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Factorize each of the following polynomials:



(i) x³ + 13x² + 31x − 45 given that x + 9 is a factor



(ii) 4x³ + 20x² + 33x + 18 given that 2x + 3 is a factor.

Question 1 (iii)
Classify $\frac{2\sqrt{7}}{7\sqrt{7}}$ as rational or irrational.

The curved surface area of a cylinder is $176c{m}^2$ and its base area is $38.5c{m}^2$. Find the volume of the cylinder and justify your answer.
[Use $\pi =\frac{22}{7}$]

If $(x+a)$ is a factor of $x^2+px+q$ and $x^2+mx+n$, then the value of $a$ is

Solve the following system of linear equations graphically:

4x - 5y - 20 = 0

3x + 5y - 15 = 0

Determine the vertices of the triangle formed by the lines representing the above equation and the y-axis.

Three chairs and two tables cost Rs. 1850. Five chairs and three tables cost Rs. 2850. Then the total cost of one chair and one table is:

In a quadrilateral ABCD AB = 6 cm, BC = 8 cm, CD = 8 cm and AC=10cm.The area of the quadrilateral is 60.67 cm². Find DA.
[4 MARKS]

In the figure, O is the centre of a circle and PQ is a diameter. If $\angle ROS={40}^{\circ }$, find $\angle RTS$.

The greater among $\sqrt{17}-\sqrt{12}$ and $\sqrt{11}-\sqrt{6}$ is:

The marks obtained by 17 students a mathematics test (out of 100) are given below:

90, 79, 76, 82, 65, 96, 100, 91, 82, 100, 49, 46, 64, 48, 72, 66, 68.

Find the range of the above data.

In the figure $△ABC$ is a right angled triangle with right angle at B. BD is perpendicular to AC. Then which of the following options will hold true?

Find the actual lower and upper class limits and also the class marks of the classes:

1.1-2.0 ,2.1-3.0 , 3.1-4.0

Question 6

ABC is a right-angled triangle and O is the mid-point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. ( The dotted lines are drawn additionally to help you.)

Two dice are rolled simultaneously. The probability that they show different faces is:

The ratio of the circumference of a circle to the diameter of the circle is

What is the closest fractional approximation to the irrational number pi?

Paralallelogram $ABCD$, triangle $ABE$ and rectangle $ABFG$ are on the same base $AB$ and between same parallel lines. Area of parallelogram is ${}^{\prime }{p}^{\prime }$, area of triangle is ${}^{\prime }{t}^{\prime }$ and area of rectangle is ${}^{\prime }{r}^{\prime }$. Find the relation between $p,t$ and $r$.

In the given figure, if m || n and ∠1 and ∠2 are in the ratio 3 : 2, determine all the angles from 1 to 8.

(a-b)-a^{​​​​​2}+b^{​​​​​​2}

^{Factorize it}

The area of an $A_0$ paper is one square metre. What are the lengths of the sides of an $A_3$ paper ? (answer in millimetres)

Let E denote an event where "India scores less than 300” in a cricket match between India and South Africa. How many elements are there in the sample space which will favour the event E?

If the line represented by the equation $3x+4y+c=0$ passes through the origin, then $c$ =.

A distance of 1 unit on the map of a city represents an actual distance of 1 km. On the map, Sanjay’s house is located at (4, 3). To go to his school, he first goes to a nearby bus stand which is located at (4, 0).

If the school is located at the origin, then what is the total distance that Sanjay travels to reach his school from his house?

In the given figure, O is the centre of the circle. Find the value of $X$.

Question 55

In a histogram, ___ are drawn with width equal to a class interval without leaving any gap in between.

The points (2,0) (-3,0) (5,0) and (0,0) all lie on the

1. 24.01

If A (-1, 8), B(4, -2) and C(-5, -3) are the vertices of a triangle. Median through(-1, 8) intersect line segment BC at D. Find the co-ordinates of point D.

Find the length of the shadow cast by a 10-foot Lamp-post when the angle of depression is ${60}^{\circ }$?