If \(\sqrt { 3 } =1.732\) and \(\sqrt { 2 } =1.414\) , the value of \(\frac { 1 }{ \sqrt { 3 } -\sqrt { 2 } } \) is:

For what value of a, is the polynomial \(x^3+2x^2-3ax-8\) divisible by x-4?

The distance of the point (1,0) from O is:

Any point on the line y = 3x is of the form:

John Playfair was a 

We can draw two different lines in

The symbol for correspondence is

ABCD is a rhombus such that \(\angle \)ABC=\(40°\) then \(\angle \)ADC is equal to 

In given figure, ABCD is a parallelogram. If ar(\(\Delta\)BFC) = 40 cm², then ar(\(\Delta\) AEB) is equal to:

A and B are points on the circle with centre O. If a chord CD of the circle subtends an angle of 50° at the point A on the circle and \(\angle BDC=70°\), then  \(\angle BCD\) equals:

The sides of a triangular park are in the ratio 25: 17: 12 and its perimeter is 540 m. Find the smallest side of the park.

The lateral surface area of a cuboid of length l, breadth b and height h is

The mean of 3,4,5,6,7 is

An experiment has two outcomes E and F P(E)+P(F) is equal to:

Find the rational numbers a and b such that \(\frac { 2+5\sqrt { 7 } }{ 2-5\sqrt { 7 } } =a+\sqrt { 7 } b\)

Write \((3a+4b+5c)^2\) in expanded form.

Plot the points A(6,6), B(4,4), C(-1,-1) in the Cartesian plane and show that the points are collinear.

Solve 4x - 7 = 9. Represent the solution
(i) on the number line
(ii) in the Cartesian plane.

In a triangle PQR, X and Y are the points on PQ are QR respectively. If PQ = QR and QX = QY, Show that PX = RY.

In figure if AB||CD||EF and x:y=3:2. Find z

D is any point on side BC of ΔABC, such that AD = AC. Show that AB > AD.

Two parallel lines I and m are intersected by a transversal ' t'.Show that the quadrilateral formed by bisectors of interior angles is a rectangle.

In the figure, the vertex A of \(\Delta \) ABC is joined to a point D on the side BC. The mid-point of AD is E. Prove that ar(\(\Delta \) BEC) =\(\frac { 1 }{ 2 } ar(\Delta ABC)\) 

PQRS is a cyclic quadrilateral, in which \(\angle P=2x°\), \(\angle Q=y°\), \(\angle R=3x°\) and \(\angle S=2y°\). Find the values of x and y. 

Construct a triangle of sides 3 cm, 3.5 cm and 5 cm. Bisect the smallest angle of the triangle.

Find the area of the triangle whose two sides are of measure 13 cm and 14 cm and perimeter is 42 cm.

The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20 cm and height 10 m, how much concrete mixture would be required to build 14 such pillars?

A family with monthly income of Rs 20,000 had planned the following expenditures per month under various heads:

Draw a graph for the data above.

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes

Compute the probability of getting
(i) less than 2 heads
(ii) 3 heads.

If a = 2 + √5 and b = \(\frac{1}{a}\), find a² + b²

Write the degree of the following polynomials:
5x³ + 4x² + 7x

Find the coordinates of the vertices of a rectangle placed in III quadrant, in the Cartesian plane with length 'p' units on x-axis and breadth 'q' units on y-axis.

Write four solutions for each of the following equations:
x=4y

In the given figure, if \(\angle1=\angle3, \angle2=\angle4\ and\ \angle3=\angle4\), write the relation between \(\angle1\ and\ \angle2\) using Euclid's axiom.

In the given figure, \(PO\bot AB\), If x:y:z=1:3:5, then find the degree measure of x,y and z.

Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.

ABCD is a parallelogram. P and Q are points on DC and AB respectively, such that \(\angle DAP=\angle BCQ\) .Show that AQCP is a parallelogram.

A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.

Draw AB = 6 cm. Construct an angle of \(30°\) at A and also draw the perpendicular bisector of AB.

