If \(\sqrt { x } \) is an irrational number, then x is:

In the polynomial \(1-\sqrt{11} x,\) the coefficient of x is:

The points (-5,2) and (2,-5) lie in the:

Graph of linear equation 2x+by+c=0, a≠0, b≠0 cuts x-axis and y-axis respectively at the points:

'Lines are parallel if they do not intersect' is stated in the form of:

In the following figure a transversal c intersects two parallel lines a and b The angles formed at A and B have been marked.Tell which pair of angles need not be equal?

In two triangles ABC and DEF, ㄥA = ㄥD, ㄥB = ㄥE and AB = EF, then are the two triangles congruent? If yes, by which congruency rule?

If only one pair of opposite sides of a quadrilateral are parallel, then the quadrilateral is a 

If a rectangle and a square stand on the same base and between the same parallels, then the ratio of their areas is

In the adjoining figure, O is the centre of the circle and P, Q and R are points on the circle such that \(\angle PQR=100°\), then  \(\angle OPR\) equals:

The sides of a triangle 40 cm, 70 cm, and 90 cm.The area of the triangle is

If the edges of a cuboid are l, b and h respectively, then the total surface area of the cuboid is

If the mode of 4,9,5,4,9,5,4,9, and x - 10 is 9, then value of is:

The following table shows the birthday of 30 students of class X:

Find the probability that student was born either on Tuesday or on Wednesday

Evaluate: \(\frac { \sqrt { 5 } +\sqrt { 3 } }{ \sqrt { 5 } -\sqrt { 3 } } \) , given that \(\sqrt { 15 } =3.87\)

Using identity find the following product \((2x-y+3z)(4x^2+y^2+9z^2+2xy+3yz-6zx)\)

Plot the points (0,-5) and (-2,5) in the coordinate plane.

Write  the following as an equation in two variables:
5y=2

Consider the following statement: There exists a pair of straight lines that are everywhere equidistant from one another. Is this statement a

If (3x-\(58^{ 0 }\)) and (x+\(38^{ 0 }\)) are supplementary angles,find x and the angles.

PS is an altitude of an isosceles triangle PQR in which PQ = PR. Show that PS bisects \(\angle P\)

In a parallelogram PQRS, if \(\angle \)QRS=2x, \(\angle \)PQS=4x, and \(\angle \)PSQ=4x, find the angles of the parallelogram.

ABCD is a parallelogram with area 80 sq. cm. The diagonals AC and BD intersect at O. P is the mid-point of OA. Calculator ar (\(\Delta\)BOP).

If two intersecting chords of a circle make equal angles with the diameter passing through their point of intersection, prove that the chords are equal.

Construct a \(\Delta \)ABC in which BC = 7.5 cm, \(\angle B=45°\) and AB - AC = 4 cm.

Sanya has a piece of land which is in the shape of a rhombus. She wants her one daughter and one son to work on the land and produce different crops to suffice the needs of their family. She divided the land in two equal parts. If the perimeter of the land is 400 m and one of the diagonals is 160 m, how much area each of them will get?

A hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is 17.6 cm, find the cost of painting it, given the cost of painting is Rs 5 per 100 cm². \(\left( Take\ \pi =\frac { 22 }{ 7 } \right) \)  

Consider a small unit of a factory where there are 5 employees: a supervisor laborers. The laborers draw a salary Rs 5,000 per month each while the supervisor gets Rs 15,000 per month. Calculate the mean, median, mode of the salaries of this unit of the factory.

A die is thrown 1000 times with the frequencies of outcomes 1,2,3,4,5, and 6 as given below:

Find the probability of getting each outcome

Find \({ 125 }^{ 1/3 }\)

Factorize: 9x²+y²+z²-6xy+2yz-6xz. Hence, find its value when x=1, y=2 and z=-1.

In which quadrant or on which axis do each of the points (-2,4), (3,-1), (-1,0), (1,2) and (-3,-5) lie?Verify your answer by locating them on the Cartesian plane.

Draw the graph of the following linear equations in two variables:
y=3x

Does Euclid 's fifth postulate simply the existence of parallel lines? Explain.

In the figure AB||CD and DE||PF. If \(\angle APF=50^o\) and \(\angle CDG=40^o.\) Find
\((i)\angle AQD\)
\((ii)\angle EDG\)
\((iii) \angle DPF\)

In the figure, if AF = CD are \(\angle\)AFE = \(\angle\)CDE, prove that EF = ED.

In the figure, ar (\(\Delta\)DRC) = ar(\(\Delta\) DPC) and ar(\(\Delta\)BDP) = ar(\(\Delta\)ARC). Show that both the quarilaterals ABCD and DCPR are trapeziums.

If the non-parallel sides of a trapezium are equal, prove that it is cyclic.

Construct a right triangle whose base is 4 cm and sum of its hypotenuse and other side is 8 cm.

Find the cost of leveling a ground in the form of a triangle with sides 40 m, 70 m and 90 m at Rs.4 per square metre. (Use\(\sqrt { 5 } \) = 2.24).

