Revision Worksheet-1/Mathematics/10/2024-25

Section A(MCQ)
Q1 The LCM of the smallest two-digit composite number and the smallest composite
number is

a) 4 b) 12 c) 20 d) 44
Q2 LCM of two numbers is 1200. Which of the following cannot be their HCF?

a) 600 b) 500 c) 400 d) 200

Q3 The least number which divides 80 and 128 leaving remainders 5 and 8 respectively is

a)1750 b) 875 c) 70 d) 15
Q4 If the zeroes of the quadratic polynomial x2 +(a+1) x+ b are 2 and -3, then
a) a=7, b= -1 (b) a=5, b= -1 (c) a=2, b= -6 (d) a=0, b= -6
Q5 The quadratic polynomial, the sum of whose zeroes is 9 and their product is 20, is
a) x2+ 9x +20 b) x2 - 9x +20 c) x2 - 9x – 20 d) - x 2+ 9x +20

Q6 The roots of the equation x2 -3x –m(m+3)=0, where m is a constant are:

a) m, m+3 (b) –m, m+3 (c) m, -(m+3) (d) -m, -(m+3)
Q7 The value(s) of p for which the quadratic equation px 2 +8x-2=0 has real roots is/are
a) p≥−8 b) p≤−8 c) p = 8 d) p > -8
Q8 Let p be a prime number. The quadratic equation having its roots as factors of p is
(a) x2 – px + p=0 (b) x2 – (p+1)x + p=0
2
(c) x + (p+1)x + p=0 (d) x 2 – px + p+1=0
AB BC
Q9 If in triangles ABC and DEF, = , then they will be similar, if
DE FD
(a) ∠B = ∠E (b) ∠A = ∠D (c) ∠B = ∠D (d) ∠A = ∠F
Q10 The probability of selecting a blue marble at random from a jar that contains only
blue, black and green marble is 1/5. The probability of selecting a black marble at random
from the jar is ¼. If the jar contains 11 green marbles then the total number of marbles in
the jar are
a) 20 b) 21 c) 30 d) 35

Q11 For an event E , if P(E) + P( E ) = x , then the value of x2- 3 is

a)  3 b) - 3 c) 2 d) -2

Q12 The ratio in which the x-axis divides the segment joining (3, 6) and (12, -3) is
(a) 2:1 (b) 1:2 (c) -2:1 (d) 1: -2
Q13 The value of tan230. sin30 -2tan45. cos2 0. sin90 is equal to
a) 13/6 b) -11/6 c) -1/2 d) 
Q14 If tanA=1 and tanB=  3, then the value of CosA . CosB – SinA.SinB is
1+  3 1+  3 1+  2 1− 3
a) b) c) d)
2 2 2 2 3 2 2

sinB
Q15 In  ABC ,right angled at A, AB = 8 cm and BC = √ 113 cm, then the value of is
cosC
a) 7 b) 8/ √ 113 c) 1 d) 0

Q16 In ABC , right angled at B, AB = 7cm and AC-BC = 1 cm, then the value of Cos C is
a) 7/25 b) 24/25 c) 25/7 d) 25/24

Q17 If the difference of Mode and Median of a data is 24, then the difference of Median
and
Mean is
a) 6 b) 8 c) 10 d) 12

Q18 In the formula X =a +

∑ f i di ,for finding the mean of grouped data d ' s are deviations
∑fi i

from ‘a ‘of
a) lower limits of classes c) mid-points of classes
b) upper limits of classes d) frequency of the class marks

Q19 Assertion(A): If mode = 12.4, mean = 10.5, then median is 11.13.

Reason (R): If the median of a series exceeds the mean by 3, then mode exceeds the
mean by 10.
Choose the correct option.
a) Both (A) and (R) are true and reason (R) is the correct explanation of assertion
(A).
b) Both (A) and (R) are true but (R) is not a correct explanation of (A) .
c) (A) is true but (R) is false.
d) (A) is false but (R) true.

Q20 Assertion(A): cotA is a product of cot and A.