A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and side 6cm each is to be made of three different shades as shown in figure. How much paper of each shade has been used in it?

If the lateral surface of a cylinder is 94.2 cm² and its height is 5 cm, then find
(i) radius of its base
(ii) its volume.

The length of 40 leaves of a plant are measured a correct one millimeter, and the obtained data is represented in the following table:

(i) Draw a histogram to represent the given data.
(ii) Is there any suitable graphical representation for the same data?
(iii) Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?

Given below is the frequency distribution of salary in Rs of 80 workers in a factory.

Find the probability that the salary of a worker selected at random is:
(i) Less than 4000
(ii) More than or equal to 3000
(iii) More than or equal to 2000 but less than 5000

Prove that \(\frac { 1 }{ 3+\sqrt { 7 } } +\frac { 1 }{ \sqrt { 7 } +\sqrt { 5 } } +\frac { 1 }{ \sqrt { 5 } +\sqrt { 3 } } +\frac { 1 }{ \sqrt { 3 } +1 } =1\)

State Factor theorem. Using Factor theorem, factorise x³-3x²-x+3.

Plot the points A(3,0), B(3,3) and C(0,3) in a Cartesian plane.Join OA, OB, BC and CO.Name the figure so formed and write its one property.

Rohit is driving his car at a uniform speed of 80 km per hour. Draw time-distance graph taking time along x-axis and distance along y-axis.

In the given figure AB = BC and BX = BY. Show that AX = CY. State Euclid's Axiom used.

If l,m,n are three lines such that l || m and n \(\bot \) l , then prove that n \(\bot \)m

In \(\triangle\)ABC and \(\triangle\)PQR, AB = PQ, AC = PR and altitude AM and PN are equal. Show that, \(\triangle ABC\cong \triangle PQR.\)

Show that the bisectors of angles of a parallelogram form a rectangle

PQRS and ABRS are parallelogram and X is any on side BR.Prove that
(i)area PQRS=are ABRS

(ii)area AXS=\(1\over2\) area ABRS
(iii)are AXS=\(1\over2\) area PQRS
(iv)Itwari comments that if X is the mid-point of BR, then area ABX = area SXR.Is he correct?Which value is depicted by his comments?
(iv)Write the formulae used in the solution

In the figure, diameter AB and a chord AC have a 'common end point A. If the length of AB is 20 cm and of AC is 12 cm, how far is AC from the centre of the circle?

(i)Construct a triangle XYZ in which \(\angle\)Y = 30°, \(\angle\)Z = 90° and XY + YZ + ZX = 11cm
(ii) Measure \(\angle\)XYZ
(iii)Measure \(\angle\)XZY
(iv)Measure XY
(v)Measure YZ
(vi)Measure Zx
(vii)Is XY+YZ+ZX=11cm?
(viii)Apala says that\(\angle\)YXZ=60⁰.Is she right?which value is depicted by her statement?

The base of an isosceles triangle measures 24 cm and its area is 60 cm², Find its perimeter.

The diameter of a cylindrical roller 120cm long is 84cm.It takes 500 complete resolution to level a playground.Find
(i)radius of roller
(ii)curved surface area
(iii)area of the playground levelled in one revoluation
(iv)area of the playground levelled in 500 revolution
(v)cost of levelling at TRs.7.50 per sq.m
(vi)Apala is confident that the volume of the roller is 665280 cm³.Is Apala correct?Which value is depicted by her confidence?
(vii)write the formulae used in the solution

The following table gives the pocket money (in Rs) given to children per day by their Parents:

Represent the data in the form of a historgram

The percentages of marks obtained by a student in examination are given below:

Find the probability that the student gets
(i) a first class i.e. at least 60% marks
(ii) a distinction i.e. 75% or above
(iii) marks between 70% and 80%

If x = 3-2√2, find the value of √x+\(\frac{1}{\sqrt{x}}\)

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.

Represent the following data by means of a frequency polygon.