2 + y + 10$ is a polynomial in $y$ of degree
Question 242 :
The _________ power of the variable in a polynomial is called its degree.
Question 243 :
What is the degree of the polynomial $p(x) = 5x^3 - 8x^2 + 4x?$
Question 245 :
Assertion: Degree of the polynomial $5x^2+3x+4$ is $2$.
Reason: The degree of a polynomial of one variable is the highest value of the exponent of the variable.
Question 246 :
The difference of the degrees of the polynomials <span>$3x^2y^3\, +\, 5xy^7\,-\,x^6$ and $3x^5\, - 4x^3\, +\, 2$ is:</span>
Question 247 :
Degree of the polynomial $\displaystyle \left ( a^{2}+1 \right )\left ( a+2 \right )\left ( a^{3}+3 \right )$ is
Question 248 :
The expression ${ \left[ x+{ \left( { x }^{ 3 }-1 \right) }^{ 1/2 } \right] }^{ 5 }+{ \left[ x-{ \left( { x }^{ 3 }-1 \right) }^{ 1/2 } \right] }^{ 5 }$ is a polynomial of degree
Question 250 :
Which of the following expressions is equivalent to $\dfrac { 1 }{ 2 } { y }^{ 2 }\left( 6x+2y+12x-2y \right) $?
Question 251 :
The remainder when $\displaystyle x^{3}-2x^{2}+4x$ is divided by $\displaystyle x^{2}$ is
Question 252 :
$p(x) = 6x^2 - 2x^6 $ is a polynomial in $x$ of degree
Question 253 :
For real x, the value of expression $\dfrac{x^2-2x+2}{2x-2}$ cannot !is in the interval
Question 260 :
The degree of the polynomial <span>$5x^3\, - \,6x^3y \,+\, 4y^2\, -\,8$ is</span>
Question 262 :
What is the degree of the polynomial $p(x) = 8x^8 + 9x^9 + 10x^0$?
Question 263 :
Identify the degree of the given equation:<span> $\displaystyle { x }^{ 2 }+3x-5={ x }^{ 2 }+9x-23$</span>
Question 264 :
State the degree of the polynomial $9{ x }^{ 3 }-7{ x }^{ 2 }+\dfrac { 5 }{ 3 } { \left( \dfrac { { x }^{ 2 } }{ 2 } \right) }^{ 3 }$
Question 265 :
If ${ 4 }^{ x }-{ 4 }^{ x-1 }=24,$ what is the value of ${ \left( 2x \right) }^{ x }?$
Question 266 :
If when $f(x)$ is divided by $3x + 1$, the quotient is $x^{2} - x + 3$ and the remainder is $2$, then find $f(x)$.
Question 267 :
The number to be added to make $x^2-\frac {1}{2}$ x a perfect square is
Question 268 :
If P(x) is polynomial of degree $4$ with leading coefficient as three such that $P(1) = 2, P(2) = 8, P(3) = 18, P(4)= 32$, then the value of $P(5)$ is :
Question 271 :
Which out of the following options is a trinomial, having degree 7?<br/>
Question 272 :
Write whether the following statement is True or False. <br/>A binomial may have degree $3$.
Question 273 :
$\displaystyle \left ( 14x^{2}yz-28x^{2}y^{2}z^{3}+32y^{2}z^{2} \right )\div \left ( -4xy \right )$ is equal to
Question 274 :
Identify the degree of the polynomial $6a^4 - a^4 b^3 + ab^3 + b^4$.
Question 276 :
Simplify: $\displaystyle \left( { 8m }^{ 2 }-9m \right) \div 3m$
Question 277 :
Write whether the following statements are True or False. <br/>Every polynomial is a binomial
Question 278 : Classify the following polynomials as monomials,bionomials, trinomials. Which polynomials do not fit <span>in any of these three categories?<br/>$x+y, 1000, x + x^2+ x^3 + x^4, 7+ y + 5x, 2y -3y^2, 2y - 3y^2 + 4y^3$</span><div><span>$ 5x -4y + 3xy, 4z - 15z^2, ab + bc + cd + da, pqr, p^2q + pq^2, 2p + 2q$</span></div>
Question 283 :
$p(a) = 3a^2 + 4a - 4$ is a polynomial in $a$ of degree
Question 284 :
$(x^2 + 3x + 1) = (x -2)^2$ is an equation of degree <br>
Question 285 :
The degree of the differential equation ${ \left( \dfrac { { d }^{ 2 }y }{ d{ x }^{ 2 } } \right) }^{ 2 }+{ \left( \dfrac { dy }{ dx } \right) }^{ 2 }=x\sin { \left( \dfrac { { d }^{ 2 }y }{ d{ x }^{ 2 } } \right) } $ is
Question 286 :
Given the polynomial $a_{0}x^{n} + a_{1}x^{n - 1} + ... + a_{n - 1}x + a_{n}$, where $n$ is a positive integer or zero, and $a_{0}$ is a positive integer. The remaining $a's$ are integers or zero. Set$h = n + a_{0} + |a_{1}| + |a_{2}| + .... + |a_{n}|$. The number of polynomials with $h = 3$ is
Question 287 :
Find the value of K if (x + 1) is a factor of $x^8 + Kx^3 - 2x + 1$.
