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Question 54

Fill in the blanks to make the statement true.

___ $\times$ (-1) = 47

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 ___

Concentric circles have same

If $\frac{log\left(ab\right)}{logb}=\frac{3}{2}$,Given that b = 4, find the value of a.

Question 1 (i)
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
$x^2-2x-8$

Question 6
Give an example of a polynomial, which is:

(i) Monomial of degree 1.

(ii) Binomial of degree 20.

(iii) Trinomial of degree 2.

The base of a prism is an equilateral triangle of perimeter 15 cm and its height is 10 cm. What is its total surface area ?

The blood groups of 30 students of Class VIII are recorded as follows:
A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.
By representing this data in a frequency distribution table, find out the most common and the rarest blood group among these students.

What is the solution for the following pair of linear equations?

$\frac{1}{2x}-\frac{1}{y}=-1$

$\frac{1}{x}+\frac{1}{2y}=8$

(Where $x\ne 0,y\ne 0)$

The area of a parallelogram is 4 ares. Its base is 20 m. Find its height.

If $lo{g}_{10}x=ythenlo{g}_{1000}{x}^2$ is equal to

1. 10

Identify the following figure.

The value of $(243{)}^{\frac{1}{5}}$ is

(a) 3 (b)-3 (c) 5 (d)$\frac{1}{3}$

In the figure, O is the centre of the circle. If $\angle BOD={160}^{\circ }$, find the values of x and y.

If two sides of a triangle are 8 cm and 6 cm and its perimeter is 26 cm. Find the third side of the triangle.

In square ABCD, P and Q are the midpoints of sides AB and CD respectively. If AB = 8 cm and PQ and BD intersect at O, then find the area of $△OPB.$

Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where
$\left(px\right)=x^3-a{x}^2+6x-a,g\left(x\right)=x-a$

In the formula for mode of a grouped data,

mode $=l+\left[\frac{f_1-f_0}{2f_1-f_0-f_2}\right]\times h$ ,

where symbols have their usual meaning, $f_1$ represents ___.

Find the area of this right angled triangle.

How many digits are in between 500 and 600 which have only one 9 in them?

Which of the following is a row matrix?

A cuboid ABCDEFGH is anisotropic with

${\alpha }_x=1\times {10}^{-5}°C^{-1}$

${\alpha }_y=2\times {10}^{-5}°C^{-1}$

${\alpha }_z=3\times {10}^{-5}°C^{-1}$

Coefficient of superficial expansion of faces can be

Find the values of $a$ and $b$

if $\frac{5+2\sqrt{3}}{7+4\sqrt{3}}=a+b\sqrt{3}$

In the figure, if$AB\left|\right|CD,EF\left|\right|BC,$, $\angle BAC={65}^{\circ }$ and $\angle DHF={35}^{\circ },$ find $\angle AGH.$

If V is the volume of a cuboid of dimensions a, b, c and S is its surface area, then prove that

$\frac{1}{V}=\frac{2}{S}(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})$

If 37a = 37b = 5661, what is the average of a and b?

In the figure, O is the centre of the circle. If $\angle APB={50}^o$, find $\angle AOBand\angle OAB$.

O is any point in the interior of $\Delta ABC.$

Prove that

$\left(i\right)AB+AC>OB+OC$

$\left(ii\right)AB+BC+CA>OA+OB+OC$

$\left(iii\right)OA+OB+OC>\frac{1}{2}(AB+BC+CA)$

Pythagoras was a student of

(a) Euclid

(b) Thales

(c) Archimedes

(d) Bhaskara

If a + b + c = 0 and $a^2+b^2+c^2=16$, find the value of ab + bc + ca.

In a parallelogram ABCD, $\angle DAB={55}^{\circ }$. Find the angle $\angle CBA$.

The circus tent is in the shape of right circular cone, with base radius and height from the ground as 12 m and 16 m respectively. The area of tarpaulin required to make the tent is(Use $\Pi$ = 3.14)

The set of numbers which include both positive and negative numbers and do not have a fractional component and are denoted by letter $Z$ is known as ___

Solve:
$2x-9y=9,5x+2y=27$

P, Q and R are partners in a firm sharing profits in the ratio of 2 : 2 : 1. R retires and the Balance Sheet of the firm as at that date was as under :

BALANCE SHEET

As at .................

$\begin{array}{ccccc}\text{Capital and Liabilities}& & \text{Amount}& \text{Assets}& \text{Amount}\\ & & \text{Rs}& & \text{Rs}\\ \text{Creditors}& & 30,000& \text{Cash}& 8,000\\ \text{General Reserve}& & 60,000& \text{Debtors}& 75,000\\ \text{Profit \& Loss Account}& & 15,000& \text{Stock}& 90,000\\ \text{Workmen's Compensation}& & & \text{Plant}& 1,40,000\\ \text{Reserve}& & 10,000& \text{Patents}& 22,000\\ \text{Capital Accounts :}& & & & \\ P& 1,00,000& & & \\ Q& 80,000& & & \\ R& \underset{–}{40,000}& \underset{–}{2,20,000}& & \\ & & \underset{–}{\underset{–}{3,35,000}}& & \underset{–}{\underset{–}{3,35,000}}\end{array}$

It was agreed that stock is to be brought down to Rs 82,000 and plant is reduced by Rs 20,000. Patents were found valueless. There was no liability on account of workmen's compensation reserve.

Record necessary entries at the time of retirement.

If AD is a median of a triangle ABC, then AB + AC __________________

Given f(x) defined on f: R $\to$ R is a periodic function with the fundamental period 2 then f(3) is not equal to -

Prove that the sum of three altitude of a triangle is less than the sum of its sides.

In a$△ABC$, D, E and F are the mid points of sides BC, CA and AB respectively. If $ar\left(△ABC\right)=16c{m}^2,$ then ar(trapezium FBCE) =

For a circle of radius $r=\frac{10}{\pi }$ cm.
Angle subtended by arc $\theta ={12}^{\circ }$ .
What is the length of the arc in cm?

Five years hence a man’s age will be three times his son’s age. If the man's age is given by 'x' and his son's age by 'y', The correct equation is.

Directions:- Study the following information carefully to answer the question given below.

Eight persons — A, B, C, D, E, F, G and H are sitting around a regular octagonal table but not necessarily in the same order. Out of them, A and B are facing towards the centre of the table while the rest of them are facing outside. G sits second to the left of E. A sits second to the left of G. Only one person sits between A and H. B sits to the immediate right of A. D is not an immediate neighbour of G. B is not an immediate neighbour of G. Both the immediate neighbours of F face towards the outside.

Which of the following pairs represents the immediate neighbours of E?