A bag contains 4 white and 6 blue balls. If a ball is drawn at random, the probability that the drawn ball to blue is:
3/5
If a coin is tossed twice, the probability of getting at least one head is
3/4
The distance of a point (3, 3) from x-axis is
3 units
If an angle is 3 times its complementary angle, then the measure of the angle is
67.5°
If an angle of a parallelogram is four times of its adjacent angle, then these two angles of the parallelogram are
144°, 36°
Two sides of a triangle are 5 cm and 9 cm. Which of the following length can be the length of the third side?
13 cm
Positive rational number
Which of the following is a factor of the polynomial 2t4 + 3t3 – 2t2 – 9t – 12?
t2 – 3
The length of the chord of a circle is 30 cm and its distance from the centre is 8 cm. Then, the radius of the circle is
17 cm
Mode of data 24, 17, 13, 24, 26, 20, 26, 30, 8, 41, 24 is
24
Let the sides of a triangle be 4 cm, 7 cm and 11 cm, then area of the triangle is_____ cm2.
In geometrical figures, sides decide sizes and _____ decide shapes.
In geometrical figures, sides decide sizes and angles decide shapes.
An algebraic expression in which the variables involved have only non-negative integral powers is called a _________.
An algebraic expression in which the variables involved have only non-negative integral powers is called a polynomial.
The number of circle passing through three non-collinear points is ____.
The number of circle passing through three non-collinear points is one.
On comparing 4x – 17 = 23 y with ax + by + c = 0, the value of a + b + c is _____.
The given equation, 4x – 17 = 23 can be written as 4x – 23y – 17 = 0.
On comparing this equation with ax + by + c = 0, we
get, a = 4, b = – 23 and c = – 17
Then, a + b + c = 4 + (– 23) + (– 17)
= 4 – 40
= – 36
On comparing 4x – 17 = 23y with ax + by + c = 0, the value of a + b + c is –36.
If the graph of a polynomial y = p(x) intersects the x-axis at three points, then what is the number of zeros of p(x)?
The number of zeros is 3, as the graph intersects the x-axis at three points.
, then find x is rational or irrational number.
a rational number?
is non-terminating and non-recurring so it is not rational number.There are 4 kings in a deck of cards. Let E be the event of the card which is a king.
The number of outcomes favourable to E = 4
The number of possible outcomes = 52
Therefore,
P(a king) = (4/52)
= 1/13.
POR : ROQ = 5 : 7, find all the angles. 
Find the zeros of polynomial 2x2 - 8.
2x2 - 8 = 0
⇒ 2x2 = 8
⇒ x2 = 4
⇒ x = 2 and -2
Hence, 2 and -2 are the zeros of the polynomial.
.
Inner radius of well (r) = 8/2 m
= 4 m
Width of embankment = 3 m
Radius of well with embankment (R) = 4 + 3 = 7 m
Depth of well = 21 m
Volume of earth taken out from well = 
r2h
= (22/7)
(4)221
= 22163
= 1056 m3
Area of embankment = (R2 - r2)
= (22/7){(7)2 - (4)2}
= (22/7)113
= (726/7) m2
Height of embankment = (Volume of earth taken out from well)
(Area of embankment)
= 1056 / (726/7)
= (10567)
726
= 10.2 approx.
Area of quadrilateral ABCD = (area of 
ABD+ area of CDB)
Hence, area of quadrilateral ABCD = 35 cm2.
Factorise:
(i) 
= 4.79583 ……. [By square root method]
Which is non- terminating and non -recurring.
SO, by the decimal - expansion property of irrationals, is irrational.
(ii) 
Which is terminating.
SO, by the decimal expansion property of rational, 
is rational.
(iii) By the decimal expansion property of rational, 
is rational.
B=60
To Construct:-
ABC
Step 1. Draw a line segment AB 5.8 cm
Since 1 kg.=1000 gm
So, the weight of one cubic cm of wood is 62.89 gm and one cubic cm of sand is 101.01 gm.
Let the cost of 1 kg apples be x and the cost of 1 kg grapes be y.
According to the question, linear equation is
5x = 150 +7y
5x – 7y =150
It is the required equation.
Since the cost of one kg grapes is 70.
By putting y = 70 in the above equation,
we get
5x – 7(70) = 150
5x = 490 + 150
x = 640/5
= 128
Thus, the cost of 1 kg apples is 128.
. 
BCD) = ar(ACD)= 1/2ar(ABC) ...(i) (Median divides the triangle into two triangles of equal areas.) ar(DPQ) = ar(PDC) (Two triangles having same base and between same parallel lines are equal in area.)
ar(DPQ) + ar(BDP) = ar(PDC)) + ar(BDP)
ar(BPQ)= ar(BCD)
ar(BPQ) = 1/2ar(ABC) [ from (i)]
In PQR, PR>PQ
so, PQR>PRQ ...(1) [angle opposite to greater side is greater]
QPS=RPS ...(2) [PS is bisector of P]
Add QPS both sides of relation (1), we get
PQR+QPS>PRQ+QPS
PQR+QPS>PRQ+RPS [From equation (2)]
180°-PSQ>180°-PSR [By angle sum property]
-PSQ>-PSR
So, PSR>PSQ
PQT=TQR and PRT=TRS
To Prove:-QTR=(1/2)QPR
Proof:-In PQR,
Ext.PRS=PQR+QPR
2TRS=2TQR+QPR [Since TQ and TR are angle bisectors]
2(TRS-TQR)=QPR
TRS-TQR=(1/2)QPR ...(1)
In TQR,
Ext.TRS=TQR+QTR
TRS-TQR=QTR ...(2)
from equation (1) and equation (2), we have
QTR =(1/2) QPR
It is given that AS = SD = DA
Therefore, ASD is an equilateral triangle.
OA (radius) = 20 m
Medians of equilateral triangle pass through the circumcentre (O) of the
equilateral triangle ASD. We also know that medians intersect each other
in the ratio 2: 1. AB is the median of equilateral triangle ASD,
(OA/OB) = 2/1
(20/OB) = 2/1
OB = 10 m
AB = OA + OB = (20 + 10) m = 30 m
In ABD, 
ABD=90
, So by Pythagoras Theorem
AD2 = AB2 + BD2
AD2 = (30)2 + (AD/2)2
AD2 = 900 + (1/4)AD2
(3/4)AD2 = 900
AD2 = 1200
AD = 20
3
Therefore, the length of the string of each phone will be 203 m.
Construct a frequency polygon for the following data:
Age ( in years) Frequency 0-2 4 2-4 2 4-6 12 6-8 18 8-10 25
| Age ( in years) | Class marks | Frequency |
| 0-2 | 1 | 4 |
| 2-4 | 3 | 7 |
| 4-6 | 5 | 12 |
| 6-8 | 7 | 5 |
| 8-10 | 9 | 2 |
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