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A machine was purchased 2 years ago. Its value decreases by 10 % every year. Its present value is ₹ 97200. Find the purchase price of the machine

To construct an angle of ${60}^{\circ }$ with a compass and ruler,

Steps of construction are:
Step1: Draw a ray AB
Step 2 will be

Fill in the blanks so as to make the following statements true:
(i) If one angle of a linear pair is acute, then its other angle will be___.
(ii) A ray stands on a line, then the sum of the two adjacent angles so formed is ___.
(iii) If the sum of two adjacent angles is ${180}^{\circ }$, then the ___ arms of the two angles are opposite rays.

Fill in the blanks to make the following statements true.

(i) In a right triangle, the hypotenuse is the ___ side.

(ii) The sum of three altitudes of a triangle is ___ than its perimeter.

(iii) The sum of any two sides of a triangle is ___ than the third side.

(iv) If two angles of a triangle are unequal, then the smaller angle has the ___ side opposite to it.

(v) The difference of any two sides of a triangle is ___ than the third side.

(vi) If two sides of a triangle are unequal, then the larger side has ___ angle opposite to it.

Represent $\frac{1}{3}$ in decimal form.

Find the value of x from the given figure, in which O is the centre of the circle.

Make a bar graph

$\begin{array}{cc}\text{Weight (kg)}& \text{Number Of Students}\\ 35.5-40.5& 5\\ 40.5-45.5& 2\\ 45.5-50.5& 12\\ 50.5-55.5& 2\\ 55.5-60.5& 45\end{array}$
[3 MARKS]

Draw the graph of the function y = $a^x$. When a > 1.

Matrix A is such that $A^2=2A-I,$ where I is the Identity matrix. Then for $n\ge 2,A^n$ is equal to

The value of $(1-cosA)(1+cosA)\left(cose{c}^{2}A\right)$ is___.

If two bars in a histogram have unequal widths but the same height, then which class interval will have a higher density of observations?

x-a is a factor of p(x)= ax²+bx+c. Which of the following is true?

Two circles of radii 10 cm and 8 cm intersect each other, and the length of the common chord is 12 cm. Find the distance between their centres.

If $p\left(x\right)=5-4x+2x^2$, find

(i) p(0)

(ii) p(3),

(iii) p(-2)

The slant height of a cone is increased by 10 %.If the radius remains the same, the curved surface area is increased by

Is it possible to draw a triangle with sides of length 2 cm, 3 cm and 7 cm?

Which of the following cannot be determined graphically?

(a) Mean (b) Mode (c) Median (d) None of these

In a quadrilateral ABCD,it is given that BD=16 cm.If $AL\perp BD$ and $CM\perp BD$ such that AL=9 cm and CM=7 cm then ar(quad .ABCD)=?

(a) $256c{m}^2$

(b) $128c{m}^2$

(c) $64c{m}^2$

(d) $96c{m}^2$

In the figure, the sides BA and CA have been produced such that BA = AD and CA = AE, Prove that segment DE || BC.

The value of k if x = 2, y = 1 is a solution of equation 2x - k = - 3y is:

If $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$ for the system of equations $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$, then;

$5x\times (-4yz)\times 3xz$ = ___$x^{2}y{z}^2$

In a rhombus ABCD show that diagonal AC bisects $\angle A$ as well as $\angle C$ and diagonal BD bisects $\angle B$ as well as $\angle D$.

Prove that the quadrilateral formed by angle bisectors of a cyclic quadrilateral ABCD is also cyclic. [4 MARKS]

If each of the two lines is perpendicular to the same line, what kind of lines are they to each other?

Prove that two triangles on the same base (or equal bases) and between the same parallels are equal in area.
[4 MARKS]

Question 3
AD and BC are equal perpendiculars to a line segment AB.
Show that CD bisects AB.

What is the compound interest on a principal of Rs 5000 at the rate of 10% for 2 years?

The length of a rectangle is twice the width of it. If the perimeter of the rectangle is 42m. Then the area of the rectangle is _____ .

Question 12
Mean of 50 observations was found to be 80.4. But later on, it was discovered that 96 was misread as 69 at one place. Find the correct mean.

Find the value of k if(x-3) is a factor of 4x^3 +3x^2 -4x +2k

If (3, 4) is a solution of the linear equation 3y = ax + 7, then which of the following is the value of a? ​

The mean of five number is 30. If one number is excluded their mean become 28. Find the excluded number.

Factorise:1-2a-2b-3(a+b).(a+b)

There is a narrow rectangular plot, reserved for a school in Mahuli village . The length and breadth of the plot are in the ratio 11:4 .At the rate Rs .100 per m it will cost the village panchayat Rs 75,000 to fence the plot . What are the dimensions of the plot ?

If 'a' and 'b' are rational numbers, find 'a' and 'b' given that $\frac{3}{\sqrt{3}-\sqrt{2}}=a\sqrt{3}-b\sqrt{2}$.

ABCD is a quadrilateral such that A is the centre of the circle passing through B, C and D. Which one of the following options is correct?

The longest side of a triangle is 3 times the shortest side and the 3^rd side is 2cm shorter than the longest side. If the perimeter of the triangle is atleast 61cm. Find the minimum length of the shortest side.

5x-9=1/y

X+1/y=3

Factorise :

(a + b)³ - 8

My attempt

= (a + b)³ - (2)³

= (a + b - 2) {(a + b)² ​​​​​+ (2)² + 2(a + b)}

What should I do not?

Factorise:

12x²-7x+1

Factories $y^2-5y+6$ by using splitting middle term.

$Ifco{s}^{4}A–si{n}^{4}A=\frac{3}{5},then2co{s}^{2}A-1$= ?