Reason(R): The value of sinθ increases as θ increases in the interval of 0 to 90 .
Choose the correct option.
a) Both (A) and (R) are true and reason (R) is the correct explanation of assertion
(A).
b) Both (A) and (R) are true but (R) is not a correct explanation of (A).
c) (A) is true but (R) is false.
d) (A) is false but (R) true.
Section B
Q21 A rectangular courtyard is 18.72 m long and 13.20 m broad. It is to be paved with
square tiles of the same size. Find the least possible number of such tiles.
Q22 Find the zeros of the polynomial y2 + 4√ 3y -15 and verify the relationship between
the zeros and the coefficients of the polynomial.
Or
Find a quadratic polynomial whose zeros exceed the zeros of x2 + 5x +6 by a number 2
Q23 The mode of the following data is 67. Find the missing frequency x.
Class 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90
Interval
Frequency 5 x 15 12 7

Q24 If cosθ + sinθ =√ 2 cosθ , show that cosθ−sinθ = √2 sinθ .

Or
sin  −cos 
−sin . cos 1
3 3

sin −cos
Prove that

Q25 If 152x -378y = -74 and -378x + 152y = - 604 , then find the value of x and y.
Section C
Q26 Given that 3 is irrational, prove that 7-5 3 is an irrational number.
Q27 For what value (s) of k the following pair of linear equations have infinite solutions.
kx +y = k2 and x + ky = 1 .
or
Find the value of k so that the following equations have no solution .
3x + y = 1 ; (2k – 1)x + (k – 1)y = 2k + 1
Q28 ABCD is a trapezium with AB ∥ DC. Diagonals AC and BD intersect each other at O.
If AO = 3cm , OC =( x – 3)cm , OB =( x – 5)cm and OD = (3x – 19)cm, then find the
value of x.
29 The line segment joining the points A(2,1) and B(5,-8) is trisected at the points P and Q
such that P is nearer to A. If P also lies on the line given by 2x-y +k=0, find the value of k.
Or
Prove that the points (-2,5) , (0,1) and (2,-3) are collinear using distance formula .
30. If sin  + cos  = 3, then prove that tan  + cot  = 1.
3
31. The probability of selecting a blue marble at random from a jar that contains only
blue, black and green marble is 1/5. The probability of selecting a black marble at random
from the same jar is 1/4. If the jar contains 11 green marbles, find the total number of
marbles in the jar. 3
Section – D
32. Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the
coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade
the triangular region. 5
33. A two digit number is such that the product of its digits is 8. When 18 is
subtracted from the number, the digits are reversed. Find the number.

OR
A plane left 30 minutes later than the schedule time and in order to reach its
destination 1500 km away in time it has to increase its speed by 250 km/hr from its
usual speed. Find its usual speed.
34. Sides AB and AC and median AD of a triangle ABC are respectively
proportional to sides PQ and PR and median PM of another triangle PQR. Show that
triangle ABC ~ triangle PQR.

OR
In given figure AB ∥ PQ ∥CD , AB = x units , CD = y units and PQ = z units . Prove
1 1 1
that : + =
x y z

35. If the median of a distribution given below is 28.5 then, find the value of an x &y.

Class Interval 0-10 10-20 20-30 30-40 40-50 50-60

Frequency 5 x 20 15 y 5

Section – E (case study based questions)

36. The below picture are few natural examples of parabolic shape which is
represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a
parabola .In structures, their curve represents an efficient method of load ,and so can
be found in bridges and in architecture in a variety of forms.
 (i) Check whether the graph of x2+1 touches or intersects x axis or not .
1
(ii) Write the polynomial if sum of its roots is -4 and product of its roots is 12.
(iii) What is the shape of given pictures ?
OR
In the graph how many zeroes are there for the polynomial?

37. Vijay is trying to find the average height of a tower near his house. He is using the
properties of similar triangles.The height of Vijay’s house if 20m when Vijay’s house casts
a shadow 10m long on the ground. At the same time, the tower casts a shadow 50m long
on the ground and the house of Ajay casts 20m shadow on the ground.

Based on the above information, answer the following questions.

(i) Find the height of the tower?

(ii) What will be the length of the shadow of the tower when Vijay’s house casts a
shadow of 12m?
(iii) What is the height of Ajay’s house?
OR
When the tower casts a shadow of 40m, same time what will be the length of the
shadow of Ajay’s house?

38. In order to conduct Sports Day activities in your School, lines have been drawn with
chalk powder at a distance of 1 m each, in a rectangular shaped ground ABCD, 100 flower
pots have been placed at a distance of 1 m from each other along AD, as shown in given
figure below. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag.
Preet runs 1/5th distance AD on the eighth line and posts a red flag.
 (i) Find the position of green flag.
(ii) Find the position of red flag
(iii) What is the distance between both the flags?
OR
If Rashmi has to post a blue flag exactly halfway between the line segment joining the two
flags, where should she post her flag?