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A dice is thrown, what is the probability of getting a number which is neither divisible by 2 nor 3?

Solve$\left[\begin{array}{cc}x& 1\end{array}\right]\left[\begin{array}{cc}1& 0\\ -2& -3\end{array}\right]\left[\begin{array}{c}x\\ 5\end{array}\right]=0$

Find the point on $y$-axis which is at a distance of 4 units from a point P(4,2).

How many tangents can be drawn to a circle from a point in its interior?

Question 4 (xiv)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(xiv) $1^2,3^2,5^2,7^2,\dots$

Solve for $x,\frac{x^2-2x}{x-2}=2$

State the midpoint theorem.

If a and b are two prime numbers then find LCM(a, b).

Compute the mean of the following data:
$\begin{array}{ccccc}\text{Class}& 1-3& 3-5& 5-7& 7-9\\ \text{Frequency}& 12& 22& 27& 19\end{array}$

A coin is tossed two times. Find the probability of getting both heads and both tails.

In the given figure chord AB extended meets tangent DC at C. If AB = 7cm and BC =9 cm and area of $△CBD=18c{m}^2$,

then area of $△CAD=$ ______

A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying the odd places. Find the common ratio of the G.P.

The length of the tangent to a circle from a point outside the circle measures 12 cm. The distance of the point from the centre is 15 cm.
Find the radius of the circle.

The chart shows the number of sunny days and the number of windy days in six months. Ratio of sunny days in june to windy days in october is

Three sets of English, mathematics and science books containing 336, 240 and 96 books respectively have to be stacked in such a way that all the books are stored subjectwise and the height of each stack is the same. How many stacks will be there ?

If sin $\theta$= cos $(\theta -{45}^o)$, where $\theta$ and $\theta -{45}^o$ are acute angles, find the degree measure of $\theta$

A motor boat whose speed in still water is 18km/hr takes 1 hour more to g 24km up stream that to return down stream to the same spot. Find the speed of the stream.

The point on x-axis which is equidistant from points A(-1, 0) and B(5, 0) is

(a) 0,2 (b)(2,0) (c)(3,0) (d) (0,3)

If sin$\theta$ = cos$\theta$, then value of $\theta$ is

Find the sum of all the 11 terms of an AP whose middle most term is 3ee0

In Fig. 8.66, tangents PQ and PR are drawn from an external point P to a circle with centre O, such that $\angle RPQ={30}^{\circ }$. A chord RS is drawn parallel to the tangent PQ. Find $\angle RQS$.

In $△ABC$, the coordinates of vertex A are (0, -1) and D (1, 0) and E (0, 1) respectively the mid-pointd of the sides AB and AC. If F is the mid -point of side BC, Find the area of $△DEF$.

The value of ${\log }_{e}144$ is.

Find the length of the arc of a circle of diameter 42 cm which subtends an angle of 60${}^{\circ }$ at the centre.

Question 108

Evalutate : $\left(0.3\right)\times \left(0.3\right)-\left(0.2\right)\times \left(0.2\right)$

If $A=\left(\begin{array}{cc}-6& -1\\ 9& 1\end{array}\right)B=\left(\begin{array}{cc}2& 0\\ -3& 5\end{array}\right)$ and $C=\left(\begin{array}{cc}-1& 8\\ 7& -7\end{array}\right)$
Find A-B+C

Question 30

Fill in the blanks to make each statement true:

Convert the statements adding 15 to 4 times x is 39 into an equation.

An expression in which the variables involved have only whole numbers as exponents is called a polynomial .then what are those expressions whose power is not a whole number ?

What is the smallest number which when divided by 35,56 and 91 leaves remainder 3 in each case

If A is a $3\times 3$ non-singular matrix such that $A{A}^T=A^{T}AandB=A^{-1}{A}^T,thenB{B}^T$ is equal to

Rs. 250 is divided equally among a certain number of children. If there were 25 children more, each would have received 50 paise less. Find the number of children.

A company pays a dividend of 15% on its ten rupee shares from which it deducts income tax at the rate 22%. Find the annual income of a man who owns one thousand shares of this company ?

The rates for the entrance tickets at a water theme park are listed below

What is the dimension of the matrix formed by listing the weekday and weekend rates along the column of the matrix?

Factorise :

$a(3a-2)-1$

By increaseing the cost of entry ticket to a fair in the ratio 10 : 13, the number of visitors to the fair has decreased in the ratio 6 : 5. In what ratio has the total collection increased or decreased ?

If α, β, γ be the zeros of the polynomial p(x) such that α + β + γ = 3, αβ + βγ + γα = -10 and αβγ =24, then p(x) is

Value of the below expresssion is

$\frac{1}{\sqrt[2]{26}+\sqrt[2]{25}}$ + $\frac{1}{\sqrt[2]{27}+\sqrt[2]{26}}$ + $\frac{1}{\sqrt[2]{28}+\sqrt[2]{27}}$

If the point A (0,2) is equidistant from the points B(3, p) and C(p, 5), find P. Also find the the length of AB.

Sum of probabilities of all outcomes in an experiment is__

The angle of elevation of the top of a hill at the foot of a tower is ${60}^{\circ }$ and the angle of depression from the top of the tower to the foot of the hill is ${30}^{\circ }$. If the tower is 50 m high, find the height of the hill.

Find the area of the shaded region in the figure given below, if ABCD is a square of side 14 $cm$ and APD and BPC are semicircles.
(Take $\pi =\frac{22}{7}$)