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(i) ${\left(\frac{sin{49}^o}{cos{41}^o}\right)}^2+{\left(\frac{cos{41}^o}{sin{49}^o}\right)}^2$

(ii) $cos{48}^o-sin{42}^o$

(iii) $\frac{cot{40}^o}{tan{50}^o}-\frac{1}{2}\left(\frac{cos{35}^o}{sin{55}^o}\right)$

(iv) ${\left(\frac{sin{27}^o}{cos{63}^o}\right)}^2+{\left(\frac{cos{63}^o}{sin{27}^o}\right)}^2$

(v) $\frac{tan{35}^o}{tan{55}^o}+\frac{cot{78}^o}{tan{12}^o}-1$

(vi) $\frac{sec{70}^o}{cosec{20}^o}+\frac{sin{59}^o}{cos{31}^o}$

(vii) $cosec{31}^o-sec{59}^o$

(viii) $(sin{72}^o+cos{18}^o)(sin{72}^o-cos{18}^o)$

(ix) $sin{35}^{o}sin{55}^o-cos{35}^{o}cos{55}^o$

(x) tan ${48}^{o}tan{23}^{o}tan{42}^{o}tan{67}^o$

(xi) $sec{50}^{o}sin{40}^o+cos{40}^{o}cosec{50}^o$

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs.18. Find the missing frequency f.

If $A=\left[\begin{array}{cc}2x^2& y\\ 3y& 8\end{array}\right]$ and $A^2=A\cdot \text{adj}\left(A\right),$ then the value(s) of $x+y$ can be

Find the area of metal sheet required in making a closed hollow cone of base radius 7 cm and height 24 cm.

$△ABC$ is such that $AB=3cm,BC=2cm$ and $CA=2.5cm.$ $△DEF$ is similar to $△ABC.$ If $EF=4cm$, then the perimeter of $△DEF$ is ____.

The area of a square park is the same as of a rectangular park. If the side of the square park is 60 m and the length of the rectangular park is 90 cm, find the breadth of the rectangular park

If cos $2\theta =sin4\theta$,where 2 $\theta$ and 4 $\theta$ are acute angles, find the value of $\theta$

A box contains cards numbered 3, 5, 7, 9, ..., 35, 37. A card is drawn at random from the box. Find the probability that the number on the drawn card is a prime number.

The following table shows data during a 1hr exam for a student.

$$\begin{array}{cc}Timeduringexam\left(mins\right)& Totalnumberofquestionssolvedintheexam\\ 0-10& 2\\ 10-20& 5\\ 20-30& 10\\ 30-40& 15\\ 40-50& 20\\ 50-60& 25\end{array}$$

Plot the less than type ogive curve and hence determine the median on the graph.

If $S$ is the sum of infinite terms of a G.P., whose first term is $a,$ then the sum of the first $n$ terms is ___.

How to prove that the square of an odd integer can express in the form of (8m+1), for some positive integer m?

The height of the cone is 5.6 cm and diameter of the base is 8.4 cm. Find the area of the curved surface.

O is any point inside a rectangle ABCD. Prove that $O{B}^2+O{D}^2=O{A}^2+O{C}^2$.

A bucket is in the form of a frustum of a cone with a capacity of 12308.8 $c{m}^3$ of water. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket. $[Use\pi =\mathrm{3.14.}]$

The equation of the line which forms an intercept of length 3 units on x-axis and an intercept of length 2 units on the negative y-axis, is

A sum of Rs $1000$ is invested at $12\%$ simple interest per year. Find the sum of all the interest generated every year for a period of $30$ years.

For the following distribution draw a 'less than type' ogive and from the curve find the median.

In the given right angle triangle if AC=10cm and $\theta$ = ${30}^{\circ }$ .The vertical height AB of given triangle is…………………cm

If $sin3A=cos(A-{10}^o)$ and $3A$ is acute then, find $\angle A$ .

If the equation $x^2+2(k+2)x+9k=0$ has real equal roots, then values of $k$ are

ABC is a triangle with D as mid point. Find AB

Find the area of triangle formed by the points A(5,2), B(4,7) and C(7,-4).

Let P(n): 2ⁿ < 4n, then which of the following is true?

Question 2
In a mathematics test given to 15 students, the following marks (out of 100) are recorded:
41,39,48,52, 46, 62,54, 40, 96,52,98, 40,42,52, 60
Find the mean,median and mode of this data.

During a practice match, a softball pitcher throws a ball whose height can be modelled by the equation $h=-16t^2+24t+1$, where h = height in feet and t = time in seconds. How long does it take for the ball to reach a height of 6 feet?

Write the value of tan $1^o$ tan $2^o$ ..... tan ${89}^o$.