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If (4,k) is a point on the line represented by the equation 3x - 4y = 8, then find the value of k.

If the vectors AB=$-3\hat{i}+4\hat{k}$ and AC=$5\hat{i}-2\hat{j}+4\hat{k}$ are the sides of a triangle ABC,then the length of median through the point A is

If $\text{sin}\theta =\frac{4}{5}$ and $\text{cos}\theta =\frac{3}{5},$ then $\text{tan}\theta$ = .

Question 5
In the given figure, PR > PQ and PS bisects $\angle$QPR. Prove that $\angle$PSR > $\angle$PSQ
.

If one angle of a parallelogram is ${24}^{\circ }$ less than twice the smallest angle, then the measure of the largest angle of the parallelogram is

Question 10
Let y varies directly as x. if y = 12 when x = 4, then write a linear equation. What is the value of y when x = 5?

$\frac{1}{2}\times \text{base}\times \text{height}$ is the formula for which type of triangles?

In the adjoining figure,the point D divides the side BC of $△ABC$ in the ratio m:n.Prove that $\left(△ABD\right):ar\left(△ADC\right)=m:n$.

Without actual division, prove that $2x^4-5x^3+2x^2-x+2$ is divisible by $x^2-3x+2$.

Various modes of transport used by 1850 students of a school are given below:
$\begin{array}{ccccc}\text{School bus}& \text{Private bus}& \text{Bicycle}& \text{Rickshaw}& \text{By foot}\\ 640& 360& 490& 210& 150\end{array}$
Draw a bar graph to represent the above data.

A cylindrical bucket with base radius 15 cm is filled with water up to a height of 20 cm.A heavy iron spherical ball of radius 9 cm is dropped into the bucket to submerge completely in the water.Find the increase in the level of water.

If a + b = 10 and ab = 16, find the value of $a^2-ab+b^{2}and{a}^2+ab+b^2$.

In the figure, $\angle AOC$ and form a linear pair. If $a-2b={30}^{\circ }$, find $a$ and $b$.

If two diameters of a circle intersect each other at right angles, then quadrilateral formed by joining their end points is a

Question 83

State whether the statement is True or False.

$(-19)\times (-11)=19\times 11$

Match the two columns
$\begin{array}{cc}Column-I& Column-II\\ \text{(A) The class mark of the class interval}& \left(p\right)13\\ 145-150is& \\ \text{(B) In a frequency distribution, the mid – value of a}& \left(q\right)110\\ \text{class is 10 and width of each class is 6. The upper}& \\ \text{limit of the class is}& \\ \text{(C) The mean of eight numbers is 40. If one}& \left(r\right)22.5–27.5\\ \text{number is excluded, their mean becomes}30.& \\ \text{The excluded number is}& \\ \text{(D) The class marks of a frequency distribution are}& \left(s\right)147.5\\ 15,20,25,30,\dots \dots \text{The class corresponding to the class}& \\ mark25is& \end{array}$
Choose the correct option:

Rectangle ABCD and ||gram PQRS lie between same base and same parallels.The ratio of their areas is

6x + 5y = 9, cuts the x-axis on which point?

Which one is Greater in the following

1- √2

2- cube root 3

3- cube root 4

4- cube root 2

What are the possible expressions for the dimensions of the cuboid whose volume is 3x^2-12x

S1 : $\frac{1323}{1400}$ is a non terminating decimal.
S2 : A number $\frac{p}{q}$ where p and q are co-primes is terminating if q is of the form $2^n{.3}^m$ where n and m are non-negative integers.

Find two rational number between $\sqrt{2}$ and $\sqrt{3}$.

AD is the median of the Δ ABC. Which of the following is true?

Can linear pair also be equal ?

how to manage money

Which of the following facilities are provided by banks?

Find the value of $k$, if $x–3$ is a factor of $p\left(x\right)=x^2–2x-k$.

The value of $lo{g}_6$ $\left(216\sqrt{6}\right)$ is equal to

$\overrightarrow{V}=2\hat{i}+\hat{j}-\hat{k}$ and $\overrightarrow{W}=\hat{i}+3\hat{k}$. If $\overrightarrow{U}$ is a unit vector, then the maximum value of the scalar triple product $\left[\overrightarrow{U}\overrightarrow{V}\overrightarrow{W}\right]$ is

Prove that the straight line joining the vertex of an isosceles triangle to any point in the base is smaller than either of the equal sides of the triangle.

In the given figure, $\angle PQR={100}^{\circ }$, where P, Q and R are points on a circle with centre O. Find $\angle OPR$.

If θ lies in the first quadrant, then we can find the value of other trigonometric ratios when

The author in the above passage-

If $x=\frac{1}{\sqrt{3}+1}$ then the value of $x+\frac{1}{x}$ is

What is Remainder TheormT

A certain sum of money amounts to Rs. 23,400 in 3 years at 10% per annum simple interest. Find the amount of the same sum in 2 years and at 10% p.a. compound interest.

Which of the following statements are true?

(i) Every whole number is a rational number.

(ii) Every integer is a rational number.

(iii) 0 is a whole number but it is not a rational number.

Seven cubes each of sides 4 cm are joined end to end. The volume of the resulting cuboid would be

P(x) is a polynomial of degree 4, and $P(x+2)-P\left(x\right)=x^3+3x^2+x+1$, What is the value of P(6), if P(2)=12?

A right circular cone has an altitude of $40cm$ and a diameter of $60cm.$ The slant height of the cone is