PRE-BOARD (STANDARD)
CLASS-X
TIMEALLOWED 3HOURS SUBJECT-MATHS
General Instructions M.M-80
1. This question paper has 5 Sections A-E.
2. Section A has 20 McQs carrying 1 mark each
3. Section B has 5 questions carrying 2 marks each
4. Section C has 6 questions carrying 3 markseach.
5.Section D has 4 questions carrying 5 marks each.
6 Section E has case study based questions (4 marks each ) with subparts
SECTION-A (1x20-20)
Q1. The times (in second) taken by 150 athletes to run a 110m hurdles race are tabulated below.
Class 13.6-14 14-14.2
14.2-14.4 14.4-14.6 14.6-14.8 14.8-15
2 4 5 71 48 20
Frequency
The number of athletes who have completed the race in less than 14.6 s, is
Ua82 (b) 80 (c) 74 (d) 86
Qa2. For what value of k ,-4 is a zero of the polynomial xx -2k+2) ?
a3. The probability of passing a certain test is . Ifthe probability of not passing is 7/8,then x
24
is equal to
(a) 2 (b 3 4 (d) 6
Acircle is inscribed in a A ABC having sides 8cm,10cm and 12cm as shown in fig. Find
AP,BE and CF
h9 poui
P
Inthegiven we 44ecu
APnd he erqt Bc auriora
P
drawn from point
t point P lies inside the circle ,then the number of tangents
(b) 1 2 (d) none of these
s
6f a sector of a circle has area 100cm then the perimeter of this sector
200
200 00 100
(a)r (b) 2r + (c)r+ (d) 3r+
0sas90" takes the greatest value
A7)Find an acute angle a when sina+ cose,
(a) y2 (bV3 (c) 1 (d)
8, Given that sino« = and cos6;, then the value of a +6 is
(a) 60 (b) 30 (c) (d) 90
h e non zero value of k for which the quadratic equation 3x-kx + k= 0 has equal roots
,is
(a) 10 (b) 11 (c) 12 (d)14
Q10. The sum of :he first 7 ierms
of A.P sequences
27, 30, 33, s
(a) 152 6)252 (c)100 (d) 150
Q11.If the pair of linear equations 3x+y =3 and 6xt+ky = 8 does not have a solution ,then the
value of k is
Ja) 2 ) -3 (c) 0 (d) 1
Q12. HCF of two number is 23 and their LCM is 1449. if one
of the number is
other number is 161,then the
t) 207 (b) 307 (c) 1449 (d) None of these
Q13. If the point C (K, 4) divides the join of points A (2,6) and B (5,1) in the ratio
1:3
then the value of k is
(a) 11 (b) ()
d e
H
dh
3Peds
o 14. Themean and median of a distribution are 14 and 15 ,respectively. The value of Mode
is
(a) 16 (b) 17 (c) 13 (d) 18
a 15. Tours for the national capital and the white hause begin at 8.30 am from tour agency
.Tours for the national capital leave every 15 min. Tours for the white house leave every
20 minutes.How many minutes after do the tours leave at the same point ?
(a) 60min. (b) 30min. (c) 80min. (d) 100 min.
12P 2 sin) cos0
Q16.If tanð =13 then the value oro30-siño is
312
(al 312
25 (b) 312 ( d) 5
312
,then the value of
(Q17). If HCF of 408 and 1032 is expressed in the form 1032 X2 + 408 XP
Pis
(a) 5 (b)-5 c) 4 (d)-4
Q18. Priya and Pihu are standing on either side of a river bank. A kite is fiying above the
river. The angle of elevation of kite from Priyais 60° and from Pihu is 45 Who is nearer to
thekite?
q19.Statement A (ASSERTION ) If LCM = 182, Product ofintegers is 26 x91, then HCF = 13
Statement R (REASON) LCM X Product of two integers = HCF
(a) Both Assertion (A) and Reason( R) are true and Reason (R) is the correct explanation of
assertion (A)
(b) Both Assertion (A) and Reason( R) aretrue but Reason (R) is not the correct
explanation of assertion (A)
(c) Assertion (A) is true but Reason (R) is false
(d) Assertion (A) is false but Reason (R) istrue
q20.Statement A (Assertion ) Points A (6.4), B (-4, -6) and C (4,6) are such that
AB=V200, BC =v208 and AC =V8, Since, AB +BC> AC, points A,B and C form a triangle.
Statement R (Reason). If BC = AB'+AC, then A ABC is a right angled at A.
of
correct
explanation
the
true and Reason (R ) is
Both Assertion (A) and Reason( R) are
(d
assertion (A)
correct
Reason (R) is not the
true but
(A) and Reason( R)
are
(D) Both Assertion
explanation of assertion (A)
is but Reason (R) is false
(c) Assertion (A ) true
is false but Reason (R) is true
(d) Assertion (A)
SECTION -B
each.
Section B consists of 5 questions of 2 marks
circle with centre O and AT
is a tangent .If
, AB is the diameter of a
Q21. In the given figure
<AOQ =58°, find <ATQ = .
,if the corresponding arc length is
of the sector of a circle of radius 5cm
Q22.Find the area
3.Scm
circle is 130" ,then find the angle
the angle between two radii of a
Q23. In the given fig., if B
radii
between the tangent at
the ends of two .
