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The angle of elevation of the top of a building from the foot of the tower is ${30}^{\circ }$ and the angle of elevation of the top of the tower from the foot of the building is ${60}^{\circ }$. If the tower height is $60m$ high, find the height of the building.

The median of the distribution given below is 14.4. Find the values of x and y, if the total frequency is 20.
Class interval: 0-6 6-12 12-18 18-24 24-30
Frequency: 4 x 5 y 1

The probability to see the moon in the new moon day is ____.

The point P (3, 4) is reflected to P' in the x-axis; and O' is the image of O (the origin) when reflected in the line PP'. Write :

(i) the co-ordinates of P' and O'.

(ii) the length of the segments PP' and OO',

(iii) the perimeter of the quadrilateral POP'O',

(iv) the geometrical name of the figure POP'O'.

In a morning walk a man, a woman and a child step off together. Their steps measure 90cm,80cm and 60 cm. What is the minimum distance each should walk to cover the distance in complete steps?

The equation of the horizontal line passing through the point $(4,-7)$ is:

If h is the hcf of 4052 and 12576 and h= 4052*a+12576*b find the value of h+a+b

If $cos3\theta =\frac{\sqrt{3}}{2}$; $0<3\theta <{180}^{\circ }$, then value of $\theta$ is:

Asin has a recurring deposit account in a bank. He deposits ₹ 1500 per month for 2 years. If he gets ₹ 41,250 at the time of maturity. find :

i) the interest paid by the bank

ii) the rate of interest

The system of equations 4x -3y +12 =0 and 2x +3y -15 =0 has

The ratio of lateral surface areas of two cylinders with equal heights as 'h' and radii as 'R' and 'r' respectively is :

The diameter of a sphere is decreased by $25\%$. By what percent does its curved surface area decrease?

At an annual function of a school, each student gives gift to every other student. If the number of gifts is 1980 find the number of students.

The coordinates of the mid point of the line joining the point (3p,4) and (-2,2q) (5,p) find p and q

A sphere of radius 6cm is dropped into a cylindrical vessel partly filled with water. The radius of vessel is 8cm. If the sphere is submerged completely, then find the increase in level of water.

If p(x)=x+3 the p(x)+p(-x) is equal to

Two circles intersect each other at points A and B. A straight line PAQ cuts the circles at P and Q. If the tangent at P and Q intersect at point T; show that the points P, B, Q and T are concyclic.

If Sec(7-2a)=cosec(5a-7), then find the value of a.

If one zero of 3x²-8x+2k+1 is 7 times the other, find the value of k.

In the adjoining figure O is the center of the circle. $\angle$AOD = ${120}^{\circ }$. If the radius of the circle be 'r', then find the sum of the areas of quadrilaterals AODP and OBQC:

Explain why 7*11*13+13 and 7×6×5×4×3+5 are composite numbers.

If $A=\left[\begin{array}{cc}3& 7\\ 2& 4\end{array}\right],B=\left[\begin{array}{cc}0& 2\\ 5& 3\end{array}\right]$ and $C=\left[\begin{array}{cc}1& -5\\ -4& 6\end{array}\right]$
Find: AB - 5C

the 16th term of an A.P is one more than twice its 8th term. if the twelth term of the A.P is 47, then find its n th term?

Prove that any four vertices of a regular pentagon are concyclic (lie on the same circle).

^{Solve for x and y}

^{ax + by = 2ab}

bx + ay = a^{​​​​​​2} + b^{​​​​​​2}

^{​​​​​​}

A coin is tossed two times. Find the probability of getting at most one head.

Which of the following capitals is also known as specialised capital?

5, - 2, -9, -16, ... is an ___.

Rs.480 is divided equally among `x` children. If the number of children were 20 more then each would have got Rs. 12 less. Find `x`.

If a : b = 3 : 8, find the value of $\frac{4a+3b}{6a-b}$

The sum of n terms of two arithmetic progressions are in the ratio (3n + 8) : (7n + 15). What is the ratio of their 13th terms?

If the sum of first 10 natural numbers is $S_1$ and that of first 10 whole numbers is $S_2$ . Then $S_1-S_2$ is

In the figure given A, B, C and D are four points on the circumference of a circle with centre O. Arc AB = 2 arc BC and ∠AOB = 108⁰. Calculate and justify your answer.

A man invests Rs.9,600 on Rs.100 shares at Rs.80. If the company pays him 18% dividend find:

A solid sphere of radius 6 cm is converted into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 4 cm & its height is 72 cm, find the uniform thickness of the cylinder.

Solve the following equation:

(4x-8)/x-,8/(3x-3)=0

If (y-a) is factor of f(y) then ______ is a zero of f(y), select the appropriate blank.

The greatest possible number with which when we divide 37 and 58 , leaves the remainder of 2and three is....??

Find the value of k if the quadratic equation $x^2+4x-k=0$ has real and distinct roots.

If E represents an event, P(E) + P(E’) = __

If the area of a circle is equal to sum of the areas of two circles of diameters 10 cm and 24 cm, then the diameter of the larger circle (in cm) is :

In the given figure, AB and DE are perpendiculars to BC. If AB = 9cm, DE = 3cm and AC = 24cm then AD is equal to