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Question 1 (iii)

Without actually performing the long division, state whether $\frac{64}{455}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

The following are the steps for drawing a triangle of sides 4,5 and 6 cm and a square of the same area. Arrange them in the right order.

1) Draw a $\perp$ from C to AB and let it cut the semi circle at P and Q.

2) Construct the required square with PQ as its side.

3) Draw a $\Delta$ ABC with side 6cm, 5cm, 4cm with AB = 6cm, AC = 5cm, BC=4cm

4) Draw a semi -circle with AB as diameter. Draw IC||AB.

In the given figure, a rectangle $OABC$ is inscribed in a quadrant $OPBQ$. If $AB=8\text{cm}$ and $BC=6\text{cm}$, then area of shaded region is equal to (Use $\pi =3.14$)

The lines = 2, = 5, y = 3 & y = –4 form a rectangle. Find equations of its diagonals.

In a triangle $ABC,AB=8cm,\angle B={30}^{\circ },\angle A={45}^{\circ }$. The area of the triangle will be equal to.

In a class of 100 students, 12 students drink only milk and 5 students drink only coffee and 8 students drink only tea. Other report says 30 students take both coffee and tea, 25 students take milk and tea and 20 students take only milk and coffee. 10 students drink all the three. Find the number of students who do not drink anything.

Kevin hired a cab and followed the path as shown in the figure. if all the distances in the figure are in kilometres. The difference between the total distance and displacement covered by him is ___ km.

$\cos 1^{\circ }.\cos 2^{\circ }.\cos 3^{\circ }\dots \dots ..\cos {180}^{\circ }$ is equal to:

Prove that the points (2, – 2), (–3, 8) and (–1, 4) are collinear.

Prove that none of the polynomials listed below has first degree factors:

(i) x² + x + 1

(ii) x⁴ + 1

(iii) x² − x + 1

(iv) x⁴ + x² + 1

A man goes 80 m due east and then 150 m due north. How far is he from the starting point ?

A pole 6 m high casts a shadow $2\sqrt{3}$ m long on the ground, then find the angle of elevation of the sun.

The value of $r_1^2+r_2^2+r_3^2+r^2+a^2+b^2+c^2=$

(where $r=$inradius, $R=$circumradius, $r_1,r_2,r_3$ are radii of excircle of triangle $ABC$)

In the given diagram, find the area of segment PRQS. Sides OS and SQ have lengths a and b respectively. Let the area of circle be A.

Fint the roots of the following quadratic equations (if they exist) by the method of completing the square.

$x^2-(\sqrt{2}+1)x+\sqrt{2}=0$

In the figure below, $x={30}^{\circ }$. The value of 5y – 2x is ___

It is given that -1 is one of the zeros of the polynomial $x^3+2x^2-11x-12$. Find all the zeros of the given polynomial.

Let $A=\left[\begin{array}{cc}2& 1\\ 0& -2\end{array}\right],B=\left[\begin{array}{cc}4& 1\\ -3& -2\end{array}\right]$ and $C=\left[\begin{array}{cc}-3& 2\\ -1& 4\end{array}\right]$
Find: $A^2+AC-5B$

The quotient, when $5x^2+3$ is divided by $\frac{1}{x}+2$ is

1. 0.25

In the given figure, ABCD is quadrilateral in which diagonal BD = 24 cm, AL $\perp$ BD and CM $\perp$ BD such that AL = 9 cm and CM = 12 cm. Calculate the area of the quadrilateral.

By purchasing Rs 25 gas shares for Rs 40 each, a man gets 4 percent profit on his investment. What rate percent is the company paying ? What is his dividend if he buys 60 shares ?

There is a cylinder of base radius 3 cm and length 10 cm. Ram attaches a hemispherical attachment to each flat end of the cylinder having the same radius as the base radius of the cylinder. What is the surface area of the combined solid in $c{m}^2$ ?