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Find the value of $\frac{sec{29}^{\circ }}{cosec{61}^{\circ }}$ + $2cot{8}^{\circ }cot{17}^{\circ }cot{45}^{\circ }cot{73}^{\circ }cot{82}^{\circ }$.

If the quadratic equation $(1+m^2)x^2+2mcx+c^2-a^2=0$ has equal roots, prove that $c^2=a^2(1+m^2)$.

Volume of a cylinder is 3080 cc and height is 20 cm. Calculate the radius of the cylinder.

Question 10
Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are ${60}^{\circ }$ and ${30}^{\circ }$, respectively. Find the height of the poles and the distances of the point from the poles.

Represent the given statement in the form of inequation

Twice the length of a rectangle is less than area of the rectangle ; if length is represented using $l$ and area is represented using A.

The steps to convert an irregular class interval into a regular one, are

Step 1: Compute correction factor which is $\frac{\text{upper class limit-lower class limit of previous class interval}}{2}$.

Step 2: This is added to the upper limit and subtracted from the lower limit of each class.

In the given figure, O is the center of the circumcircle of triangle ABC. Tangents at A and B intersect at T. If $\angle ATB={80}^{\circ }$ and $\angle AOC={130}^{\circ }$, Calculate $\angle CAB$. [4 MARKS]

Find the image of point (4, -6) under the following operations :

(i) $M_x.M_y$ (ii) $M_y.M_x$

(iii) $M_o.M_x$ (iv) $M_x.M_o$

(v) $M_o.M_y$ (vi) $M_y.M_o$

Write down a single transformation equivalent to each operation given above.

State whether :

(a) $M_o.M_x$ = $M_x.M_o$

(b) $M_y.M_o$ = $M_o.M_y$

If B is
the mid point of
and
C is the mid point of,
where A, B, C, D lie on a straight line, say why AB = CD?

The ${17}^{th}$ term of an AP exceeds its ${10}^{th}$ term by 7. Find the common difference.

If the areas of two similar triangles are equal,then prove that they are congruent.

The Manager, Mr. Rehman, strictly adheres to the organisational plan that lays down a maximum of 10 $\%$ discount to be offered to customers on sale of goods. But Mr. Rehman could not provide a 10.5 $\%$ discount on a large order to an old customer Mr. Ram when he demanded a discount. The firm lost the large order and hence incurred losses.

(i) Which two limitations of planning are reflecting here?

(ii) How can this limitation be overcome?

In a $\Delta ABC$, if D is a point on BC such that $\frac{BD}{DC}=\frac{AB}{AC}$, then which of the following is always correct?

The distribution of height of 50 children is given. If the mean height for the distribution is 117.8 cm, then complete the following table.
$\begin{array}{ccccccc}Height& 110& 115& x_1& 120& 121& 125\\ Numberofstudents& 6& 8& 14& f_1& 4& 3\end{array}$

Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are of the corresponding sides of the first triangle.

Give the justification of the construction.

$\Delta ABC\sim \Delta DEF$ such that ar $\left(\Delta ABC\right)$ = 64 $c{m}^2$ and ar $\left(\Delta DEF\right)=169c{m}^2$. If BC = 4 cm, find EF.

If $pcot\theta$ = $\sqrt{q^2-p^2}$, then the value of $sin\theta$ is ___.

The multiples of 2, written in order given 2, 4, 6, 8, …… Is this an arithmetic sequence? What about the powers 2, 4, 8, 16, …… of 2?

Mr. Suraj invested Rs 29,040 in 15% Rs 100 shares quoted at a premium of 20%. Calculate:-

i) Mr. Suraj’s income from the investment.

ii) The percentage return on his investment

Question 14(iv)

50 students enter for a school javelin throw competition. The distance (in metres) thrown are recorded below :



$\begin{array}{cccccc}Distance\left(inm\right)& 0-20& 20-40& 40-60& 60-80& 80-100\\ Numberofstudents& 6& 11& 17& 12& 4\end{array}$





Are the median distance calculated in (ii) and (iii) same?

If $A=\left[\begin{array}{cc}3& 1\\ -1& 2\end{array}\right]$ and $I=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],$ then the correct statement is

There is a pack of 52 cards. Ram removes the queen of hearts and the jack of spades from this pack. Ram now picks a card at random from this reduced pack. What is the probability that Ram picks is a Jack card?

150 spherical marbles, each of diameter 1.4 cm are dropped in a cylindrical vessel of diameter 7 cm containing some wate, which are completely immersed in water. Find the rise in the level of water in the vessel.