Q1. If $P(-1, 1)$, $Q(3, -4)$, $R(1, -1)$, $S(-2, -3)$, and $T(-4, 4)$ are plotted on the graph paper, the points in the fourth quadrant are

Q2. The distance of the point $P(2, 3)$ from x-axis is

Q3. If $x$ is negative and $y$ is positive, then the point $(x, y)$ lies in

Q4. On which axis does the point $(-7, 0)$ lie?

Q5. In the equation $y = 4x + 5$, what does the constant 5 represent?

Q6. If $p(x) = 7 – 3x + 2x^2$, then value of $p(-2)$ is:

Q7. Which of the following numbers is an irrational number?

Q8. $\sqrt{12} \times \sqrt{8}$ is equal to …………

Q9. If $\frac{x}{y} + \frac{y}{x} = -1$, find the value of $x^3 – y^3$

Q10. The value of $(a + 1)(a – 1)(a^2 + 1)$ is:

Q11. If $a – b = 7$ and $ab = 9$, then $a^2 + b^2 =$

Q12. A triangle is drawn with one of its sides as diameter, then the measure of angle opposite to diameter is .

Q13. Equal chords of a circle subtend ……

Q14. The area of a rhombus is $72\text{ sq. cm}$. If its perimeter is $32\text{ cm}$, then its altitude.

Q15. PQRS is a square land of side 28 m. Two semi-circular grass covered positions are to be made on two of its opposite sides as shown in the figure. The area left uncovered is….. (Take $\pi = 22/7$)

Q16. During a cricket match, a batswoman hits a boundary 15 times out of 25 deliveries played. Calculate the probability that she does NOT hit a boundary on a delivery chosen at random.

Q17. A box contains 30 chits which are numbered from 1 to 30. If one chit is drawn at random from the box then find the probability that the number is multiple of 5 is ……

Q18. The sum of first 67 natural number is ………

Direction: (Q19- Q20) In the questions given below, there are two statements marked as Assertion (A) and Reason (R). Read the statements and choose the correct option.
Options:
(a) Both (A) and (R) are true and (R) is the correct explanation of (A)
(b) Both (A) and (R) are true and (R) is not the correct explanation of (A)
(c) (A) is true but (R) is not true.
(d) (A) is false but (R) is true

Q19. Assertion (A): $x = -4$, $y = 5$ is a solution of the equation $2x + y = -3$
Reason (R): At $x = -4$, $y = 5$ the LHS of equation $2x + y = -3$ is equal to the RHS of the equation.

Q20. Assertion (A): Product of $3.333$ and $\frac{5}{9}$ is a rational number.
Reason (R): Product of two rational numbers is a rational number.

Q21. Write the co-ordinates of the point M
a) Whose ordinate is -5 and which lies on y-axis
b) Whose abscissa is 3 and which lies on x-axis

Q22. Find the value of the linear polynomial $-8a + 17$ at $a = -5$

Q23. Find the decimal form of $\frac{3}{13}$ and write what kind of decimal it is.

Find the decimal form of $\frac{7}{8}$ and write what kind of decimal it is?

Q24. The base of an isosceles triangle is 10 cm and one of its equal sides is 12 cm. Find its area by using Heron’s formula.

Q25. A coin is tossed 60 times and tails turn up 33 times. Find the probability of getting a head.

A bag contains 12 white, 4 red and 4 black balls. A ball drawn at random. Find the probability that it is a white or a black ball.

Q26. Plot the points $A(2, 1)$, $B(-1, 2)$, $C(-2, -1)$ and $D(1, -2)$ in the Cartesian plane. Is ABCD a square? Find the distance between A and C.

Plot the points $P(2, -2)$, $Q(8, 4)$, $R(4, 8)$ and $S(-2, 2)$ in the Cartesian plane. Find the length the diagonal.

Q27. The present age of Ramesh’s father is four times Ramesh age. After 6 years, their ages will be add upto 72 years. Find their present ages.

If the length of a rectangle is 5 more than twice its width and its perimeter is 34 cm, what are the dimensions of the rectangle?

Q28. Find six rational numbers between $\frac{-6}{7}$ and $\frac{1}{6}$

Q29. Draw $\Delta PQR$ with $PQ = 6\text{cm}$, $\angle P = 110^\circ$ and $PR = 5\text{cm}$. Draw the circumcircle of $\Delta PQR$. Is the centre inside or outside the triangle?

Q30. Factorise: $36x^2 + 25y^2 + 49z^2 + 60xy – 70yz – 84xz$.

Q31. Find the 5th term of a GP with common ratio 2, whose 8th term is 192.

Q32. See figure and write the answer of the following:

(a) The coordinates of B
(b) The point identified by the coordinates $(2, -4)$.
(c) The point identify by the coordinates $(-5, -3)$.
(d) The mirror image of $(-5, 2)$ along y-axis.
(e) The coordinates of D

Q33. a) Locate $\sqrt{13}$ on the number line and show proper working of it. Draw neat diagram of it.
b) Simplify: $(8\sqrt{7} + 5\sqrt{2}) \times (8\sqrt{7} – 5\sqrt{2})$

a) Locate $\sqrt{5}$ on the number line and show proper working of it. Draw neat diagram of it.
b) Simplify: $\sqrt{45} + 28\sqrt{20} – 4\sqrt{5}$

Q34. a) Evaluate: $103 \times 107$ by using suitable identity
b) If $x + y = 12$ and $xy = 27$, find the value of $x^3 + y^3$

If $a + b + c = 5$ and $ab + bc + ca = 10$, then prove that $a^3 + b^3 + c^3 – 3abc = -25$.

Q35. Find the total perimeter of all the petals in the given figure

Q36. A professional photographer buys a high end DSLR camera for ₹ 45,000. Due to the release of newer models and wear and tear, the market value of the camera decreases at a constant rate of ₹ 3,500 per year.
(a) Find the market value of the camera exactly 7 years after the date of purchase.
(b) Explain why this specific relationship represents linear decay.
(c) Create a table showing the value of the camera as ‘v’, for time as ‘t’ varying from 1 to 4 years.

Find the value of the camera exactly 8 year after the date of purchase.

Q37. A travel agency surveyed 2,000 people to find out their preferred mode of travel for long-distance trips. The results are categorized by age group in the table below:

If a person is chosen at random from this survey, find the probability that the person:
(a) Is over 50 years old and prefers to travel by Train.
(b) Is under 30 years old and does not prefer a Private Car.
(c) Is in the 30-50 age group and prefers either a Train or a Bus.

Is in the over 50 years age group like Aeroplane or Private car.

Q38. A school auditorium has seats arranged in rows. The first row has 20 seats, the second row has 24 seats, the third has 28 seats, and so on. The number of seats increase by 4 seats in each successive row. Answer the following questions.
(a) What is the first term of the AP?
(b) What is the common difference?
(c) How many seats are there in 10 rows?

How many seats are there in 25 row?