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The angle of elevation of the top of a tower from the top and foot of 100m building are ${30}^{\circ }and{45}^{\circ }$ respectively. The height of the tower is

A bicycle wheel has a diameter of 7 cm. What distance does the wheel cover on the ground if it completes 1 full rotation?

(Assume $\pi =\frac{22}{7}$)

If $cosec\theta -cot\theta =\frac{1}{2},0<\theta <{90}^{\circ }$ then $cos\theta$ is equal to _______.

Question 2

During the medical check-up of 35 students of a class, their weights were recorded as follows:

$\begin{array}{cc}Weight\left(inkg\right)& Numberofstudents\\ Lessthan38& 0\\ Lessthan40& 3\\ Lessthan42& 5\\ Lessthan44& 9\\ Lessthan46& 14\\ Lessthan48& 28\\ Lessthan50& 32\\ Lessthan52& 35\end{array}$

Draw a less than type ogive for the given data. Hence, obtain the median weight from the graph verify the result by using the formula.

In this series, you will be looking at both the letter pattern and the number pattern. Fill the blank in the middle of the series or end of the series.
$B_{2}CD$, ___ , $BC{D}_4$, $B_{5}CD$, $B{C}_{6}D$

A number consists of two digits whose sum is 9. If 27 is subtracted from that number the digits are reversed.Find that number.

In a $△ABC$, BD and CE are the altitudes. Prove that $△ADBand△AEC$ are similar. Is $△CDB\sim △BEC$ ?

A field is 80 m long and 50 m broad. In one corner of the field a pit which is 10 m long, 7.5 m broad and 8 m deep has been dug out. The earth taken out of it is evenly spread over the remaining part of the field. If the rise in the level of the field is x(in cm), then x-0.3 =

If f(x) is divided by g(x), g(x) ≠ 0 , then there exist two polynomials q(x) and r(x) such that

Given are the steps to construct tangents from an external point P to a circle with centre O. Order the steps correctly.

STEPS:

i) Join PM and PN.



ii) Draw a circle with centre as L and radius LO. Let it cut the given circle at points M and N.



iii) Bisect the segment OP, at L.



iv) Join OP.

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?

A circus artist is climbing a 20m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. The height of the pole is

On comparing the ratios, find out whether the lines representing the following pairs of linear equations at a point, are parallel or coincident:

Distance of the centre of mass of a solid uniform cone from its vertex is $z_0$. If the radius of its base is $R$ and its height is $h$, then $z_0$ is equal to.

Find the number of terms in each of the following APs:
$\left(i\right)7,13,\mathrm{19....},205$
$\left(ii\right)18,\frac{31}{2},13,...,-47$

The following table gives the distribution of the life time of 400 neon lamps:

$\begin{array}{cc}Lifetime\left(inhours\right)& Numberoflamps\\ 1500-2000& 14\\ 2000-2500& 56\\ 2500-3000& 60\\ 3000-3500& 86\\ 3500-4000& 74\\ 4000-4500& 62\\ 4500-5000& 48\end{array}$

Find the median life time of a lamp.

Given $U$ is the set of natural numbers between 11 and 19.

$A=\{x:x\text{is divisible by 3}\}$

$B=\{12,14,15,16\}$

Find $A\cap B$.

Question 3 (iv)

On comparing the ratios $\frac{a_1}{a_2}$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$ find out whether the following pair of linear equations are consistent, or inconsistent.

5x - 3y= 11 ; -10x+ 6y= -22