Question 1 :
In an acute angled triangle $ ABC $, the internal bisector of angle $ A $ meets base $ BC $ at point $ D $. $ DE  \perp  AB $ and $ DF \perp AC $; then the traingle $ AEF $ is an isosceles triangle
Question 3 :
In $\Delta ABC$, AB = AC and AD is perpendicularto BC. State the property by which $\Delta ADB\, \cong\,\Delta ADC$.
Question 4 : <p class="wysiwyg-text-align-left"> State the congruency of following pairs of triangles.</p><p class="wysiwyg-text-align-left">In $\Delta\,ABC$ and $\Delta PQR $, $BC = QR, $ $\angle\,A\,=\,90^{\circ}, \, \angle \,C \,=\,\angle R = 40^{\circ} $ and $ \angle\, Q \,=\,50^{\circ}$.</p>
Question 6 :
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 7 :
If in two triangles $PQR$ and $DEF$, $PR=\,EF$, $QR=\,DE$ and $PQ=\,FD$, then  $\triangle PQR\cong$ $\triangle$ ___.
Question 8 :
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 9 :
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 10 :
If in two triangles $\Delta ABC$ and $\Delta PQR$, $AB = QR, BC = PR$ and $CA = PQ,$ then :<br/>
Question 11 :
The solution of<br>$\displaystyle 0.2\left ( 2x-1 \right )-0.5\left ( 3x-1 \right )=0.4 $ is<br>
Question 14 :
Algebraic expression for the statement: $6$ times $a$ taken away from $40$
Question 17 :
A, B and c can do a piece of work in 12 days, 15 days and 10 days respectively. In what time will they all together finish it?
Question 18 :
If $x$ satisfies the inequalities $x + 7 < 2x + 3$ and $2x + 4 < 5x + 3$, then $x$ lies in the interval.
Question 19 :
Two numbers have the property that their sum is equal to their product. If one of the numbers is 6, what is the other number?
Question 20 :
$ \sqrt{2^x} = 32$ then $ \dfrac {x-1}{x} $ is equal to :
Question 24 : Eleven bags of wheat flour, each marked $5\: kg$, actually contained the following weights of flour $($in $kg):$<span class="wysiwyg-font-size-medium"><br/>$4.97,\,\,  5.05,\,\, 5.08,\,\,  5.03,\,\,  5.00,\,\,  5.06,\,\,  5.08,\,\,  4.98,\,\,  5.04,\,\, 5.07,\,\,  5.00$<p>Find the probability that any of these bags chosen at random contains more than $5\: kg$ of flour.</p>
Question 25 :
In a cricket match, a bats-woman hits a boundary $6$ times out of $30$ balls she plays. Find the probability that she did not hit a boundary.<br/>
Question 28 :
The mean of the median ,the mode,and the range of the following data are:<br/>$84,56,39,45,54,39,56,54,84,21,77,56$ 
Question 29 :
If the probability of an event of a random experiment is $P(E)=0$, then the event is called an impossible event is <br/>
Question 30 :
The mean of prime numbers between 20 and 30 is :<br><br>
Question 32 :
The mean age of a group of persons is 40.Another group has mean age 48. If the ratio ofnumber of persons in two groups is 5 : 3, thenmean age of all the persons in two groups is
Question 34 :
Oblique sketches of solid shapes can be drawn as per measurements on _____ paper.
Question 36 :
What cross-sections do you get when you cut a die vertically?
Question 39 :
The ratio of the number of sides of a square and the number of edges of a cube is
Question 40 :
In the following, state if them statement is true $(T)$ or false $(F)$<br/>A cube has twelve vertices. 
Question 41 :
One side of a parallelogram is 8 cm. If the corresponding altitude is 6 cm, then its area is given by
Question 42 :
The length of the arc of a sector having central angle $90$ degrees and radius 7 cm is 
Question 43 :
The lengths of two sides of a right angles triangle which contain the right angle are 'a' and 'b' respectively. Three squares are drawn on the three sides of the triangle on the outer side. What is the total area of the triangle and the three squares?
Question 44 :
From a circle of radius 7 cm the largest possible square is cut and removed Find the area of the remaining portion (in cm$\displaystyle ^{2}$)
Question 46 :
If the area of a rectangle is equal to the area of a square and if one side ($l$) of the rectangle is equal to the perimeter of the square, then the other side ($b$) of rectangle is _______ .
Question 47 :
If the length of circumference of a circle is $60$cm more than its diameter, then length of its circumference is?
