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A box has 4 red socks and 6 yellow socks. What is the probability of picking a red sock?

In each of the following, one of the six stigonometric ratios is given. Find the values of the other trigonometric ratios.

(i) $sinA=\frac{2}{3}$

(ii) $cosA=\frac{4}{5}$

(iii) $tan\theta =11$

(iv) $sin\theta =\frac{11}{15}$

(v) $tan\alpha =\frac{5}{12}$

(vi) $sin\theta =\frac{\sqrt{3}}{2}$

(vii) $cos\theta =\frac{7}{25}$

(viii) $tan\theta =\frac{8}{15}$

(ix) $cot\theta =\frac{12}{5}$

(x) $sec\theta =\frac{13}{5}$

(xi) $cosec\theta =\sqrt{10}$

(xii) $cos\theta =\frac{12}{15}$

A child draws the figure of an aeroplane as shown. Here, the wings ABCD and FGHI are parallelograms, the tail DEF is an isosceles triangle, the cockpit CKI is a semicircle and CDFI is a square. In the given figure, BP $\perp$CD, HQ $\perp$FI and EL $\perp$DF. If CD = 8 cm, BP = HQ = 4 cm and DE = EF = 5 cm, find the area of the whole figure. [ Take $\pi$ = 3.14]

Find the mean of the following frequency distribution using step-deviation method.
$\begin{array}{cccccc}\text{Class}& 0-10& 10-20& 20-30& 30-40& 40-50\\ \text{Frequency}& 7& 10& 15& 8& 10\end{array}$

A bucket of height 24 cm is in the form of frustum of a cone whose circular ends are of diameter 28 cm and 42 cm. Find the cost of milk at the rate of Rs 30 per litre, which the bucket can hold.

In the figure, find the values of x and y hence show that $AB\parallel CD$. [3 MARKS]​

A circle is drawn with AB as the diameter whose endpoints are $A(2,4)$ and $B(4,12)$. If another circle with diameter one-third of the above circle is drawn with the same centre, what are the points that the circle cuts AB?

Among the given options, the point of intersection of the lines $x-y-1=0$, $4x+3y-25=0$ and $2x-3y+1=0$ is

6$x^2$ + ax + 7 when divided by x-2 gives remainder 13. Find the value of a.

A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby getting a sum of Rs 1008. If she had sold the saree at 10% profit and the sweater at 8% discount, she would have got Rs 1028. Find the cost price of the saree and the list price (price before discount) of the sweater.

Prove that the points (–3, 0), (1, –3) and (4, 1) are the vertices of an isosceles right angled triangle. Find the area of this triangle.
[4 MARKS]

Suppose a population A has 100 observations 101, 102,……200 and another population B has 100 observation 151, 152….., 250. If $V_A,V_B$ represent the variances of the two populations respectively, then $\frac{V_A}{V_B}$ is

Find the L.C.M. of $a^{2}bc,$ $a{b}^{2}c$ and $ab{c}^2$

Solve each of the following systems of eqautions by the method of cross-multiplication:

2x-y=6

x-y=2

The mid-point of a line segment $AB$ is $P(-3,3)$. If $A$ has coordinates $(-4,4)$, then the coordinates of point $B$ are

A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins,respectively.The dimension of the cuboid are $10cm\times 5cm\times 4cm$.The radius of each of the conical depression is 0.5 cm and the depth is 2.1 cm.The edge of the cubical depression is 3cm.Find the volume of the wood in the entire stand.

sin (A + B) = 1, cos (A – B) = 1, $0^{\circ }<A+B\le {90}^{\circ }$. Find the value of A and B.

A triangular advertisement board has sides 11m,15m and 6m. If the advertisement yields an earning of Rs$\frac{1000}{m^2}$ per month.So how much the company will earn in 3 and half years? [3 MARKS]

If three quantities are in continued proportion ; show that the ratio of the first to the third is the duplicate ratio of the first to the second.

Find a point on 2x + 3y = 10 which is at a distance of 2 units to the right of the Y axis

An equilateral triangle is reflected about one of its sides. The figure formed by the triangle and its reflection is

Solve the following systems of inequalities graphically:

$3x+4y\le 60,x+3y\le 30,x\ge 0,y\ge 0$

The measure of a line segment is known as its __.

Sum of zeroes of the polynomial $x^2-25$ is

The sum to n term of the AP 5, 2, -1, -4, -7, ... is $\frac{n}{2}(13-3n)$. State True/False.

A company with 10,000 shares of nominal value Rs 100 declares an annual dividend of 8% to the share-holders.

(i) Calculate the total amount of dividend paid by the company.

(ii) Ramesh has bought 90 shares of the company at Rs 150 per share. Calculate the dividend he receives and the percentage of return on his investment.

$\text{If}△ABC\text{is a right triangled with}\angle B={90}^{\circ },\text{and BD is perpendicular to AC,}\text{then AC}\times \text{DC will be equal to:}$

Find the values of p, q, r and s in the given cumulative frequency distribution.
$\begin{array}{ccc}x& \text{frequency}& \text{Cumulative frequency}\\ 10& 3& p=----\\ 15& 10& q=----\\ 20& 25& r=----\\ 25& 7& s=----\\ 30& 5& 50\end{array}$

Two tangents PA and PB are drawn to a circle with center O from an external point P. Prove that $\angle APB=2\angle OAB$ [3 MARKS]

What is forming square

A cone is of maximum size is carved out from a cube of edge $14cm.$ Find the surface area of the remaining solid after the cone is carved out.

1. 12

A steel box has dimensions of 2 m, 3 m, and 0.5 m. It has to be gold plated using electrolysis. If each square metre of gold plating costs Rs.100, then gold plating the outer surface of the box costs.

One of the factors of $x^3-2x^2+2x-1$ is

If $\frac{m+n}{m+3n}=\frac{2}{3}$, find $\frac{2n^2}{3m^{+}mn}$

Find the mean of the following data using step-deviation method:
$\begin{array}{ccccccc}\text{Class}& 500-520& 520-540& 540-560& 560-580& 580-600& 600-620\\ \text{Frequency}& 14& 9& 5& 4& 3& 5\end{array}$