Question 1 :
Consider the following statements and identify which are correct:<br>i) A secant to a circle can act as a chord.<br>ii) A chord cannot be a secant to the circle.<br>
Question 2 :
If a diameter is drawn it divides the circle into____equal parts
Question 3 :
The radius of a circle is increased by 1 cm, then the ratio of the new circumference to the new diameter is
Question 4 :
The points $A,\,B\;and\;C$ be on a circle in such a way that the $\angle ABC=52^{\circ}$ and $\angle ACB=78^{\circ}$. The measure of the angle subtended at the centre by the arc $BC$ will be
Question 5 :
$\triangle ABC$ is inscribed in a circle. Point $P$ lies on the circle between $A$ and $C$. If $m(\text{arc}\, APC) = 60^\circ$ and $\angle BAC = 80^\circ$, find $m\angle ABC.$
Question 6 :
The polynomials $ax^3 + 3x^2 - 13$ and $ 2x^3 -5x+a$ are divided by $x+2$ if the remainder in each case is the same, find the value of $a$.<br/>
Question 7 :
The remainder when $x^{3} - 6x^{2} + 11x - 6$ is divided by $x + 2$ is<br>
Question 9 :
When $3x^{3} + 2x^{2} + 2x + k$ is divided by $x + 2$, the remainder is $4$. Calculate the value of $k$.
Question 10 :
Two parallelograms stand on equal bases and between the same parallels. The ratio of their areas is
Question 11 :
The measure of an angle of a parallelogram is $70^0$. Find its remaining angles.
Question 12 :
$ABCD$ is a square with centre $O$. If $X$ is on the side $CD$ such that $DX=DO$, find the ratio $\angle DOX:\angle XOC$
Question 13 :
In a $\triangle DEF$; $A,B$ and $C$ are the mid-points of $EF,FD$ and $DE$ respectively. If the area of $\triangle DEF$ is $14.4{ cm }^{ 2 }$, then find the area of $\triangle {ABC}$.
Question 14 :
If two sides of a parallelogram are $6$ and $8$ and one diagonal is $7$, what is the length of the other diagonal?
Question 15 :
The number of sides in a polygon of equal distance whose one interior angle is 108 will be
Question 17 :
What is the volume (in cu. cm) of a spherical shell with $8$ cm and $10$ cm as its internal and external diameters respectively?
Question 18 :
Find the volume of a sphere whose diameter is  $7.2$  mm.
Question 19 :
If the surface area of a sphere is $9856 cm^2$. Find its diameter.
Question 20 :
The shape of a solid is a cylinder surmounted by a cone. If the volume of the solid is $40656\space cm^3$, the diameter of the base is $42\space cm$ and the height of the cylinder is $20\space cm$, find the slant height of the conical portion.
Question 21 :
The ratio between the radius of the base and height of the cylinder is $2:3$. If the volume is $12936 cm^{3}$, what is the total surface area of the cylinder?
Question 22 :
If x – 1 is a factor of $p(x) = x^2 + x + k$ , k is-
Question 25 :
A card is drawn from a well shuffled deck of $52$ cards. Find the probability of getting a club card?
Question 26 : <p>The record of a weather station shows that out of the past $250$ consecutive days, its weather forecasts were correct $175$ times. What is the probability that on a given day it was correct?</p>
Question 27 : <p>Two dice are thrown. The number of sample points in the sample space when six does not appear on any one side is</p>
Question 28 :
A box contains $40$ red and blue marbles. If a marble is drawn at random, the probability of picking a blue marble is $\dfrac {3}{8}$. Ansh takes out one red and nine blue marbles and then draws a marble at random. Find the probability of drawing a blue marble
Question 29 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d1a8f59b460d7261f49b.JPG' />
In the above fig, A, B and C are three points on a circle with centre O such that ∠ BOC = 30° and∠ AOB = 60°. If D is a point on the circle other than the arc ABC, find ∠ADC.
Question 30 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d120f59b460d7261f3d6.PNG' />
In the above figure, two congruent circles have centres O and O′. Arc AXB subtends an angle of $75^{\circ}$ at the centre O and arc A′YB′ subtends an angle of $25^{\circ}$ at the centre O′. Then the ratio of arcs AXB and A′YB′ is
Question 31 :
State true or false: If P, Q and R are the mid-points of the sides BC, CA and AB of a triangle and AD is the perpendicular from A on BC, then P, Q, R and D are concyclic.
Question 32 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d20cf59b460d7261f52a.PNG' />
In the above fig, ABCD is a parallelogram in which P and Q are mid-points of opposite sides AB and CD. If AQ intersects DP at S and BQ intersects CP at R, then DPBQ is a ______________.
Question 33 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d207f59b460d7261f523.PNG' />
Using the above fig, we can say that the diagonals of a parallelogram ___________ each other.
Question 34 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d21ef59b460d7261f544.PNG' />
In the above fig, ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F. F ____________ BC.
Question 35 :
A coin is tossed 1000 times with the following frequencies: Head : 455, Tail : 545. Compute the probability of the event of getting a Head.
Question 36 :
Two coins are tossed simultaneously 500 times, and we get Two heads: 105 times, One head: 275 times, No head: 120 times. Find the probability of the event of getting two heads.
Question 37 :
In a diagnostic test in mathematics given to students, the following marks (out of 100) are recorded : 46, 52, 48, 11, 41, 62, 54, 53, 96, 40, 98, 44. Which ‘average’ will be a good representative of the above data?
Question 38 :
A total of 25 patients admitted to a hospital are tested for levels of blood sugar, (mg/dl) and the results obtained were as follows : 87, 71, 83, 67, 85, 77, 69, 76, 65, 85, 85, 54, 70, 68, 80, 73, 78, 68, 85, 73, 81, 78, 81, 77, 75. Find mode (mg/dl) of the above data.
