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Question 80

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

The value of $(a+1)(a-1)(a^2+1)$ is $a^4-1$.

Prove that $△$AOD $\cong$ $△$BOC.

What is the best way to express $998$ so that $(998{)}^2$ can be calculated easily using an algebraic identity?

Select the equation whose graph is given alongside:

Ajit was asked to form the largest and the smallest five digit number by using digits 4, 9, 7, 2 and 1 without repeating any of the numbers. What is the difference between the largest and the smallest number thus formed?

Q6. Consider the following statements about Promoter pledging:

1. Promoter pledging refers to the practice of promoters giving their shares as collateral.

2. Promoters, in order to raise funds for either personal or company needs, pledge their holding shares to any financial institution.

Which of the above statements are correct?

ABCD is a paralleologram in which diagonal AC bisects $\angle BAD.$ If $\angle BAC={35}^{\circ }$, then $\angle ABC=$

If the length of a chord of a circle is 16 cm and is at a distance of 15 cm from the centre of the circle, then the radius of the circle is

$\text{Each of the two equal sides of an isosceles right triangle is 10 cm long. Its area is}\left(a\right)5\sqrt{10}c{m}^2\left(b\right)50c{m}^2\left(c\right)10\sqrt{3}c{m}^2\left(d\right)75c{m}^2$

If k is ratio of zeroes of the polynomial $4x^2-5x-3,$ then the value of ${(k+\frac{1}{k})}^{-2}$ is

Question 3 (i)

The relative humidity (in %) of a certain city for a month of 30 days was asfollows:

$\begin{array}{cccccccccc}98.1& 98.6& 99.2& 90.3& 86.5& 95.3& 92.9& 96.3& 94.2& 95.1\\ 89.2& 92.3& 97.1& 93.5& 92.7& 95.1& 97.2& 93.3& 95.2& 97.3\\ 96.2& 92.1& 84.9& 90.2& 95.7& 98.3& 97.3& 96.1& 92.1& 89\end{array}$

(i) Construct a grouped frequency distribution table with classes

84 - 86, 86 - 88,etc.

The difference between the upper limit and the lower class limits is called

If the area of an equilateral triangle is $9\sqrt{3}{cm}^2$. What is the length of the side of the triangle.

The surface area of a sphere of radius 7 cm is

If y = 2x + 3 and y = 5, then what is the value of x?

The sides of a square are 4 centimetres long. The midpoints of the sides are joined to form another square as shown below

What is the perimeter of the smaller square?

What is magnitude ?

Find the area of the figure ABCDE given below:

Area of a square of side 5 cm is

Find the area of the quadrilateral (in sq.units) as shown in the figure below. $\angle$EAB = $\angle$AED = 90°. Given that: AB + AE = 4 units and EC = 7 units.

1. 22

A man speaks truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.

$si{n}^2{24}^{\circ }-si{n}^2{6}^{\circ }=\frac{\sqrt{5}-1}{8}$

If 14.287628762876........ can be represented in $\frac{p}{q}$ form, then 'p - q ' is ________.

$In\Delta ABC,\angle C=\angle A,\text{BC = 4 cm and AC = 5 cm. Then, AB =?}\text{(a) 4 cm (b) 5 cm (c) 8 cm (d) 2.5 cm}$

In the figure, AB||CD||EF and GH||KL. Find $\angle HKL$.

Question 88

A square sheet of paper is converted into a cylinder by rolling it along its side. What is the ratio of the base radius to the side of the square?

A vessel is in the shape of a square prism, with each side of the base 16 centimetres long. It contains water 10 centimetres high. If a cube of side 8 centimetres is completely immersed in it, how high would the water level rise?

Question 1: Use the figure to name:

(a) Four rays

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Two angles are making a linear pair. If one of them is one-third of the other, then find the angles.

In the given figure, AM $\perp$ BC and AN is the bisector of $\angle$A. Then $\angle$MAN is