UCO Sample Paper Solution Class 10

UNIFIED COUNCIL
A n I S O 9 0 0 1 : 2008 C e r t i f i e d O r g a n i s a t i o n

UNI FI ED C YBER OLYMP IA D
Solutions for Sample Questions
class : 10
Mental Ability 2
 2  q  1  0   +1 =  q
1. (C) h2 = a2 + b2, since, a and h are consecutive 2
integers, h = a + 1 2  q  1  0   + 1 = q

 (a + 1)2 = a2 + b2 (  ) (  ) (  ) (  )

 b2 = 2a + 1  [  ( )  2 ] [  (  )  2 ]

b2  1 
 (1  p   2 ) 1  p  2 
a
2  (p  q)(p  q)

b2  1  (p  q)(p  q)
 h
2  (p2  q2 )  q 2  p2
a b2  1 5. (C) Let the original sides be a, b, c, then
So, sin  
h b2  1 1
2. (C) The unit digit of each term successively 1,
s a  b  c
2
9, 1, 9, 1, 9, .....
and area of the triangle
The unit digit of sum of first two terms is 0.
The unit digit of sum of first three terms is 1. = s  s  a  s  b  s  c 
The unit digit of sum of first four terms is 0.
For the new triangle,the sides are 2a, 2b, 2c
Hence, the digit in units place is 0 or 1
depending on number of terms i.e., even or 1
odd respectively. So, the unit digit of the
Then, S   2a  2b  2c 
2
sum of 2009 terms is 1.
= a + b + c = 2s
40  Area of new triangle
3. (D) 36000  {2a1 + (40 – 1)d}
2
= S  S  2a  S  2b  S  2c 
 1800 = 2a1 + 39d ..... (i)

2 30 = 2s  2s  2a  2s  2b  2s  2c 
and  36000  {2a1  (30  1)d}
3 2
 1600 = 2a1 + 29d ..... (ii) = 16s  s  a s  b  s  c 
From (i) and (ii), a1 = 510 d = 20.
= 4 s  s  a  s  b  s  c 
Value of 12th instalment = a12
= 510 + (12 – 1)  20 = 730 = 4  (area of original triangle)
4. (D) 2
 and  are the roots of x + px + 1 = 0  Area becomes 4 times of original area.
      p,   1
 and  are the roots of x2 + qx + 1 = 0

   1

Reasoning From 2: F is the mother of B. Hence, F is
also the mother of A. Hence, D is the father
6. (C) Draw a vertical line at the centre in each
of A. Thus, 2 is sufficient to answer the
figure. Turn the book 90o clockwise, the
question.
figures are water images of the letters I, J,
K, L and M. Hence the next one is N. C ompu t er s
11. (A) Bluetooth is a wireless technology built in
7. (A) electronic gadgets used for exchanging data
over short distances.
12. (C) Verification of login name and password is
known as authentication.
13. (D) Cache memory has the shortest access
time.
14. (B) The collection of user messages on various
8. (B) According to P  Q + R – S subjects that are posted on world wide
network is called usenet.
Q P
15. (C) JPEG stands for “Joint Photographic
Experts Group”.
R S
English
 S is in the South-east of Q.
16. (A) Having ornithophobia, vivek does not like
9. (C) C R E A T I V E birds.
3 18 5 1 20 9 22 5 17. (C) He said that he had been studying since
morning.
Hence, 3 pairs are possible. 18. (D) Allegiance means Loyalty.
10. (B) A and B are children of D. 19. (A) The correct spelling of Sarcofhagus is
Sarcophagus.
From 1: C is the brother B and son of E.
Since, the sex of D and E are not known. 20. (B) Dog in the manger
Hence, 1 is not sufficient to answer the
question.