Question 289 :
The survey of a manufacturing company producing a beverage and snacks was done. It was found that it sells orange drinks at $ $1.07$ and choco chip cookies at $ $0.78$ the maximum. Now, it was found that it had sold $57$ food items in total and earned about $ $45.87 $ of revenue. Find out the equations representing these two.
Question 290 :
Find $p$, if $\displaystyle \frac { 21 }{ 105 } =\frac { p }{ p+3 } $
Question 292 :
Kishore has Rs.$p$. Hari has Rs.$3$ more than Kishore and Ashok has Rs.$7$ less than Hari. Altogether the three boys have Rs.$20$. How much money does Kishore have?
Question 293 :
The average age of a father and his two sons is 27 year. Five year ago, the average age of the two sons was 12 years. If the difference between the ages father is <br>
Question 294 :
If a boat goes $7$ km upstream in $42$ minutes and the speed of the stream is $3$ kmph, then the speed of boat in still water is:
Question 295 :
A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class are:
Question 296 :
The sum of three numbers is $98$. The ratio of the first to the second term is $\displaystyle\frac{2}{3}$ and the ratio of the second to the third is $\displaystyle\frac{5}{8}$. Then the second number is
Question 298 :
If $x$ and $y$ are positive integers, the value of $p$ in the equation $px=y$ is always
Question 299 :
If $\sqrt { 23+x\sqrt { 10 } } =\sqrt { 18 } +\sqrt { 5 } $, then $x=$..........
Question 301 :
A number is doubled and $9$ is added. If the result is tripled it becomes $75$. What is that number?
Question 303 : <span>State whether true or false.</span><div>Power of variable in a simple linear equation is $1$.</div>
Question 304 :
In a caravan, in addition to 50 hens, there are 45 goats and 8 camels with some keepers. If the total number of feet be 224 more than the number of heads in the caravan, find the number of keepers.
Question 305 :
A boy is now $a$ years old and his father is $5a$ years old. How old will the father be when the boy is $3a$ years old? How old was the father when the boy was born?
Question 307 :
The two consecutive multiples of $3$ whose sum is $51$ are __________.
Question 309 :
Fill in the blanks.<br/>(i) An expression with a variable, constant and the sign of equality in called an _________.<br/>(ii) $8$ more than $2$ times the number $x$ can be written in algebraic form as __________.<br/>(iii) An equation is a condition on a ________.
Question 310 : Find the value of $x$<div><br/></div><div> $\sqrt 3 x - 2 = 2\sqrt 3 + 4$.</div>
Question 311 :
Ramu's father is thrice as old as Ramu. If father's age is 45 years then <span>Ramu's age is</span>
Question 312 :
A number is multiplied by $2\displaystyle\frac{1}{3}$ times itself and then $61$ is subtracted from the product obtained. If the final result is $9200$, then the number is __________.
Question 313 :
If $\cfrac{x}{3}+1 = \cfrac{7}{15}$, then $x = -\cfrac{m}{5}$. So, the value of $m$ is
Question 314 :
Mohan gets $3$ marks for each correct sum and loses $2$ marks for each wrong sum. He attempts $30$ sums and obtains $40$ marks. The number of sums solved correctly is<br/>
Question 315 :
Mayank is $1\dfrac{2}{5}$ times as tall as vansh. If Mayak is 38 cm taller then Vansh, what is Mayank's height
Question 317 :
If one-fourth of two-fifths of a number is $36$, what is the number?
