SMART COACHING CENTRE,GODDA

By:- Gurunath Sir Suggestion(Maths2024-25) Contact No. 07979852922

5 marks question 3 marks question

1. Find the discriminant of quadratic equation, nature of roots and 1.ग्राफिय फिफि से हल कीफिएsolve by graphical method
roots from quadratic formula. i) 2x + y – 6 = 0 ; 2x - y- 2= 0 ii) x + y = 10 ; y – x = 4
a. 3x2 – 5x + 2 = 0 b. 4x2 + 4√3x + 3 = 0 c. 2x2 – 6x iii) x -2 y = 0 ; 3x + 4y = 20 iv) x + 3y = 6 ; 2x – 3y = 12
+ 3 = 0 d. 6x2 – x - 2 = 0 2. i) |Given a = 5, d= 3 and an = 50. Find n and Sn.
2. Write Thales’ rational and verify it ii) The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find
3. I) From the top of a 7m high building, the angle of elevation of the number of terms and the common difference.
the top of a cable tower is 60 degrees and the angle of depression iii) Find the sum of the first 22 terms of an A.P. in which d = 7 and the 22 nd
of its foot is 45 degrees. Find the height of the tower. term is 149.
ii) From a point on the ground, the angles of elevation of the base iv) If the nth term in an A.P. is an = 3 + 4n, then find the first, common
and the top of a communication tower mounted on the top of a difference and the sum of the 15 terms.
20m high building are 45 and 60 degrees respectively. v) other questions of A.P.
Remember the height of the tower. 3. i) A quadrilateral ABCD is drawn circumscribing a circle. Prove that
iii) Due to a storm, a tree breaks and the broken part bends in AB + CD = AD + BC
such a way that the top of the tree touches the ground and makes ii) Prove that the tangents drawn at the ends of a diameter of a circle are
an angle of 60 degrees with it. The distance of the foot of the tree parallel.
from where the top of the tree touches the ground is 8m. Find the iii) Prove that the lengths of tangents drawn from an external point to a
height of the tree. (iv) From a point on a bridge over a river, the circle are equal.
angles of depression of the opposite banks of the river are 30 iv) Questions related to tangent, radius and line drawn from the centre.
degrees and 45 degrees. If the bridge is at a height of 3m from 4. i) Prove that √5 is an irrational number. Ii) Prove that 3 + 2 √5 is an
the bank, find the width of the river. irrational number. Iii) Prove that 5 - √3 is an irrational number.
4. माध्य/ माध्यक/ बहु लक Mean/ Median/ Mode 5. Prove that:- Exercise 8.3(From updated book) 4. i ) , ii), vi), and vii)
5. i) A solid is in the shape of a cone standing on a hemisphere 6.i) |Find the coordinates of the point which divides the line segment
whose radius is 1cm and the height of the cone is equal to its joining the points (4, – 3) and (8, 5) internally in the ratio 3 : 1. Ii) In what
radius. Find the volume of this solid in terms of π. ratio does the point (-1,6) divide the line segment joining the points (-3,10)
ii) A toy is in the shape of a cone of radius 3.5cm, which is and (6,-8)? Iii) Find the ratio in which the line segment joining the points
superimposed on a hemisphere of radius 15.5cm. The total height A(1,-5) and B(-4,5) is divided by the x-axis. Iv) If the points
of this toy is 15.5cm. Find the total surface area of this toy. Iii) (1,2),(4,y),(x,6) and (3,5), taken in this order, are the vertices of a
A pen holder is made of a cuboid shaped piece of wood with four parallelogram, then find x and y. v) Find the coordinates of point A, where
conical depressions in it to hold pens. The dimensions of the AB is the diameter of a circle with centre (2,-3) and the coordinates of B
cuboid are 15cm x 10cm x 3.5cm. The radius of each depression are (1,4). Vi) Find the area of a rhombus whose vertices are, in that order,
is 0.5cm and the depth is 1.4cm. Find the volume of the wood in (3,0), (4,5), (-1,4) and (-2,-1).
the pen holder. 7. i) |A bag contains 3 red and 5 black balls. A ball is drawn at random
iv) A solid toy is in the shape of a hemisphere surmounted by a from the bag. What is the probability that the ball is (A) red (B) not red? Ii)
right circular cone. The height of the cone is 2cm and the A box contains 5 red marbles, 8 white marbles and 4 green marbles. Is one
diameter of the base is 4cm. Find the volume of the toy. marble from the box (A) red? (B) white? (C) not green? Iii) A dice is
6. i) A chord of a circle of radius 10cm subtends a right angle at the thrown once. Find the probability of getting the following : A. A prime
