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In ch .1

A question

to simplify

64^1/3(64^1/3 - 64^2/3)

in this the solution is given as

= (4^3)^ -1/3[ ( 4^3)^1/3 - (4^3)^2/3 ]

how -1/3 came ?

The triangular side walls of a fly-over have been used for advertisements. The sides of the walls are 122m, 22m and 120m. The advertisements yield an earning of Rs. 5000 per m² per year. A company hired one of its walls for 3 months. The rent paid by the company is

The abscissa or x-coordinate of any point on Y-axis is:

There is hollow cube. Its external edge is 5 cm long and its internal edge is 3 cm long. What is its surface area in $c{m}^2$ ?

If the slant height and base radius of a right circular cone are 6.5 and 3.5 respectively, the total surface area of the cone is___(Take $\pi =22/7$ )

If the vertices of a quadrilateral be A=1+2i B=-3+i C=-2-3i and D=2-2i, then the quadrilateral is

Identify the following figure:

Multiplication of $6\sqrt{5}$ and $2\sqrt{5}$ is

If the verticles of a rectangle are (0,3),(0,0) and (4,0), the length of its diagonals are ____

In the figure a small square is inserted inside the bigger square. The area of the shaded region of the square is__ sq.cm.

Sum of the measure of an angle and its vertically opposite angle is always.

A wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?

If a tank is in the shape of a right circular cylinder whose radius and height are 7 cm and 14 cm respectively, then the capacity of cylinder is ___ $\times {10}^{-4}{m}^3$. Give the answer up to 2 decimal places.

What is the length of an arc which subtends angle $\theta$ (degrees) at the center in a circle of radius r?

A point C is said to be lie between the points A and B if

(a) AC=CB

(b) AC+CB=AB

(c) points A,C and B are collinear.

(d) none of these

In the given figure, O is the centre of a circle and $\angle AOB={130}^{\circ }.Then,\angle ACB=?$

(a) ${50}^{\circ }$

(b) ${65}^{\circ }$

(c) ${115}^{\circ }$

(d) ${155}^{\circ }$

Factorise:
$x^2+7\sqrt{6}x+60$

Which of the following expressions are polynomials? In case of a polynomial, write its degree.

(i) $x^5-2x^3+x+\sqrt{3}$

(ii) $y^3+\sqrt{3}y$

(iii) $t^2-\frac{2}{5}t+\sqrt{5}$

(iv) $x^{1000}-1$

(v) $\frac{1}{\sqrt{2}}{x}^2-\sqrt{2}x+2$

(vi) $x^{-2}+2x^{-1}+3$

(vii) $1$

(viii) $\frac{-3}{5}$

(ix) $\frac{x^2}{2}-\frac{2}{x^2}$

(x) $\sqrt[2]{22}{x}^2-8$

(xi) $\frac{1}{2x^2}$

(xii) $\frac{1}{\sqrt{5}}{x}^{\frac{1}{2}}+1$

(xiii) $\frac{3}{5}{x}^2-\frac{7}{3}x+9$

(xiv) $x^4-x^{\frac{3}{2}}+x-3$

(xv) $2x^3+3x^2+\sqrt{x}-1$

In th figure, for which value of x is $l_1\left|\right|l_2$?

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

In the given figure, AB || CD. If $\angle CAB={180}^{\circ }$ and $\angle EFC={25}^{\circ }$ then $\angle CEF=?$

$\left(a\right){65}^{\circ }$

$\left(b\right){55}^{\circ }$

$\left(c\right){45}^{\circ }$

$\left(d\right){75}^{\circ }$

If AB and CD are the smallest and largest sides of a quadrilateral ABCD, then what is the relation between $\angle$B and $\angle$D?

Solve $tan(\frac{\pi }{4}+\frac{1}{2}co{s}^{-1}\frac{a}{b})+tan(\frac{\pi }{4}-\frac{1}{2}co{s}^{-1}\frac{a}{b})$

If $x+y=12$ and $xy=32$, find the value of $x^2+y^2$.

Solve for '$x$' and '$y$', using the method of substitution:
$4x+3y=12$; $x-3y=9$.

If a linear equation has solutions (–3, 3), (-1,1), (1, -1) and (3, – 3), then find the X and Y intercepts of the graph of that equation.

If the pair of linear equations $kx–y=5,x+ky=5$ has a unique solution $(x=2,y=1)$, then the value of k is ____.

How many outcomes are there for tossing 3 coins simultaneously?

If a polynomial $(x^2+ax-c)$ cuts x-axis at $2$ and $-4$, the value of $a+c$ is ___

In a triangle, halves of two equal side is are equal or not ?

Following are the ages (in years) of 360 patients, getting medical treatment in a hospital:

$\begin{array}{ccccccc}\text{Age}& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70\\ \text{(in years)}& & & & & & \\ \text{Number of patients}& 90& 50& 60& 80& 50& 30\end{array}$

One of the patients is selected at random.

What is the probability that his age is

(i) 30 years or more but less than 40 years?

(ii) 50 years or more but less than 70 years?

(iii) 10 years or more but less than 40 years?

(iv) 10 years or more?

(v) less than 10 years?

If the sides of a triangle are produced in order, prove that the sum of the exterior angles so formed is equal to four right angles.

When 2 is subtracted from $p\left(x\right)$, we get a polynomial whose factors are $(x+2)$ and $(x+3)$. What is $p\left(x\right)$ ?

If a universal set $U=\{3,4,5,6,7,8,9,10,11,12\}A=\{4,6,8,10,12\}B=\{3,5,7,9,11\}$ then $(A\cup B{)}^{\prime }$ is

A ball is chosen from the bag that contains 30 balls numbered from 1 to 30. What is the probability that the ball chosen will have a number that is divisible by 3?
[1 MARK]

Which of the following algebraic expressions explain the following

$\frac{1}{2}$ + $\frac{1}{3}$ = $\frac{5}{6}$

In a programming assignment, the instructor found that 26 people take 2-3 hours, 34 people take 3-4 hours, and 20 people take more than 4 hours to finish an assignment. What is the probability that the assignment can be done in 4 hours or less?

In a given figure of parallelogram ABCD,

$\angle BAC=$.