नोट यहां पर Δ को एंगल माना माना गया है
Note here Δ is taken as angle
1.multiple choice questions
1.Which of the following number is rational
(a) √23
(b) √225
(c) √3+2
(d) 1.101001000100001….
2.What is the degree of the polynomial 4x² – 3x + 7?
(a) 2
(b) 4
(c) –3
(d) 7
3.The coordinates of the origin are?
(a) 0,0
(b) 0,1
(c) –1,1
(d) 10, 10
4.What is the value of the equation x –2y – 4? (a) 0,2
(b) 2,0
(c) 4,0
(d) 1,1
5.The sum of three angles of a triangle is ………. ?
(a) 720°
(b) 360°
(c) 180°
(d) 90°
6.A quadrilateral whose four sides and angles are equal to each other is-
(a) rectangle
(b) rhombus
(b) parallelogram
(d) square
7.If a triangle and a parallelogram lie on the same base and between the same parallel lines, then the area of the triangle is ………… of the area of the parallelogram?
(a) quarter
(b) double
(c) equal
(d) half
8.The angle of a semicircle is…………. ?
(a) acute angle
(b) right angle
(c) obtuse angle
(d) straight angle
9.Find the volume of a sphere whose radius is 3 cm?
(a) 27π
(b) 36π
(c) 54π
(d) 72π
10.What is the probability of getting a prime number when a dice is thrown once?
(a) ½
(b) ⅔
(c) 0
(d) 1
2.Fill in the blanks—
1.Every irrational number is a ………. number.
2. The infinitesimal form of a linear equation in two variables has ………. solutions.
3.The largest chord of the fast is the ………….. of the fast.
4.If the sides of a triangle are a b and c, then by Heron’s formula, the area of the triangle is………… 5.
5.The volume of a cone of same radius and height is ………… part of the volume of a cylinder.
3.Very short answer soul questions
1..Find 4 rational numbers between 3/5 and 4/5?
2.Find the zeroes of the polynomial p(x)-2x+1?
3.In which quadrant do the points (-2,4)(3,-1)(1,2) and (-3,-5) lie?
4.Find four different solutions of the equation x+2y=6?
5.Write any two postulates of Euclid?
6.Construct an angle of 90° at the initial point of a given ray.
7.Find the mode of the data 14,25,14,28,18,17,18,14,23,22,14,18? 4. If x-1 is a factor of 4x³+3x²-4x+k, then find the value of k?
8.The first question of Exercise 6.2 was not written due to a typing problem.
6..Question 1 of Exercise 7.1.
7.Show that each angle of an equilateral triangle is 60°.
8.The angles of a quadrilateral are in the ratio 3:5:9:13. Find all the angles in the quadrilateral?
10.P and Q are points on the sides DC and AD of a parallelogram ABCD respectively. Show that ar(APB) = ar(BQC).
11.Prove that equal chords of a circle subtend equal angles at the centre.
12.Find the area of a triangle whose two sides are 18 cm and 10 cm and its perimeter is 42 cm.
13.Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.
14.The dimensions of a match box are 4cm x 2.5cm x 1.5cm. What will be the volume of a packet of 12 such boxes?
15.When a coin is tossed 1000 times, the following frequencies are obtained: Head: 455, Tail: 545. Calculate the probability of each event.
16.AD is a vertex perpendicular to an isosceles triangle ABC such that AB = AC. show that
(i) AD bisects the line segment BC.
(ii) AD bisects angle A.
17.Diagonal AC of a parallelogram ABCD bisects angle A. EXERCISE 8.1 Question 6.
(i) It also bisects ΔC.
(ii) ABCD is a rhombus.
18.Show that the two diagonals of a parallelogram divide it into four triangles of equal areas.
19.The curved surface area of a right circular cylinder of height 14 cm is 88 cm 2 . Find the diameter of the base of the cylinder.
20.The following table gives the lifetimes of 400 neon lamps.
(i) Represent the given information with the help of a histogram.
(ii) How many lamps have a life span of more than 700 hours?
- ABC is a right angled triangle in which ΔA = 90°. Find ΔB and ΔC.
Or
Prove that a cyclic parallelogram is a rectangle. - ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. Show that quadrilateral PQRS is a rectangle.
Or
Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm. - The diagonals AC and BD of a trapezium ABCD in which AB DC intersect each other at O. Show that ar (AOD) = ar (BOC).
Or
The slant height and base diameter of a dome of a conical base are 25 m and 14 m respectively. Find the cost of whitewashing its curved surface at the rate of ₹ 210 per 100 m².