Do you want 100% Marks with less
effort Prepare the Following YSA Paper for YOU.?
Class
– X
Subject – Mathematics
Time:
3 hours Marks: 80
SECTION-A
(MARKS 10 x 1 =10)
The
LCM and HCF of two numbers are 180 and 6 respectively. If one
of the number is 30. Write the relation between LCM, HCF and
of two numbers and hence find the other number. Ans:
LXH = aXb , 36
2.
If α and β are the zeroes of the quadratic
polynomial f(x) = 6x2+x-2, find the value of
(HOTS) Ans: (-25)/12
3.
Find the values of k for which the equation x2+Kx+4
has equal roots? Ans: k =±4
4.
Express sin A in terms of tan A. ( HOTS)
Ans:
5.
Find the 12th term from the end of the A.P.
3, 8, 13, 18, ……..,98 Ans: 43
6.
In a ΔABC, P and Q are point on sides AB and AC
respectively, such that PQ║BC. If AP =
2.4cm, AQ=2cm, QC=3cm and BC = 6cm, find AB and PQ.
Ans:
AB =6, PQ=2.4
7.
If triangle ABC and triangle DEF are similar such that
AB = 1.2cm and DE = 1.4cm. Find the ratio of the
areas of triangle ABC and DEF. Ans: 36:49
8.
Find the area of the sector with radius 7cm if angle of
the sector is one-third of right angle. Ans:
51.33 cm2
9.
A die is thrown once, Find the probability of
getting (i) a prime number (ii) a number greater
than 5.
10.
Find the mean of all prime numbers up to 20. Ans:
9.625
SECTION-B
Marks (5x2 =10)
11.
ABC is an equilateral triangle of side 3a. Find
its altitude from A.
12.
A lot consists of 144 pens of which 20 are defective and the
others are good. A girl will buy a pen it it is
good, but will not buy if it is defective. The shopkeeper
draws one pen at random and gives it to her. What
is the probability that (i) She will buy it? (ii) She will not
buy it? Ans: (i) 31/36 (ii) 5/36
13.
In what ratio is the line segment joining the points (-2,-3)
and (3,7) divided by y-axis? Ans:
2:3
(OR)
Find
the point on X-axis which is equidistant from (2,-5) &
(-2, 9). Ans: (-7,0)
14.
If A, B, C are interior angles of a ∆ABC, then show that
Sec
15.
Check whether the following pair of linear equations 3x-5y =
20 and 6x-10y =40 will represent intersecting or coincident or
parallel lines.
SECTION_-C
Marks: (10x3=30)
16.
Prove that (√3 +√5) is an irrational number.
17.
The cost of 2kg of apples and 1kg of grapes on a day
was found to be Rs.160. After a month, the cost
of 4kg of apples and 2kg of grapes is Rs.300. Represent
the situation algebraically and geometrically and hence find
the solution if any.
18.
Find
the value of x in the following: 34 +32+30+….+x
= 286 (HOTS) Ans: x = 10,
(-8)
(OR)
PAGE:
02
If
the first, Second and last term of an A.P are a , b and 2a
respectively then find the sum of all terms. (HOTS)
Ans:
19.
Find the lengths of the medians drawn from A and B of the
ΔABC if its vertices are A(-1,3), B(1,-1)
and C(5,1) Ans: 5 and √10
20.
If D,E and F are the mid points of sides BC , CA and AB
respectively of a ΔABC then prove that Area
of ΔABC = 4x ΔDEF.
21.
The 7th and 13th terms of A.P are 34 and
64 respectively, Find the sum of its first eighteen terms.
Ans : 837
22.
The area of an equilateral triangle ABC is 17320.5cm2.
With each vertex of the triangle as centre, a circle is
drawn with radius equal to half the length of the side of the
triangle. Find the area of the region which is
outside of circles and inside the triangle. (Use Π = 3.14
and √ 3= 1.73205) Ans: 1620.5cm2
If
Cos (40 ○+A) – Sin (50○-
A) + + 3cos230 = 3k . Find k.
24.
Draw a pair of tangents to a circle of radius 5cm, which are
inclined to each other at an angle of 800 and
measure their length approximately.
25
In a right triangle ABC right angled at C, P and Q are the
points on the sides CA and CB respectively, which divide these
sides in the ratio 2:1 then prove that 9(AQ2+BP2)
= 13 AB2. (HOTS) (OR)
ABC
is an isosceles triangle right angled at B. Similar
triangles ACD and ABE are constructed on sides AC and AB. Find
the ratio between the areas of triangle ABE and triangle ACD.
(HOTS)
SECTION:
D Marks: (5x6 = 30)
26.
Places A and B are 100Km apart on a highway. One
car starts from A and another from at the same time. If
the cars travel in the same direction at different speeds they
meet in 5 hours. If they travel towards each
other, they meet in 1 hour. What are the speeds
of the two cars? Ans: 60, 40Kms/hour
27.
The median of the following data is 28.5. Find the missing
frequencies x and y if the total frequency is 60.
|
class
|
0-10
|
10-20
|
20-30
|
30-40
|
40-50
|
50-60
|
|
frequency
|
5
|
x
|
y
|
15
|
7
|
5
|
Ans:
x=8,y=20
28.
A right circular cylinder having diameter 12cm and height 15cm
is full of . ice-cream. The ice-cream is to be
filled in cones of height 12cm and diameter 6cm having a
hemispherical shape on the top. Find the number
of such cones which can be filled with ice-cream. Ans:
10
(OR)
An
engineering student was asked to make a model, which was
shaped like a cylinder with two cones attached to its two ends
using thin aluminums sheet. The diameter of the model is 3cm
and its length is 12cm, if each cone has a height of 2cm, find
the volume of air contained in the model. Ans:
66cm3
PAGE:
03
29.
The angles of depression of the top and the bottom of an 8m
tall building from the top of a multi storeyed building are 300
and 450, respectively. Find the height
of the multi-storeyed building and the distance between the
two building.. Ans: 4(3+√3) both.
(OR)
From
an aeroplane vertically above a straight horizontal road, the
angles of depression of two consecutive mile stones on
opposite sides of the aeroplane are observed to be α and
β . Show that the height in miles of
aeroplane above the road is given by
(HOTS)
30.
In a right triangle prove that the square of the hypotenuse is
equal to the sum of the square of its other two sides. Using
this to solve the following: In a right
triangle ABC in which angle C is right angle, if D is the mid
point of BC, Prove that AB2= 4AD2-3AC2.
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