The value of \({ \left( 243 \right) }^{ \frac { 1 }{ 3 } }\) is equal to:

(x+2) is a factor of \(2x^3+5x^2-x-k.\) The value of k is:

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

The maximum number of points that lie on the graph of a linear equation in two variables is:

Two interesting lines cannot be parallel to the same line, is started in the form of:

The angle which exceeds its complimentary angle by \(30^{ 0 }\)

ΔABC ≅ ΔPQR.If AB = 5cm, ㄥB = 40⁰and ㄥA = 80⁰, then which of the following is true?

The quadrilateral formed by joining the mid-point of the sides of a rectangle taken in order is a

In the figure, ABCD is a square. E and F are midpoints of AD and BC respectively. The ratio of areas of \(\Delta\)GAB and \(\Delta\)HAB is:

In the given figure, AD || BC and \(\angle BCA=40°\). The measure of \(\angle DBC\) is equal to:

The area of a rhombus is 96 cm².If one of its diagonals is 16 cm, then the length of its sides is

The side of a cube is 1 cm. The total surface area of the figure formed by joining two such cubes is

The median of the distribution 2,3,4,7,5,1 is:

The following table depicts the scores of 200 students in a test:

Find the probability that a student selected at random has his score in the interval 650-700.

Are the following statements true or false? Give reasons for your answers.
(i) Every whole number is a natural number.
(ii) Every integer is a rational number.
(iii) Every rational number is an integer.

If 2 is a zero of polynomial \(4y^2-6y-k,\)find the value of k. Also, find the other zero.

Plot the points A(-3,-3), B(3,-3), C(3,3), D(-3,3) in the Cartesian plane.Also, find the length of the line segment AB.

Write  the following as an equation in two variables:
2x=3

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

In the given figure AB || C Find the value of x.

In the given figure, T is a point on the side QR of ΔPQR and S is a point such that TR = TS.Prove that PQ + PR > QS.

In the figure, points A and B are on the same side of a line i. AD \(\bot\)  l and BE \(\bot\) l at D  and E respectively. If C is the mid-point of AB, prove that CD = CE.

In the figure, ABCD is a parallelogram. P is a point on AB produced and \(DN\bot AB\) . If AB = 8 cm and DN = 3 cm. Find the area of \(\Delta \) CPD.

Two circles intersect at two points A and B. AD and AC are diameters of the two circles. Prove that 1),13, and C are collinear.

Draw an angle of an equilateral triangle,using protrator. Bisect it using compass

A triangle and a parallelogram have the same base and same area. If the sides of the triangle are 15 cm.14 cm and 13 cm and the parallelogram stands on the base 14 cm. find the height of the parallelogram.

A rectangular piece of paper is 22 cm long and 10 cm wide. A cylinder is formed by rolling the paper along its length. find the volume of the cylinder.

Find the median of the following observations:
46,64,87,41,58,77,35,90,55,92,33

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 2^xx4^x = (8)^1/3x(32)^1/5 then, find the value of x.

Factorize: 250x³-432y³.

Plot the points (x,y) given in the following table on the plane, choosing suitable units of distance on the axes.

Write three solutions of the equation 3x=y+3. Draw its graph and find the points where the graph intersects the axes.

In the given figure, if \(\angle BCD=25^0,\angle BAQ=110^o\ and\ \angle ACR=125^o\), then find the values of x, y, z.

Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of \(\angle PQR\) (see figure). Show that:
(i) \(\triangle ABM\cong \triangle PQN\) (ii) \(\triangle ABC\cong \triangle PQR\)

In a parallelogram PQRS of the given figure, the bisectors of ㄥP and ㄥQ meet SR at  O. Show that ㄥPOQ=90°

In \(\Delta \)PQR, A and B are points on sides QR such that they trisect QR, Prove that: ar(\(\Delta \)PQB) = 2ar (\(\Delta \)PBR)

In \(\Delta\)ABE, AE = BE. Circle through A and B intersects AE and BE at D and C. Prove that DC II AB.

