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The prodcut of two numbers is $16x^4-1$.If one number is 2x-1,find the other.

$(x+y{)}^3-(x-y{)}^3$ can be factorized as

Question 68

In the following question, state whether the given statement is true (T) or false (F).
1 is the identity for multiplication of whole numbers.

State division algorithm for polynomials.

IN the figure, ABCD is a trapezium in Which AB = 7 cm, AD = BC = 5 cm, DC = x cm, and distance between AB and DC is 4 cm.
Find the value fo x and area of trapezium ABCD.

If the mean of x + 2, 2x + 3,3x + 4,4x + 5 is x + 2, find x.

Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as under:
8, 4, 8, 5, 1, 6, 2, 5, 3, 12, 3, 10, 4, 12, 2, 8, 15, 1, 6, 17, 5, 8, 2, 3, 9, 6, 7, 8, 14, 12.

(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class interval as 5-10.

(ii) How many children watched television for 15 or more hours a week?

Mr. Batra invested an amount of Rs. 16500 in two different mutual funds A and B at the simple interest rate of 15% p.a. and 10% p.a. respectively. If the total amount of simple interest earned in 2 years is Rs. 3600, what was the amount invested in scheme B?

The point (15.2, -18.92) lies on the ___ quadrant.

Sides AB and AC of a $△$ ABC are equal. BC is produced through C upto point D such that AC = CD.

D and A are joined and produced (through vertex A) upto point E.

If $\angle$ BAE = ${108}^0$; find $\angle$ ADB.

The place values of 2 in 428721 is/are

Is it possible to construct a triangle ABC when BC = 7cm, ∠B = 60° and AB - AC = 13 cm?

The area of a square field is 8 hectares how long wooden men take to cross a diagonally by walking at the rate of 4 km per hour

A rabbit covers y metres distance by walking 10 metres in slow motion and the remaining by x jumps , each jump contains 2 metres.

Express the information in linear equation.

Chunnu and Munnu went to Ganesh sweets shop. At the shop, they saw two barfis of different shapes, but of same ingredients. One of them had a rectangular area of 4cm x 3cm and other a parallelogram, of size 4cm x 3cm. Both the barfis had same price. Chunnu took the rectangular barfi and Munnu took the parallelogram-shaped one. Who has more barfi by area?

The construction of a triangle ABC, given that BC = 6 cm, B = 45^o is not possible when difference of AB and AC is equal to :

If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

In ΔABC fig., ∠x + ∠y + ∠z is equal to :

The parallel sides of a trapezium are 12 cm and 16 cm and the perpendicular distance between them is 5 cm. Find its area

Which of the following numbers are the same as whole numbers?

The base of a prism is a right-angled triangle having base and altitude 3 and 4 cm respectively. The lateral surface area of the prism if the height of prism is 10 cm will be equal to_____

$\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\frac{1}{\sqrt{4}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{6}}+\frac{1}{\sqrt{6}+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{8}}+\frac{1}{\sqrt{8}+\sqrt{9}}=$__________.

In a map, a distance of 10 km on land is equal to $\frac{1}{10}cm$. If two places are $5\frac{1}{2}cm$ apart on the map, then what is the actual distance between them?

The length of the hypotenuse of a right triangle is $\sqrt{3}$ m.Lengths of other two sides are 1 m and $\sqrt{2}$ m respectively. To approximate the value of the new number $\sqrt{3}$, we need to select the numbers and square them to see if its equal to 3.which of the following is the range of numbers we can select?

The total surface area in $m^2$ of a cuboid with dimensions of 26m, 14m and 6.5m respectively is

If x + $\frac{1}{x}$ = 2, find the value of $x^{64}+\frac{1}{x^{64}}$

Question 73

In the following question, state whether the statement is True (T) or False (F):

$Factorisationof-3a^2+3ab+3acis3a(-a-b-c)$.

ABCD is a rectangle with O as any point in its interior. If $ar\left(△AOD\right)=3c{m}^2$ and $ar\left(△BOC\right)=6c{m}^2,$ then area of rectangle ABCD is

K, L, M and N are points on the sides AB, BC, CD and DA respectively of a square ABCD such that AK = BL = CM = DN. Prove that KLMN is a square.

In the figure , PQRS is a rhombus in which the diagonal PR is produced

$\angle SRT={152}^{\circ }$, find x, y and z.

If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube is

The value of $(249{)}^2-(248{)}^2$ is
(a) $1^2$ (b) $477$ (c)$487$ (d) $497$

Which of the following is an irrational number?

If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are _______(in degrees).

An equilateral triangle of side 9 cm is inscribed in a circle. Find the radius of the circle.

Find the coordinates of a point P on the line segment joining A(1, 2) and B(6, 7) in such a way that $AP=\frac{2}{5}AB$.

Find the value of k for which the polynomial x3-4x2+k has 3as it's zero

If the perimeter of a square is same as the circumference of a circle, then which of the following is true?

A wooden cask contains some tools i.e. exactly 12 nuts and 24 bolts. of each of these are defective. If 2 tools are picked up one after the other without replacement, then what is the probability that both are not defective?

Find the total surface area of a closed right cylinder whose radius is 14 m and height is 10 m.

Define adjacent angles.

Where does the orthocentre of a right angled triangle lie?