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When the sun is at an elevation of ${35}^{\circ }$, the shadow of a tree is 10 m. What would be the length of the shadow, when the sun is at an elevation of ${25}^{\circ }$?

$\left[\begin{array}{c}Tan{25}^{\circ }=0.46\\ Tan{35}^{\circ }=0.7\end{array}\right]$

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?

A box of 15 chocolates has 6 that are caramel, 5 that contain nuts, and 4 that contain cashews. If you randomly select a chocolate, what is the probability that you will get one that contains nuts? [2 MARKS]

Two towers A and B of heights 200 ft and 150 ft respectively. The distance between the base of the towers is 250 ft. Two birds on top of each tower fly down with the same speed and meet at the same instant on the ground to pick up a grain. What is the distance between the foot of the tower A and the grain?

Use the suitable identity and simplify the given expression.$2(si{n}^6\theta +co{s}^6\theta )-3(si{n}^4\theta +co{s}^4\theta )+1$

A parachute is tied to a stone (A).Initially a man was there on parachute when it makes ${60}^{\circ }$ with the horizontal plane. After sometime the man ties the rope to himself and then jumps off from the parachute. At some point C man makes ${30}^{\circ }$ with the horizontal plane. From B, an imaginary line is drawn perpendicular to the ground so that it cuts AC (in the fig) in D. Distance BD is……………………………m

Which of the following theorems is a prerequisite for proving Apollonius Theorem?

The model of building is constructed with scale factor 1 : 30.

i) If the height of the model is 80 cm, find the actual height of the building in metres.

ii) If the actual volume of a tank at the top of the building is 27m³, find the volume of the tank on the top of the model.

Fourth term of a G.P is 3 and the product of the $3^{\text{rd}}$ and $8^{\text{th}}$ term is 243. Find its $7^{\text{th}}$ term.

In an equilateral triangle with side a, prove that area $=\frac{\sqrt{3}}{4}{a}^2$.

Draw a circle of any radius. From a point outside the circle, draw tangents to the circle inclined at 45${}^{\circ }$ to each other. [4 MARKS]

Find all pairs of consecutive odd natural number,both of which are larger than 10,such that their sum is less than 40.

Question 1 (iv)
In which of the following situations does the list of numbers involved make an arithmetic progression and why?
(iv) The amount of money in the account every year, when Rs. 10000 is deposited at compound interest at $8\%$ per annum.

Tangents are drawn from (4, 4) to the circle $x^2+y^2-2x-2y-7=0$ to meet the circle at A and B. The length of the chord AB is

$se{c}^4\theta -se{c}^2\theta$ is equal to

In the given figure, DC is diameter then $x$ = ___.

A takes 6 days less than the time taken by B to finish a piece of work. If both A and B together can finish it in 4 days, find the time taken by B alone to finish the work.

What is the most probable outcome for the sum of values when two dice are rolled? What is the probability of getting this outcome? [3 MARKS]

The following table shows the number of students sorted according to marks in Maths exam.

$\begin{array}{cc}\text{Marks}& \text{No. of students}\\ 30-40& 3\\ 40-50& 5\\ 50-60& 8\\ 60-70& 11\\ 70-80& 14\end{array}$

Find the Approximate Median Marks obtained by the students.

In a flag race, a pole is placed at the starting point, which is 10m from the first flag and the other flags are placed 6m apart in a straight line. There are 10 flags in the line. Each competitor starts from the pole, picks up the nearest flag, comes back up the next flag and continues the same way until all the flags are on the pole. The total distance covered is

In a class, following were the marks obtained by 20 students in a maths test.
20, 40 ,50 ,20 , 60 , 50 ,100, 20, 50, 100, 40, 60, 100, 50, 20 ,60, 100 , 50, 40 , 20. Make a frequency distribution table. [2 MARKS]

The number of polynomials having zeroes -2 and 5 is:

What is the probability of getting a sum of 13 when rolling a pair of dice?

$\sqrt{182.25}$ = ____.

Two isosceles triangles have equal angles and their areas are in the ratio 16 : 25. The ratio of corresponding heights is :

In the figure, the area of the portion in orange color is

Find the point that divides A(2, 4) and B(6, 8) in the ratio a : 1.

If the probability of happening of an event is $\frac{m}{n}$. The probability of event not happening is:

In parallelogram ABCD, A(0,-7), B(5,-7) and D(2,-2). Then the coordinates of C are

Which of the following is not an irrational number?

A box contains 10 red flowers, 6 white flowers, 4 pink flowers and 8 yellow flowers. Swetha picked a flower randomly from the box. What is the probability that Swetha picks a pink flower?

Diagonals AC and BD of a trapezium ABCD with AB ||DC intersect each other at the point O. Using similarity criterion for two triangles, show that $\frac{OA}{OC}=\frac{OB}{OD}$

25 circular plates, each of radius 10.5 cm and thickness 1.6 cm, are placed one above the other to form a solid circular cylinder. Find the curved surface area and the volume of the cylinder so formed.

The orthocentre of the triangle with vertices
$(2,\frac{\sqrt{3}-1}{2}),(\frac{1}{2},-\frac{1}{2})and(2,-\frac{1}{2})$ is

(i) One year ago, a man was 8 times as old. as his son. Now, his age is equal to the square of his son's age. Find their present ages.
(ii) A man is $3\frac{1}{2}$ times as old as his son. If the sum of the squares of their ages is 1325, find the ages of the father and the son.

For the following arithmetic progressions write the first term a and the common differnced:
(i) $-5,-1,3,7\dots$
(ii) $\frac{1}{5},\frac{3}{5},\frac{5}{5},\frac{7}{5},\dots$
(iii) $0.3,0.55,0.80,1.05,\dots$
(iv) $-1.1,-3.1,-5.1,-7.1,\dots$

$\frac{1+ta{n}^{2}A}{1+co{t}^{2}A}$ = ______.

Split 207 into three parts such that these parts are in A. P. and the product of the two smaller parts is 4623.

In the following figure, DE // AC and DC // AP. Prove that: $\frac{BE}{EC}=\frac{BC}{CP}.$