UIMO Sample Paper Class 10

CLASS - 10 UIMO

UIMO SAMPLE QUESTIONS
CLASS - 10
MATHEMATICS - 1

01. Two circles with centres P and Q are as shown in the figure. The area of rectangle ABCD is 15 sq. cm.

Q P
D C

A T B
Find the area of ∆QPT.
12 2 16 2
(A) cm (B) 3.75 cm2 (C) 2.84 cm2 (D) cm
7 5
02. If the ratio of mean and median of a certain data is 2 : 3, what is the ratio of its mode and mean ?
(A) 3 : 2 (B) 5 : 2 (C) 3 : 5 (D) 2 : 3

! 
03. Find the quadratic polynomial one of whose zeros is and the product of zeros is − .
4
(A) 4 3 x + 5 x + 3 (B) 4 3 x + 5 x − 3

5 1
(C) 4 3 − 5 x + 2 3 (D) x + x−
4 3
T#
0". In an arithmetic progression, if = 5 and T4 – T3 = –5, find the sum of its first five terms.
T2

2 3 35 2
(A) 28 (B) −43 (C) (D) 17
5 4 2 3
05. Roshan walked 48 m due north and turned left. He again walked to a distance so that he is 60 m from
his starting point. How far did he walk after turning left ?
(A) 36 m (B) 39 m (C) 54 m (D) 46 m

MATHEMATICS - 2

01. If α, β are roots of aN2 + bN + c = 0, find one root of the equation aN2 – bN (N – 1) + c (N – 1)2 = 0.
⎛ α ⎞ ⎛  − β⎞ ⎛ α ⎞ ⎛ β ⎞
(A) ⎜⎝  − α ⎟⎠ (B) ⎜⎝ β ⎟⎠ (C) ⎜⎝  + α ⎟⎠ (D) ⎜⎝  + β ⎟⎠

02. If N + pN + q = 0 and N + qN + p = 0 have a common root, which of following is/are true ?
(A) p = q (B) 1 + p + q = 0 (C) p + q = 0 (D) p – q = 0

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CLASS - 10 UIMO

03. Which of the following have the same value ?
(A) sin2θ + cos2θ (B) sin2θ cosec2θ
(C) cosec2θ – cot2θ (D) sec2θ – tan2θ
04. Which of the following statements are not true ?
(A) Ratio of heights of two objects is equal to ratio of the length of their corresponding shadows at the
same time.
(B) Two similar triangles of equal areas are not congruent.
(C) ∆ABC with sides 5, 12 and 13 is an obtuse angled triangle.
(D) Similar figures are always congruent.
05. In the given figure, ∆ABC is right angled at B. If BD ⊥ AC thenwhich of the following is/are true ?
A

D

B C

(A) (B)
(C) (D)

REASONING

01. Ram is the brother of Shyam, and Mahesh is the father of Ram, Jagat is the brother of Priya and Priya
is the daughter of Shyam. Who is the uncle of Jagat ?
(A) Shyam (B) Mahesh
(C) Ram (D) Both Ram and Shyam
02. The positions of how many alphabets will remain unchanged if each of the alphabets in the word
WALKING is arranged in alphabetical order from left to right ?
(A) Zero (B) One
(C) Two (D) Four
03. Identify the missing word in the following.

(BLOAT, COAT) (CLING, DING) (SHOUT, ?)
(A) TUOT (B) HUTS
(C) SHOT (D) TOUT
04. Identify the second pair which has same relationship as in the first pair.

5 : 126 : : ?

(A) 8 : 127 (B) 6 : 218
(C) 3 : 28 (D) 2 : 10

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CLASS - 10 UIMO

05. A die is thrown three times and its three different positions are noted as follows.

" " "
!  ! $

What number occur at the opposite face of number 4 ?
(A) 1 (B) 4 (C) 5 (D) 2

CRITICAL THINKING

01. Following operations, in the given order have been performed on the figure shown in the box.
(i) Rotate 180° (ii) Flip horizontal (iii) Rotate 180° (iv) Flip vertical
Identify the resultant figure.

