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Question 64

Fill in the blanks to make the statement true.

$(-225)÷5=$ ___

Classify the data in Q1 above as primary or secondary data.

What is $y=mx+c$? Explain

Convert the following fraction into decimal form:

$\frac{448}{2500}$

In ∆ABC, if L and M are points on AB and AC respectively such that LM || BC then ar (LMC) is equal to

In a triangle ABC if O is any point inside the triangle then prove that AB + BC + CA < 2 (AO + BO + CO ).

AB and CD are the chords of a circle whose center is O. They intersect each other at P. If PO is the bisector of $\angle APD$, prove that AB = CD. [2 MARKS]

Which of the following figures,you find polygons on the same base and between the same parallels?

If a+b+c=0 and |a|=3, |b|=4 and $|c|=\sqrt{37}$, the angle between a and b is

An organization selected $2400$ families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below:

Suppose a family is chosen, find the probability that the family chosen is (i) earning Rs $10000-13000$ per month and owning exactly $2$ vehicles.

(ii) earning Rs $16000$ or more per month and owning exactly $1$ vehicle.

(iii) earning less than Rs $7000$ per month and does not own any vehicle.

(iv) earning Rs $13000-16000$ per month and owning more than $2$ vehicles.

(v) owning not more than $1$ vehicle.

The ratio in which the line segment joining the points (1, – 7) and (6, 4) is divided by x-axis is

Question 8

In figure, if DEIIBC, find the ratio of ar $\left(\Delta ADE\right)$ and ar $\left(DECB\right)$.

Two rational number between√2 and √3

In the given figure, AB is the diameter of the circle with centre O. If $\angle COB={60}^{\circ },AC=AD,$ then $\angle ABD$ is equal to

Identify the correct diagram related to cross-multiplication method for following pair of equations.

$2x+3y=44$

$3x+5y=76$

In right triangle $ABC$, right angled at $C$, $M$ is the mid-point of hypotenuse $AB$.$C$ is joined to $M$ and produced to a point $D$ such that $DM=CM$. Point $D$ is joined to point $B$ (see the given figure). Show that:

(i) $\Delta AMC\cong \Delta BMD$

(ii) $\angle DBC$ is a right angle.

(iii) $\Delta DBC\cong \Delta ACB$

(iv) $CM=\frac{1}{2}AB$

Question 5 (ii)

Rationalize the denominator of :

$\frac{1}{(\sqrt{7}-\sqrt{6})}$ .

Let $\overrightarrow{a}=2\hat{i}+\hat{j}-2\hat{k}and\overrightarrow{b}=\hat{i}+\hat{j}.$ If $\overrightarrow{c}$ is a vector such that $\overrightarrow{a}.\overrightarrow{c}=|\overrightarrow{c}|,|\overrightarrow{c}-\overrightarrow{a}|=2\sqrt{2}$ and the angle between $(\overrightarrow{a}\times \overrightarrow{b})and\overrightarrow{c}is{30}^{\circ },then|(\overrightarrow{a}\times \overrightarrow{b})\times \overrightarrow{c}|$ is equal to

Identify constant, linear, quadratic, cubic and quartic polynomials from the following.

(i) $-7+x$

(ii) $6y$

(iii) $-z^3$

$(\text{cosec}\theta -\text{sin}\theta )(\text{sec}\theta -\text{cos}\theta )(\text{tan}\theta +\text{cot}\theta )=$ ___

How many numbers of measurements be sufficient to make a quadrilateral?

Solve: $30-(2\times 4)\times 3$

The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V, prove that $V^2=xyz.$

The sum of two numbers is $\frac{3}{4}$, one number is $\frac{1}{8}$. Find the other one.

Convert 0. 003522222... In the form of p/q

Find two numbers such that the larger number added to three times the smaller number gives 7 and twice the larger number added to the smaller number gives 9.

On a particular day, at a crossing in a city, the various types of vehicles going past during a time interval were observed as follows:

$\begin{array}{cccc}\text{Type of vehicle}& \text{Two-wheelers}& \text{Three-wheelers}& \text{Four-wheelers}\\ \text{Frequency}& 84& 68& 88\end{array}$

Out of these vehicles, one is chosen at random. What is the probability that the chosen vehicle is a two-wheeler?