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If $\theta$ is any acute angle, what is the area of a square with adjacent sides $sin\theta$ and $tan\theta$?

Find the range of values of x, which satisfy :

$-\frac{1}{3}\le \frac{x}{2}+1\frac{2}{3}<5\frac{1}{6}$

Graph, in each of the following cases, the values of x on the different real number lines :

(i) $x\in W$ (ii) $x\in Z$ (iii) $x\in R.$

A number sequence which leaves the remainder 0 on dividing by 7 is

The ratio of the sum and the product of the roots of $5x^2–14x+8=0$ is ___.

Question 1 (viii)
Solve the following pairs of equations by reducing them to a pair of linear equations:
$\frac{1}{3x+y}+\frac{1}{3x-y}=\frac{3}{4}$
$\frac{1}{2(3x+y)}-\frac{1}{2(3x-y)}=\frac{-1}{8}$

Question 2 (ii)
On comparing the ratios $\frac{a_1}{a_2}$ , $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$ , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.
9x + 3y + 12 = 0
18x + 6y + 24 = 0

ABCDE is a cyclic pentagon with centre of its circumcircle at point O such that AB = BC = CD and angle ABC = ${120}^o$.

Calculate :

(i) $\angle$ BEC (ii) $\angle$ BED

If two rectangles ABCD and PQRS whose sides are parallel to the coordinate axes are drawn as shown in below figure then the coordinates of 'D' is ___

If one root of a Quadratic equation is m + √2 , then the other root is

1. 4

Arrange the polynomials in the increasing order of their degree (bottom to top).

The value of $\tan 1^{\circ }\tan 2^{\circ }\tan 3^{\circ }......\tan {89}^{\circ }$ is

$△ABD\sim △PQS$ and AD and PS are the medians, then

In a triangle ABC, $\angle A={40}^{\circ },\angle B={80}^{\circ },AB=8cm.$ as shown in figure. The length of the two sides AC $\&$ BC is equal to $\left[\begin{array}{c}sin{40}^{\circ }=0.64\\ sin{60}^{\circ }=0.86\\ sin{80}^{\circ }=0.98\end{array}\right]$

What is the maximum and minimum distance of the point (9, 12) from the circle $x^2+y^2-6x-8y-24=0$

Class mark of a class interval 30-38 is

If $\frac{PQ}{QR}=\frac{YZ}{ZX}$ and $\frac{QR}{PR}=\frac{ZX}{YX}$ , then

Refer to the following figure:

Which line segment depicts the “height” of point A from the base BE?

Given that ∠ADE = ${90}^{\circ }$ and ∠ABC = ∠AEB

In the equation ax+by+c=0, how many different ways can you express x in terms of y?

How many such points exists that are at a distance k from point P, which are also on the locus of the line ax + by + c = 0.

Prove:$\frac{\cot A+cosecA-1}{\cot A-cosecA+1}=\frac{1+\cos A}{\sin A}$

why should a variable have a exponent which is a whole number, to be called as polynomial? why can't the exponent be fraction like x^1/2 or negative number like x^-2?

From the given table, find the rarest blood group.

$\begin{array}{cc}\text{Blood Group}& \text{Frequency}\\ \text{AB}& 6\\ \text{A}& 5\\ \text{B}& 3\\ \text{O}& 1\\ \text{Total}& 15\end{array}$

Identify the identity matrix from the given list

Find the equation of straight line joining the point of intersection of 3x-y+9 = 0 and 2y +x -4 = 0 and the point of intersection of 2x+y = 4 and 2y = x +3.

Six bells commence tolling together and toll at intervals of $2,4,6,8,10,12$ minutes respectively. In $30$ hours, how many times do they toll together ?

Find two numbers such that the sum of twice the first and thrice the second is 92,and four times the first exceeds seven times the second by 2.

Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.

A carton consists of 100 shirts of which 88 are good and 8 have minor defects, Rohit, a trader, will only accept the shirts which are good. But, Kamal, an another trader, will only reject the shirts which have major defects. One shirts is drawn at random from the carton. What is the probability that it is acceptable to (i) Rohit and (ii) Kamal?

If $\alpha$ and $\beta$ are the zeros of the polynomial $f\left(x\right)=6x^2+x-2$, find the value of $(\frac{\alpha }{\beta }+\frac{\beta }{\alpha }).$

In Fig. an equilateral triangle ABC of side 6 cm has been inscribed in a circle. Find the area of the shaded region. (Take $\pi =3.14$)

The difference of area of two squares is A. The difference of their perimeters is p. Then the sum of their perimeters is

P(x)=ax^2+bx+c, if a+b+c=0, find one of its zeroes.

A Technician has to repair a light on a pole of height 10 m. She needs to reach a point 1 m below the top of the pole to undertake the repair work. What should be the length of the ladder that she should use which, when inclined at an angle of ${60}^{\circ }$ to the ground, would enable her to reach the required position? Also, how far from the foot of the pole should she place the foot of the ladder?

A car made a run of 390 km in `x` hours. If the speed had been 4 km/hour more, it would have taken 2 hours less for the journey. Find `x`.

Ritu can row downstream 20km in 2 hours and upstream 4km in 2hours . Find her speed of rowing in still watervand the speed of the current