(A) (B) (C) (D)

02. Veena is as old as Meghana will be in five years. The difference between Jansi’s age and Meghana’s
age is twice the difference between Ilsa’s age and Meghan’s age. Jansi is 29. How old is Veena ?
(A) 4 (B) 10 (C) 19 (D) 24
03. 1988 rescue packages were distributed to seven regions affected by natural disasters as shown below.
P Q R S T U V
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
.. .. .. .. .. .. ..
Which region received the 1986th rescue package ?
(A) Region R (B) Region Q (C) Region T (D) Region U
04. In a class of 90, where girls are twice that of boys, shridar ranked fourteenth from the top, if there are
10 girls ahead of Shridar, How many boys are after him in rank ?
(A) 23 (B) 26 (C) 25 (D) 22
05. A and B are children of D. Who is the father of A ? To answer this question which of the statements (1)
and (2) is necessary ?
Statement (1) : C is the brother of A and the son of E.
Statement (2) : F is the mother of B.
(A) Only (1) (B) Only (2)
(C) Either (1) or (2) (D) (1) and (2) both

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CLASS - 10 UIMO

KEY & SOLUTION

MATHEMATICS - 1

01. (B) l = 2r + 2R & b = R
Given l × b = 15 cm2
2(R + r)(R) = 15 cm2

#
(R + r)(R) = cm2 = 7.5 cm2

1 1 1
Area of ∆QPT = × QP × PT = (R + r)(R) = × 7.5 cm2
2 2 2
= 3.75 cm2
02. (B) The given ratio of mean and median = 2 : 3 = 2x : 3x
But mode = 3 median – 2 mean
= 9x – 4x = 5x
The ratio of mode and mean = 5x : 2x = 5 : 2

3 −1
03. (B) Given α = & αβ =
4 2

3 −1
×β =
4 2
−2
β=
3

3 2 3 − 8 −5
∴α + β = − = =
4 3 4 3 4 3

−
αβ =

Required quadratic equation is x ` x
α + β) + αβ = 0

⎛ −5 ⎞ ⎛ 1 ⎞
x − x⎜ ⎟+⎜− ⎟ =0
⎝4 3⎠ ⎝ ⎠

4 3x + 5x − 3
=0
4 3

4 3 x2 + 3 x − 2 3 = 0

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CLASS - 10 UIMO

T5
04. (B) Given in an AP T = 5
2

= + "@
⇒ =#
=+@
a + 4d = 5a + 5d
4a = –d
Given T4 – T3 = –5
a + 3d – a – 2d = –5
d = –5
But 4a = –d
4a = – (–5)
5
a=
4
5
S5 = [2a + 4d]
2

5⎡ ⎛ 5⎞ ⎤
= ⎢2 ⎜ ⎟ + 4 ( −5)⎥
2⎣ ⎝4⎠ ⎦

5 ⎡5 ⎤
= ⎢ − 20 ⎥
2 ⎣2 ⎦

−17#
=
4

3
S5 = −43
4
05. (A) Given AB = 48 m and AC = 60 m and ∠B = 90°

+ *

60 mts 48 mts

)
∴ AC2 = AB2 + BC2
(60m)2 = (48m)2 + BC2
3600 m2 = 2304 m2 + BC2
3600 m2 – 2304 m2 = BC2

BC = 1296m2
BC = 36 m

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CLASS - 10 UIMO

MATHEMATICS - 2

b
01. (C,D) Given α + β = −
a
c
αβ =
a
given equation is ax2 – bx2 + bx + cx2 – 2cx + c = 0
− (b − 2c )
Sum of roots =
a−b + c