Question 319 :
If $17+6p = 9$, then $p = -\cfrac{4}{m}$. So, $m$ is
Question 320 :
If q= 999, then the value of $\displaystyle q\left ( q^{2}+3q+3 \right )$ is
Question 321 :
Five tables and eight chairs cost Rs. $7350$; three tables and five chairs cost Rs. $4475$. The price of a table is
Question 324 :
If $\displaystyle \frac {3}{4}\, x\, +\, 8\, =\, 17$, then the value of $x$ is
Question 325 :
Find the value of $x$.<br/>$\sqrt 5 (1 + \sqrt 5)x = 2 \sqrt 5 $
Question 328 :
Water flows at the rate of $10$ metres per minute from a cylindrical pipe $5$ mm. in diameter. The time taken to fill up a conical vessel, whose diameter at the base is $40$ cm and depth $24$ cm., is
Question 330 :
$\dfrac{3}{5}$th of a number subtracted from $\dfrac{3}{4}$th of that number gives $18$. Find the number.
Question 335 : <span>Solve for $x$:</span><div><div>$\displaystyle (81)^{\tfrac {3}{4}} - (\cfrac {1}{32})^{- \tfrac {2}{5}} + x (\cfrac {1}{2})^{-1} . 2^0 = 27$</div></div>
Question 336 :
The number of pairs of reals (x, y) such that $x =x^2+y^2$ and $y =2xy$ is
Question 337 :
Out of three numbers, the first is twice the second and is half of the third. If the average of three numbers is $56,$ then the difference of the first and third is
Question 338 :
Calculate the value of $b$ if $-\dfrac { 5 }{ 2 } =b-\dfrac { 1 }{ 2 } $.
Question 339 :
There's an online tutoring service. It provides a demo one-hour free tutoring and after that, if a person signs up, $\$30$ per hour is charged for the first ten hours and after that, a discount is given to the user. If a client pays $\$664$ for $25$ hours of tutoring , what is the service's discounted hourly rate?
Question 340 :
Amit is now $6$ times as old as his son. Four years from now, the sum of their ages will be $43$ years. Determine Amit's present age:<br>
Question 341 :
A money box contains one rupee and two rupee coins in the ratio $5:6$. If the total value of the coins in the money box is $Rs.\ 85$. Find the number of two rupee coins.
Question 342 :
A value z is multiplied by $\dfrac {1}{3}, \dfrac {1}{2}$ is subtracted from the result, and the square root of the end result is $4$. What was the original number?
Question 344 :
A certain job was assigned to a group of men to do in 20 days. But 12 men did not turn up for the job and the remaining men did the job in 32 days. The original number of men in the group was:
Question 346 :
Given that $\displaystyle \frac {-6p - 9}{3}\, =\, \displaystyle \frac {2p + 9}{5}$, find the value of $p$.
Question 347 :
State 'T' for true and 'F' for false.<br>P. $x = 15$ is the solution of the equation $41 - x = 25$.<br>Q. An equation is an algebraic expression which involves an "equal to" sign.<br>R. $'x$ exceeds $y$ by $7'$ can be expressed as $x = y + 7$.
Question 350 :
The sum of one fifth, one third and one ninth of a number is $29$. Find the number.
Question 351 :
On a number line, the coordinate of point A is $0$, and the coordinate of point B is $6$. If point P is located on the number line so that the distance from P to A is twice the distance from P to B, find the coordinate of point P.
Question 352 :
<span>If $t, w, x, y,$ and $z$ are all positive real numbers and below stated relations hold true, mark the variable having greatest value.</span><br/>$1.23w=t$<br/>$1.01x=t$<br/>$0.99y=t$<br/>$0.23z=t$
Question 353 :
Find $ v$:<br/>$\displaystyle \frac { 3v }{ 8 } -5v=-3\left( \dfrac{8}{9}+6v \right) +12v$<br/>
Question 354 :
If the sum of four consecutive odd integers is $400$, what is the value of the first odd integer?<br/>
Question 355 : <span>Solve the following simultaneous equations :</span><div>$\displaystyle \frac{1}{3x}\, +\, \frac{1}{5y}\, =\, \frac{1}{15};\quad \frac{1}{2x}\, +\, \frac{1}{3y}\, =\, \frac{1}{12}$</div>
Question 357 :
If a is a non-zero digit in the numbers $1a2a$ and $a31$, what is the value of a when $1a2a + a31 = 2659$?
Question 358 : Solve: $\displaystyle \frac{2x\, +\,1}{10}\, -\, \frac{3\, -\, 2x}{15}\, =\, \frac{x\, -\, 2}{6}$.<div><br/>Hence, find y, if $\displaystyle \frac{1}{x}\, +\, \frac{1}{y}\, +\, 1\, = 0$.</div>
Question 359 :
If $\left ( x-\cfrac{1}{2} \right )^2-\left ( x-\cfrac{3}{2} \right )^2=x+2$, then the value of $x$ is equal to<br/>
Question 360 :
If $(3)^{x + y} = 81$ and $(81)^{x - y} = 3$, then the values of $x$ and $y$ are<br>
Question 361 :
At present anil is $1.5$ times of purvis age. $8\ yr$ later, the respective ratio between Anil and Purvis ages will be $25:18$. What is Purvis present age?
