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A vertical pole of 10 m casts a shadow of 8 m at certain time of the day. What will be the length of the shadow cast by a tower standing next to the pole, if its height is 110 m?

Verify Mean Value Theorem, if $f\left(x\right)=x^2-4x-3$ in the interval $[a,b]$ , where $a=1$ and $b=4$

Find the nature of the roots and hance solve $a^2+8a+16=0$

The table below shows the number of students in class 10 of a school, classified according to their heights:

Calculate the mean height

If 2 is a zero of the polynomial find k p(x)=x³-2kx²+kx-x

In the given figure, A,B,C,D are points on a circle centred at O.The lines AC and BD are extended to meet at P and lines AD and BC intersect at Q. Then prove that $\angle APB+\angle AQB=\angle AOB$.

1. 5

cos0. Cos1...... cos44. Cosec45. Cosec46...... Cosec90 is equal to

An arithmetic sequence has its

$5^{th}$ term equal to 22 and its

${15}^{th}$ term equal to 62. Find the

${100}^{th}$ term

Draw a circle of radius $3cm$. From a point$P,7cm$ away from it centre draw two tangents to the circle. Measure the length of each tangent.

From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are ${30}^{\circ }and{45}^{\circ }$ respectively. If the bridge is at a height of 2.5 m from the banks, find the width of the river. [Take $\sqrt{3}=\mathrm{1.732.}$]

Find the circumference of the circle from the figure.

(Take $\pi$ as $\frac{22}{7}$)

Question 20

Fill in the blanks to make each statement true:

9x- ............... =-21 has the solution (-2).

$\Delta ABC$ is right angled at C with sides AB = 10 cm and AC = 6 cm. Find tan B.

A die is thrown once,the probability of getting an even prime number is___

Prove that √2. is an irrational number by contradiction method

Find the quadratic equation whose roots are the additive inverses of the roots of the equation $x^2-5x+6=0$.

Shubham painted $\frac{2}{3}$ of the wall space in his room. His sister Madhavi helped and painted $\frac{1}{3}$ of the wall space. How much did they paint together?

Find the radius of the circle with centre O. PT is a tangent and AB is perpendicular to PT. PA and PB is 4 cm and 2 cm respectively.

Question 1 (ii)

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

$p\left(x\right)=x^4-3x^2+4x+5,g\left(x\right)=x^2+1-x$

Solve;

5(2u+v)=9uv and 5(u+3v)=13uv, where u and v are not equal to zero

A line that intersects a circle in exactly one point is called a

A Retailer sells Television at Rs 25,000 to the shopkeeper and charges 10% tax. If the retailer pays a VAT of Rs 200 to the government, find the price inclusive of tax at which Retailer bought the T.V. from the wholesaler.

The following table records the number of books read by fifteen year old kids. Find the median of the data.

$\begin{array}{cc}\text{No. of books}& \text{Frequency}\\ 0& 2\\ 1& 4\\ 2& 7\\ 3& 4\\ 4& 2\\ 5& 0\\ 6& 1\\ 7& 8\\ 8& 13\\ 9& 7\\ 10& 2\end{array}$

A cylindrical jar of radius 6 cm contains oil. Iron spheres each of radius 1.5 cm are immersed in the oil. How many spheres are necessary to raise the level of the oil by two centimetres ?

Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 9 cm.

The ratio of the length of a rod and its shadow is $1:\sqrt{3}$. The angle of elevation of the sun is _________ .

Find the roots of the equation: x-5=0