P S8
B A
BS 90, A >B then find A and 8.
V3 and tan (A-B ) 1/V3,0" <A+
=
Q24.If tan (A+ B)
=
then the sun 's elevationis
pole 6 m high casts a shadow 2v3
m long on the ground,
Q25. A
SECTION -C
each
Section c consists of 6 questions of 3 marks
irrational.
Q26.PROVE that 5v2 is
is inconsistent
the following system of equations
Q27 Show graphically that
J ND aD
3 o
60
30
3x-4y-1 0, 2x-y+5 =0
628. Find four numbers in A.P whose sum is 20and the sum of whose squares is 120.
029. If d and 6 are the zeroes ofthe quadratic polynomial fx) = 3x-5x-2 ,then find the
value of a'+8.
(Q30. In the given fig. PT and PS are tangents to a circle from a point P such that PT =4cm
and< TPS = 60 .Find the length ofchord TS. How many lines ofsame length TS can be
drawn in the circle? A
OR
If the tangent at C
AB is a diameter and AC is a chord of a circle such that <BAC =30.
intersects AB produced at D, provethat BC= BD.
/sin A-1
Q 31 Prove that Cot A secA-1
1+sin A
sec A sec
1+sec A)
1+secA
SECTION-D
Section D consists of 4 questions of 5 marks each
)(a
Q32. A quadratic equation can be defined as an equation. This means that the highest
exponent of the polynomial
in it is 2 .The standard form of the quadratic equation is ax +bx
+c =0, where a, b and c are real numbers and a+0. Every quadratic equation has two roots
depending on the nature of its discriminants, D =b* -4ac.
Based on the above information, answer the following questions.
(i) Which of the quadratic equation have irrational roots, if the quadratic equations are
4x-7x +3 =0 and 6x-3x-5 =0
(Gi) Which of the quadratic equations have no real roots, if the quadratic equation are
-4x+7x -4 =0 and 2x +3x -2=0
Q33. The angle of elevation ofthe top of a tower from certain point is 30°If the observer
moves 20 m towards the tower, the angle of elevation of the top increases by 15°. Find the
height of the tower.
Q34. If the mode of the following series is 54, then find the value
off.
Class 0-15 15-30 30-45 45-60 60-75 75-90
interval
Frequency 16 12 7
Find the modal class in which the given mode lies and find the value of f.
Q35. Places P1 and P2 are 250 km
apart from each other on a national highway.A car starts
from P1 and another from P2 at the same time If
they go in the same direction then they
.
meet in Sh and if they go in
opposite directions they meet in hI3 .Find their speeds.
SECTION-E
CASE STUDY BASED QUESTIONS .
Q36. Using of mobile screen for
long hours,makes you lazy ,affect eye-sight and gives you
headache .Those who are addicted to
playing PUBG can get easily stressed out or face anxiety
issues in public due to lack of social interaction.
(2,6) ci8
BAN PUB
AL2 B8,2)
To raise social awarenss about ill effects of playing PUBG a school decided to start 'BAN
PUBG' Compaign, students are asked to prepare compaign boards in the shape of rectangle
(as shown in the fig.)
Based on the above information, answer the following questions.
(i) If we replace X-axis by Y-axis and Y-axis
by X- axis ,then find the co-ordinates of C. CI)
(ii) Find the area of the board.
C1D
(ii) Find the intersection point of the diagonals.
Case Study Based-4 (hm 4
Energy Conservation
conservation is the etect made to reduce the consumption ot energy by using
Energy less of an
energy service
Some children a sehool prepared posters on 'Save
of Energy' which are shown below
Think
Energ
Turn the
Green
Lights off
when yoou
Don't
Turn off
leave
waste it Lights
Poster I Poster 11 Poster 1i
Refer to Poster I
(a) If radius of the circle is 21 cm and angle subtended by arc at centre is 60°, the length of the arc is
(i) 22 cm (i) 28 cm (ii) 33 cm iv) None of these.
6) The area of, sector formed by the arc (radius = 21 cm and angle of sector = 60°) is
i) 124 cm (i) 231 cm (ti) 285 cm2 (iv) 310 cm
Refer to Poster 11
(c) What is the radiu_ of circular region if length of poster is 18 cm and breadth is 14 cm?
() 14 cmn (i) 18 cm (iii) 7 cm (v) 9 cm
(1)
() What is the
area of circular region if length of poster is 18 cm and breadth is 14 cm?
() 154 cm (ii) 172 cm' (i) 196 cm2
(1)
(iv) 216 cm2
Refer to Poster IHI
The area of poster if the length and breadth of it are 18 cm and 14 cm respectively, is
()155cm i ) 175 cm? (ii) 195 cm2 (i) 205 cm2
Q38. In a bridge game ,there are four persons playing in a pair of two -two persons as a
playing cards ,distributed around the table clockwise in such a partner . In a deck of 52
way that each person gets 13 cards.
On the basis of above
information answer the
following questions.
(i) Find the probability that the card drawn is a
queen of black- colour.
(ii) Find the (1)
probability that the card drawn is a card with numbers 5 or 6.
(ii) Find the (1)
probability that the card drawn is a card with numbers less
than 8.
(iv) Find the probability that the card (1)
drawn is a card with numbers
between 2 and 9.
(1)