Question 362 :
In solving an equation of the form $ax + b = 0$ (a, b having only 1 as the common factor). A made mistake in copying $b$ and got $\cfrac{7}{3}$ as the root whereas B made mistake in copying $a$ and got $\cfrac{8}{5}$ as the root. The correct root is<br/>
Question 363 :
A consultant charges $ $45$ for each hour she works on a consultation, plus a flat $ $30$ consultation fee for without registration. Find the number of hours for which she works given that she was paid $ $210$ bill for the consultation.
Question 364 :
The ten's digit of a two digit number is $2$ more than its unit's digit. If the number is divided by the unit's digit the quotient is $16$. Find the number.
Question 365 :
The solution of $64^{2x - 5} = 4 \times 8^{x - 5}$ is<br>
Question 366 :
If $2^{2x - y} = 32$ and $2^{x + y} = 16$ then $x^{2} + y^{2}$ is equal to<br>
Question 368 :
The number of students who take both the subjects Mathematics and Chemistry is $30$. This represents $10\%$ of the enrollment in Mathematics and $12\%$ of the enrollment in Chemistry. How many students take atleast one of these two subjects?
Question 369 :
Solve: $4x+\displaystyle \frac{6}{y}= 15$ and $6x-\displaystyle \frac{8}{y}= 14$. Hence, find $a$ if $y= ax-2$
Question 370 :
For which equation(s) is $x=3$ a solution?<br/>(I) $2x-5+3x=10$ (II) $\displaystyle \frac{-x+7}{2}=2 $<br/>(III) $4x-11=17$ (IV) $\displaystyle 9=-\left ( x-1 \right )+11 $
Question 371 :
Rina is $x$ years old. Her sister Bina is $5$ years older than her. If their ages add up to $15$, then Bina's age is
Question 374 :
If $\dfrac {7}{9}x - \dfrac {4}{9}x = \dfrac {1}{4} + \dfrac {5}{12}$, what is the value of $ x$?
Question 375 :
<i></i>When $x = 2,$ the value of the expression $4{x^2} + \dfrac{9}{{{x^2}}} - 12$ is:
Question 376 : <span>Solve the following pair of simultaneous equations:</span><div>$\displaystyle \frac{8}{x}\, -\, \frac{9}{y}\, =\, 1;\,\frac{10}{x}\, +\, \frac{6}{y}\, =\, 7$</div>
Question 377 : Solve the following pair of equations by reducing them to a pair of linear equations:<div><br/></div><div>$\dfrac {10}{(x+y)}+\dfrac {2}{(x-y)}=4, \dfrac {15}{(x+y)}-\dfrac {5}{(x-y)}=-2$<br/></div>
Question 379 :
The ratio between two numbers is $3 : 5$. If each number is increased by $4$ , the ratio becomes $2 : 3$. Find the numbers.
Question 380 :
The digit in the units place of a $2$ digit number is $4$ times the digit in the tens place. The number obtained by reversing the digits exceeds the given number by $54$. Find the given number.
Question 381 :
The ten's digit of a two digit number is three times the unit digit. The sum of the number and the unit digit is $32$. Find the number.
Question 382 : <div><span>Say true or false:</span><br/></div>$10$ students of Class $X$ took part in a Mathematics quiz. If the number of girls is $4$ more than the number of boys, then the number of boys and girls who took part in the quiz are $3$ and $7$, respectively.
Question 383 :
In a piggy bank, the number of $25$ paise coins are five times the number of $50$ paise coins. If there are $120$ coins, find the amount in the bank ?
Question 384 : Solve for $\displaystyle p:$<div>$2\left ( p-3 \right )+5\left ( p-2 \right )=0$</div>
Question 385 :
If $\displaystyle \frac { -6s }{ -28 } =\frac { -2s+9 }{ -7 } $, then find $ s$.
Question 386 :
Find the value of $m$.<br/>$\displaystyle \frac{2m}{3} - \frac{1}{5} = \frac{7m}{15} - \frac{13}{15}$
Question 387 :
Find the value of $p$:<br/>$\displaystyle \left( p-3 \right) \left( p+3 \right) -p\left( p+8 \right) =15$<br/>
Question 391 :
When a certain number is multiplied by $\dfrac{1}{4}$ and the product is then multiplied by $32$, the result is $60$. What is the number?