Question 48 :
The perimeter of an equilateral triangle and a square are same then $\displaystyle \frac{area\,  of \Delta }{are\, of\ \square }=$
Question 49 :
A chess-board contains $64$ equal squares and the area of each square is $6.25 cm^2$. And inside border around the board is $2$ cm. wide. The length of the chess-board is
Question 50 :
The length of a rectangle is increased by $60\%$. By what percent would the width have to be reduced to maintain the same area?<br/>
Question 51 :
A square and an equilateral triangle triangle have equal perimeters. If the diagonal of the square is $12\sqrt{2}$ cm, then area of the triangle is
Question 52 :
The length of the diagonal of a quadrilateral is $40\;cm$ and the perpendicular drawn to it from the opposite vertices are $12\;cm\;and\;7.5\;cm$. Find the area of the quadrilateral.
Question 53 :
Find the area of a triangle ABC whose vertices are A(-2 ,2) B(5 ,2) and whose centroid is (1 , 3)
Question 54 :
The area of a triangle whose vertices are (1, 2), (-3, 4) and (-5, 6) is
Question 55 :
The C.P. of $10$ pens is equal to the selling price of $9$ pens. Find the profit percentage.
Question 56 :
A cloth merchant sold half of his cloth at 20% profit, half of the remaining at 20% loss and the rest was sold at the cost price. In the total transaction, his gain or loss will be:
Question 58 :
If the price of the eraser is reduced by 25%, a person can buy 2 more erasers for a rupee. How many erasers are available for a rupee ?
Question 59 :
Gauri went to the stationery stores and bought things worth Rs.25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax-free items?
Question 60 :
Mrs Rewari spends $25\%$ of her salary on house rent, $30\%$ on the education of her children and $40\%$ on household expenditure. Find her salary if she saves $Rs\ 1470$ per month.
Question 61 :
A certain sum amounts to Rs. 5,292 in two years and Rs. 5,556.60 in three years, interest being compounded annually. Find the rate of interest.
Question 62 :
A starts a business with Rs. 4000 and B joins him after 3 months with Rs. $16000 .$ Find the ratio of theirprofits at the end of year.
Question 63 :
A shopkeeper sells two T.V. sets at the same price. There is a gain of $20\%$ on one TV. and loss of $20\%$ on the other. State which of the following statements is correct<br/>
Question 64 :
Choose the correct answer from the alternatives given :<br/>A shopkeeper listed the price of goods at $30$% above the cost price. He sells half the stock at this price, one fourth of the stock at a discount of 15% and the remaining at $30$% discount. His overall profit is
Question 65 :
Shruti lent some money to Pallavi at $5$%  p.a. simple interest. Pallavi lent the whole amount to Niki on the same day at $\displaystyle 8\frac{1}{2}$%  p.a. In this transaction after a year, Pallavi earned a profit of Rs. $350$. Find the sum of money lent by Shruti to Pallavi.
Question 66 :
The population of a country increased by an average of $2$% per year from $2000$ to $2003$. If the population of this country was $2,000,000$ on December $31$, $2003$, then the population of this country on January $1$, $2000$, to the nearest thousand would have been
Question 67 :
The heights of 10 girls were measured in cm and the results are as follows:$135, 150, 139, 128, 151, 132, 146, 149, 143, 141$. What is the mean height of the girls?
Question 68 :
Find the mode of the data : 13, 16, 12, 14, 19, 12, 14, 13, 14.
Question 69 :
State whether True or False. The data 6, 4, 3, 8, 9, 12, 13, 9 has mean 9.
Question 74 :
Out of the following, the number which is not equal to $\frac{-8}{27}$ is
Question 76 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61cc1aa178c526e972caefe5.PNG' />
In the above figure,we see two circles with the same centre. The radius of the larger circle is 10 cm and the radius of the smaller circle is 4 cm.Find the area of the smaller circle.
Question 77 :
A garden is 90 m long and 75 m broad. A path 5 m wide is to be built outside and around it. Find the area of the path. Also find the area of the garden in hectare.
Question 78 :
Find the height of parallelogram when its base and area are 20cm and $246 cm^{2}$ respectively.
Question 79 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61cc1aa778c526e972caeffb.PNG' />
In the given figure, A circular flower bed is surrounded by a path 4 m wide. The diameter of the flowerbed is 66 m. What is the area of this path? (π = 3.14)
Question 80 :
Find the base of parallelogram when its height and area are 15cm and $154.5 cm^{2}$ respectively.
