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Factorise each of the following:

(i) (ii)

(iii) (iv)

(v)

Find the logarithm of log₄16

The solution set of the following system of equations $2x-3y+6=0$ and $6x+y+8=0$ also satisfies the equation :

Following are the observations made by ram 7, 7, 7, 7, 7, x. If the range of the given observations is 0, then what is the value of x.

Candidates of 5 schools appear for a Maths test. The data is given as follows:

$\begin{array}{ccc}\text{Schools}& \text{No.of Candidates}& \text{Score}\\ A& 60& 75\\ B& 48& 80\\ C& -& 55\\ D& 40& 50\\ E& 50& 60\end{array}$

If the average score of the candidates is 64.8, find the number of candidates who appeared from School C.

If the probability of getting heads is the same as the probability of getting tails when you toss a coin, then both of these probabilities are equal to?

Factorise 6x² 17x+10 by splitting method

If the volume of a sphere is equal to the volume of the hemisphere, the ratio of the radius of the sphere to the radius of the hemisphere is .

The numbers 52,53, 54, 54, (2x+1), 55, 55, 56,57 have been arranged in an ascending order and their median is 55. Find the value of x and hence find the mode of the given data.

What is the minimum possible value of the probability of an event?

To construct a parallelogram given its length of diagonals, which of the following additional information is required?

Question 35

State whether the given statement is True or False.

If line PQ || line m, then line segment PQ || m.

If the bisector of the angles of the lines represented by $3x^2-4xy+5y^2=0$ and $5x^2+4xy+3y^2=0$ are same, then the angle made by the lines represented by first with the second, is

In which quadrant would the coordinates of any point have their abscissae and ordinates with the same signs?

Factorize: $x^2-7x+12$.

Which of the following options correctly match, when the subject of the given formula is change to m?

2p = 3q + $\sqrt{5p^2-m}$

Represent the following quantity of muffins as a fraction.

If $f\left(x\right)=\{\begin{array}{cc}{x}^3+1,& x<0\\ x^2+1,& x\ge 0\end{array},g\left(x\right)=\{\begin{array}{cc}(x-1{)}^{\frac{1}{3}},& x<1\\ (x-1{)}^{\frac{1}{2}},& x\ge 1\end{array}$ then (gof) (x) is equal to

What number should be added to $x^2+6x$ to make it a perfect square?

Question 39

The range of the data 6, 8, 16, 22, 8, 20, 7, 25 is ___.

Question 20

When two quantities x and y are in ___proportion or vary ___, they are written as $x\propto \frac{1}{y}$.

Express the ratios $cosA$ and $sinA$ respectively in terms of $tanA$.

Find the value of (x-a)³+(x-b)³+(x-c)³-3(x-a)(x-b)(x-c) when a+b+c=3x

If lifting the pen and overlapping the line is not allowed, then which of the following figure cannot be drawn?

check whether g(x) is a factor of p(x)

p(x)= 8x³-6x²-4x+3

g(x)= x/3-1/4

In the given figure, O is the centre of a circle and chords AC and BD intersect at E. If $\angle AEB={110}^{\circ }and\angle CBE={30}^{\circ }then\angle ADB=?$

(a) ${70}^{\circ }$

(b) ${60}^{\circ }$

(c) ${80}^{\circ }$

(d) ${90}^{\circ }$

Given that $y=\frac{(cx+d)}{b}\text{,where}b\ne 0.$



$\text{If}ax+by+c=0\text{, where}(a+c)\ne 0$,

then what is the value of $x$ ?

The value of ${\left({\left(\frac{3}{2}\right)}^{-1}\right)}^{-2}$ is

Find the cost of putting grass beds on a pathway having area of 200 square meters at 0.1 paise per square cm.

Find the ratio of $Ar\left(\Delta DPQ\right)$ and $Ar\left(\square ABCD\right)$.