Construct a triangle ABC in which \(\angle B=45°,\angle C=60°\) and AB + BC + CA = 12 cm.

The sides of a triangular park are in the ratio 3: 5:7 and its perimeter is 300 m. Find its area.

The radius and height of a cylinder are in the ratio 5:7. If its volume is 4400 cm³, find radius of the cylinder.

Draw a histogram of the following data:

Three coins are tossed simultaneously 250 times. The distribution of various outcomes is listed below:
(i) Three tails: 30
(ii) Two tails: 70
(iii) One tail : 90
(iv) No tail: 60
Find the respective probability of each event and check that the sum of all the probabilities is 1.

Express \(0.15\overline { 9 } \) in \(\frac { p }{ q } \) , where p and q are integers and \(q\neq 0\)

Find what must be subtracted from the polynomial 4y⁴+12y³+6y²+50y+26 so that the obtained polynomial is exactly divisible by y²+4y+2.

The perpendicular distance of a point from the x-axis is 2 units and the perpendicular distance from the y-axis is 3 units.Write the coordinates of the point if it lies in the:
(i) I quadrant
(ii) II quadrant
(iii) III quadrant
(iv) IV quadrant

Draw the graph of the linear equation \(y={2\over3}x+{1\over3}\).Check from the graph that (7, 5) is a solution of the linear equation

In the given figure, it is given that \(\angle \)1 = \(\angle \)4 and \(\angle \)3 = \(\angle \)2. By which Euclid's axiom, it can be shown that if \(\angle \)2 = \(\angle \)4, then \(\angle \)1 = \(\angle \)3.

Prove that the sum of of all the angles of a quadrllateral is \(360^{ 0 }\)

In the given figure, AD = BD. Prove that BD < AC.

ABCD is a parallelogram. Land M are points on AB and DC respectively such that
AL = MC. Prove that
(i) BL = DM
(ii) \(\Delta \)OBL \(\cong\) \(\Delta \)ODM
(iii) OB = OD
(iv) OL= OM
(v) LM and BD bisect each other.
(vi) Write the formulae used in the solution.
(vii) Apala ponders that  

In \(\Delta\)ABC, E is the mid-point of median AD. show that ar(\(\Delta\)BED) = \(\frac { 1 }{ 4 } ar(\Delta ABC)\)

In figure, EF is a line passing through the centre 0 of a circle. If EF bisects chords AB and CD of the circle, prove that AB || CD.

Construct a ΔABC in which BC = 4.7 cm,ㄥB = 45^o and AB - AC = 2cm

Find the area of a right-angled \(\Delta \)ABC, right angled at B in which AB = 24 metre and BC = 10 metre.

Find the curved surface area of a closed cylindrical petrol storage tank that is 3.8 m in diameter and 4.9 m in height.

Draw a frequency polygon to represent the following information:

A die is thrown 400 times.The frequency of outcomes of the events are given as under.

Find the probability of:
(i)Occurrence of an even number
(ii)Occurrence of an odd number
(iii)Occurrence of a number less than 2
(iv)Occurrence of a number greater than 2.
(v)Write the formula used.
(vi)Apala says that probability of occurrence of a multiple of 3 is \({8\over25}\) .Is she correct?Which value is depicted by her statement?

Find the value of \(\frac { { 3 }^{ 30 }+{ 3 }^{ 29 }+{ 3 }^{ 28 } }{ { 3 }^{ 31 }+{ 3 }^{ 30 }-{ 3 }^{ 29 } } \)

In figure, PQ = PR. Show that PS > PQ.

Ankush prepare a poster in the form of parallelogram, as in figure.
(i) If ㄥA=(5x + 7)° and LB = (3x- 3)°, find all the angles of a parallelogram ABCD.
(ii) Which mathemetical concept is used in this question?
(iii) By writing a slogan on poster which value is depicted by Ankush?

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?

A cone of height 24 cm has a curved surface area 550 cm². Find us volume.

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?