−b c
+2
−b + 2c
= = a a
a−b + c 1− + c
b
a a

α + β + 2αβ α β
⇒ = +
1 + α + β + 2β 1 + α 1 + β

c
Product of roots =
a−b + c

c
= a
b c
1− +
a a

αβ αβ
⇒ =
1 + α + β + αβ (1 − α )(1 + β )

⎛ α ⎞⎛ β ⎞
=⎜ ⎟⎜ ⎟
⎝ 1 + α ⎠⎝ 1 + β ⎠
02. (A,B,D) Let ‘α’ be the common root of both equation
α2 + pα + q = 0 ........... (1)
α2 + q 2 + p = 0 ........... (2)
α2 + pα + q = α2 + qα + p = 0
pα – qα + q – p = 0
α(p – q) – 1(p – q) = 0
(p – q) (α – 1) = 0
p – q = 0 (or) α – 1 = 0
p = q (or) α = 1
If α = 1 then 1 + p + q = 0 ............ (1)

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CLASS - 10 UIMO

03. (A,B,C,D)(A) sin2θ + cos2θ = 1

1
(B) sin2θ cosec2θ = sin2θ × =1
cosec θ
(C) cosec2θ – cot2θ = 1
(D) sec2θ – tan2θ = 1
04. (B,C,D) (B) Two similar triangles of equal area are congruent
(C) ∆ABC with sides 5 units, 12 units and 13 units is a right angled trangle [ 132 = 122 + 52]
(D) Similar figures need not be congruent.
05. (A,B,C) ∆ABC ∆ADB [ A.A similarity]
∆ABC ∆BDC [ A.A similarity]
∆ADB ∆BDC [ Transitive property]

REASONING

01. (C) Mahesh (+)

Father
Brother
Ram Shyam

Daughter
Brother
Priya Jagat
(–) (+)

Ram is the uncle of Jagat

W A L K I N G
02. (C)
A G I K L N W

Two letters are unchanged
03. (D) BLOAT – COAT
‘BL’ removed and ‘C’ added
Similarly CLING – DING
SHOUT – TOUT
04. (C) 5 : 125 : : ?
53 + 1 ⇒ 125 + 1 ⇒ 126
Similarly 33 + 1 ⇒ 27 + 1 ⇒ 28
05. (C) Adjacent faces of 4 are 2, 3, 1, 6
∴ 4 opposite number is 5.

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CLASS - 10 UIMO

CRITICAL THINKING

01. (A) (i) If we rotate the pattern 18 degree, we will get the pattern as shown in option A.
(ii) If we flip horizontally, then the pattern will look like B.
(iii) If we rotate the pattern in ii by 180 degrees, we will get a pattern as shown in D.
(iv) If we flip the pattern in iii, we get pattern shown in A.
02. (D) You should have eliminated choice a immediately. Veena can’t be four years old if Meghan is going to
be Ilsa’s age in five years. The best way to eliminate other answer choices is to try plugging them into
the information given in the problem. For instance, for choice b, if Ilsa is 10, then Meghan must be 5.
The difference in their ages is 5. The difference between Jansi’s age, 29, and Meghan’s age, 5, is 24. Is
24 two times 5? No. Then choice b is wrong. You could eliminate choice c in the same way and be left
with choice D.

1988
03. (C) ⇒ 284 R 0, 1988 = V, 1987 = u, 1986 = T
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04. (B) Explanation – No of boys = x; No of girls = 2x;
x+2x = 90 = > 3x = 90
x (Boys)= 30 ; 2x(Girls) = 60
Number of student behind Shridar = 90 – 14 = 76
No of girls behind Shridar = 60 – 10 = 50
No of boys behind Shridar = 76 – 50 = 26
05. (B) A and B are children of D.
From (1), C is the brother B and son of E.
Since, the sex of D and E are not known. Hence (1) is not sufficient to answer the question.
From (2). F is the mother of B. Hence, F is also the mother of A. Hence D is the father of A.
Thus, (2) is sufficient to answer the question.

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