A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of Rs 16 per 100 cm². 

company manufactures car tyres of a particular type. The lives (in year) of 40 such tyres are as follows:
2.6,3.0,3.7,3.2,2.2,4.1,3.5,4.5,3.5,2.3,32, 3.4,3.8,3.2, 4.6,3.7,2.5,4.4,3.4, 3.3,2.9,3.0,4.3,2.8,3.5,3.2,3.9,3.2, 32,3.1,3.7,3.4,4.6,3.8,32,2.6,2.5,42,2.9,3.6
Construct a continuous grouped frequency distribution for the above data of equal class size and with first class interval as 2 - 2.5, (2.5 is not included)

Cards with numbers 1,2,3, ..., 100 are placed in a box and mixed thoroughly. One card is drawn, what is the probability that the card drawn is:
(i) a prime number less than 30
(ii) a multiple of 5 and 7 
(Iii) a multiple of 5 or 7

Rationalize the denominator of \(\frac { 1 }{ 2+\sqrt { 3 } } \)

The polynomials bx³+3x²-3 and 2x³ - 5x+b when divided by x-4, leave the remainders R₁ and R₂ respectively. Find the value of b, if 2R₁-R₂=0.

Plot the following points on the graph sheet: A(-3,-4), B(-2,0), C(-1,4), D(1,0).These points lie in which quadrant or axes?

Express x=3y in the form ax+by+c=0 and indicate the values of a, b and c.Write two solutions of the equation.

In the fig, we have \(\angle1=\angle3 \ and\ \angle2=\angle4.\) Show that \(\angle A= \angle C.\) State which axiom you use here. Also give two more axioms other than the axioms used in the above situation.

In figure AP and DP are bisectors of two adjacent angles A and D of a quadrilateral ABCD Prove that 2 \(\angle APD=\angle B+\angle C\)

In figure OA = OB, OC = OD and \(\angle AOB=\angle COD\). Prove that AC = BD

ABC is an isosceles triangle in which AB = AC AD bisects \(\angle \) PAC and CD II AB. Show that
(i) \(\angle \) DAC =\(\angle \) BCA
(ii) ABCD is a parallelogram

ABCD is parallelogram as shown is figure. O is any point on AC. PQ||AB and LM||AD. show that ar(DLOP)=ar(BMOQ).

PQ and RS are two parallel chords of a circle whose centre is O and the radius is 10 cm. If PQ = 16 cm and RS = 12 cm, find the distance b/w PQ and RS when they lie,
(i)On the same side of centre O.
(ii)On the opposite sides of centre O.

(i) Construct a triangle ABC in which BC = 5 cm, ㄥB = 45°and AB - AC= 2.8cm.
(ii) Measure AB.
(iii) Measure AC
(iv) Verify that AB - AC = 2.8 cm.
(v)Hari comments that ㄥACB = 112°. Is he true? Which value is depicted by comment of Hari?

An isosceles triangle has perimeter 30 m and each of the equal sides is 12 cm.Find area of the triangle.

A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface area [surface area of 8 new cubes and the original cube]

Find the median of the following data:
95,65,75,70,75,100,50,40.

On  a particular day, the number of vehicles through a crossing is given below:

 A particular vehicle is chosen at random. What is the probability that it is not a four-wheeler?

Geetha told her classmate Radha that "\(\sqrt { \frac { \left( \sqrt { 2 } -1 \right) }{ \left( \sqrt { 2 } +1 \right) } } \) is an irrational number." Radha replied that "you are wrong" and further claimed that "If there is a number 'x' such that x³ is an irrational number, then x⁵ is also irrational". Geetha said, "No Radha, you are wrong". Radha took some time and after verification accepted her mistakes and thanked Geetha for pointing out these mistakes. 
(i) Justify both the statements.
(ii) What value is depicted from this question?

For spreading the message "Save Girl Child Save Future" a rally was organized by some students of a school. They were given triangular cardboard piece PQR which they divided in to two parts by drawing the angle bisectors QO and RO of base angles Q and R and wrote a slogan. Prove that \(\angle\)QOR = 90° + \(\frac{1}{2}\)\(\angle\)P. What is the benefit of these types of rallies?

In the given figure ABCD is a parallelogram and E is the mid-point of AD. A line through D, drawn parallel to EB, meets AB produced at F and BC at L Prove that
(i) AF = 2DC
(ii) DF = 2DL

Three students Priyanka, Sania and David are protesting against killing innocent animals for commercial purposes in a circular park of radius 20 m. They are standing at equal distance on its boundary by holding banners in their hands.
(i) Find the distance between each of them?
(ii) Which mathematical concept is used in it?
(iii) How does an act like this reflects their attitude towards society?

Two solid spheres made of the same metal have masses 5920 g of and 740 g respectively. Determine the radius of the larger sphere, if the diameter of the smaller sphere is 5 cm.

The % of marks obtained by students in the annual examination of a class in mathematics are given below:

(i) How many students get less than 30% of marks?
(ii) Represent the data by histogram.
(iii) Which value is depicted by a student Ram obtaining the highest marks in the interval 45-50?