centre. Find a) the area of the corresponding minor segment b) number B. Any number between 2 and 6 (C) An odd number l iv) Due to
the area of the corresponding major sector some reason 12 bad pens are mixed with 132 good pens. It cannot be told
ii) An arc of a circle of radius 21cm subtends an angle of 60 by just looking at them whether a pen is bad or good. From this mixture, a
degree at the centre. Find 1) the length of the arc 2) the area of pen is drawn at random. Find the probability that the pen drawn is good.
the minor sector 3) the area of the corresponding sector V) A box contains 90 discs labelled with numbers from 1 to 90. If a disc is
iii) A chord of a circle of radius 15cm subtends an angle of 60 drawn at random from the box, find the probability that the disc will bear:
degree at the centre. Find the areas of the corresponding minor A. a two-digit number (B) a perfect square number (C) a number
and major sector segments. ( π = 3.14, √3 = 1.73) divisible by 5.
iv) A horse is tied with a 5m long rope at the corner of a square
grass field of side 15m. Find the area of that part of the field
where the horse can graze.
8. i) Find the area of the sector of a circle of radius 6 cm if the angle of the 12.Questions from distance formula, midpoint
sector is 60°. Ii) Find the area of a quadrant of a circle whose 13. 3 questions from similar, congruent triangles
circumference is 22 cm. iii) The length of the minute hand of a clock is 14 14. Questions related to tangent line
cm. Find the area covered by the minute hand in 5 minutes. Iv) Find the 15. Questions on trigonometry ratio
area of the sector of a circle of radius 4 cm if the angle of the sector is 30°. 16. 4 to 5 questions related to trigonometry formulas, angle, height,
Also find the area of the larger sector. distance, etc.
2 marks question 17. Questions related to area, circumference of circle
1. i) Find a quadratic polynomial whose sum and product of zeros are -3 18. Questions related to surface area, volume of solid
and 2 ii) ¼ and -1 iii) √2 and 1/ 3 iv) 0 and √5 v) Find and verify the zeros 19. Questions from mean, median, mode, class mark, frequency
of the quadratic polynomial x2 + 7x + 10 vi) Find and verify the zeros of 20. Questions related to probability
the quadratic polynomial x2 – 3
2. i) A Which term of the AP 3, 8, 13, 18,… is 78? Ii) Find the 31 st term of
the AP whose 11th term is 38 and 16th term is 73 iii) Find the 11th term from
the last term of the AP 10, 7, 4,…. Iv) Which term of 21, 18, 15…. Is -81.
V) How many two-digit numbers are divisible by 3?
3. i)Find the value:- Exercise 8.2(Updated Book) 1. i, ii, 2. ,i , iv,
ii) If tan(A+ B) = √3 and tan(A -B ) = 1/√3 then find the values of A and
B. iii) If sinA = ¾ then find the values of cosA and tan A. iv) If 15cotA = 8
then find the values of sinA and secA. v) If tanA = 4/3 then find other
trigonometric ratios of angle A.
4. i) Find the distance between the points (2, 3) and (4, 1). Ii) Find the point
on x-axis which is equidistant from (2, - 5) and (- 2, 9). Iii) Find the value
of y for which the distance between the points P (2, - 3) and Q (10, y) is 10
units. Iv) Find the relation between x and y such that the point (x, y) is
equidistant from the points (3, 6) and (- 3, 4). V) Determine whether the
points (1, 5), (2, 3) and (-2, -11) are collinear.
5. i) If LM || CB and LN || CD, then prove that AM/MB = AN/AD ii)
ABCD is a trapezium in which AB || DC and its diagonals intersect each
other at point O. Show that AO/BO = CO/DO. Iii) D is a point on the side
BC of a triangle ABC such that ∠ADC = ∠BAC. Show that CA2 = CB.CD
iv) Questions related to similarity
6. i) Questions related to probability
7. Find the value of x and y :-i) x + y = 5 ; 2x – 3y = 4 ii) Difference of two
numbers is 26 and one number is three times the other number. Find the
number. Iii) Some other questions
8. Questions related to HCF/LCM
Topic Of Objective Questions (30 Marks)
1 . Prime Factors
2. Questions related to Dividend, Quotient, Remainder
3. Number of Zeros
4. Nature of Zeros, Zeroes etc.
5. Value of k related to Linear Equation
6. Questions related to Graph of Linear Equation
7. Questions related to Pair of Linear Equations
8. Testing of Quadratic Equation
9. Nature of Roots
10. Finding the value of k in Quadratic Equation
11. 2 questions from A.P.

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