Question 1 1.2 / -0
Select a figure from the options which will continue the same series as established by the Problem Figures.
Solution
The following transformations occurs alternately:
Also, encircled elements increase by 2 and move up and down alternately.
Question 2 1.2 / -0
Select the correct water image of the given figure.
Question 3 1.2 / -0
Q is the brother of R, P is the sister of Q, T is the brother of S and S is the daughter of R. Who are the cousins of Q?
Solution
Q is the brother of R and P is the sister of Q. So, R and P are the cousins of Q.
+ represents a male and - represents a female.
Question 4 1.2 / -0
Study the given Venn diagram carefully.
How many males are neither civil servants nor married?
Solution
Only number 4 does not lie in rectangle and triangle. So, there are 4 males who are neither civil servants nor married.
Question 5 1.2 / -0
Sukul walks 5 km from her school. Then she turns to her right and after walking 3 km, again she turns to her right and walks 1 km to reach her home. How far is she now from her school?
Solution
AE = AC - EC
= 5 - 1 = 4 km
In
AEB,
By using Pythagoras theorem,
AB
2 = AE
2 + EB
2 AB
2 = 4
2 + 3
2 = 16 + 9 = 25
AB = 5 km
Sukul is now 5 km away from her school.
Question 6 1.2 / -0
If it is possible to make a meaningful English word with the second, third, sixth, ninth and tenth letters of the word PREDOMINANT, then the third letter of the word is the answer. If no meaningful word is formed, give 'X' as your answer. If more than one words are formed, give 'Y' as your answer.
Solution
The second, third, sixth, ninth and eleventh letters of the word PREDOMINANT are R, E, M, A and N.
Question 7 1.2 / -0
In a certain code language, '543' means 'give my water'; '247' means 'water is life' and '632' means 'enjoy my life'. Which of the following stands for 'enjoy' in that language?
Solution
543
give my water ...(i)
247
water is life ...(ii)
632
enjoy my life ...(iii)
From (ii) and (iii), 2 stands for life.
From (i) and (iii), 3 stands for my.
So, from (iii), 6 stands for enjoy.
Question 8 1.2 / -0
If '-' stands for 'division', '+' stands for 'multiplication', '
' stands for 'subtraction' and '×' stands for 'addition', then which of the following statements is CORRECT?
Solution
After interchanging the symbols, we get:
(1) 265 - 11 × 2
14 = 256 - 11 × 0.14 = 256 - 1.54 = 254.46
22
(2) 46 × 10 - 10
5 = 460 - 2 = 458
92
(3) 66
3 × 11 - 12 = 22 × 11 - 12 = 242 - 12 = 230
(4) 2 × 14
4 - 11 = 2 × 3.5 - 11 = 7 - 11 = - 4
16
Question 9 1.2 / -0
Choose a box from the options that is similar to the box formed from the given sheet of paper.
Solution
Only the box given in option (1) is similar to the box formed when the given sheet of paper is folded to form a box.rd option not possible)nd option not possible)th option not possible)
Question 10 1.2 / -0
Count the number of cubes in the given figure.
Solution
Number of cubes in layer 1 = 5 × 5 = 25
Number of cubes in layer 2 = 4 × 5 = 20
Number of cubes in layer 3 = 3 × 5 = 15
Number of cubes in layer 4 = 2 × 5 = 10
Number of cubes in layer 5 = 1 × 5 = 5
Total number of cubes in the figure
= 25 + 20 + 15 + 10 + 5 = 75
Question 11 1.2 / -0
Select a figure from the options in which Fig. (X) is exactly embedded as one of its parts.
Solution
In option (2), figure X is embedded as
.
Question 12 1.2 / -0
Find the missing term in the series given below.
Solution
The rule being followed is:
Question 13 1.2 / -0
A square transparent sheet with a pattern and a dotted line on it is given. Select a figure from the options which shows the given sheet when folded along the dotted line.
Question 14 1.2 / -0
Group the given figures into three classes on the basis of their identical properties using each figure only once.
Solution
(1, 3, 5): Figures containing line segments which are half the number of sides of the figure
Question 15 1.2 / -0
Select the figure from the given options, which satisfies the same conditions of placement of dots as in the given figure.
Solution
One dot in circle and square.
One dot in triangle and square.
One dot in all three.
The only option that satisfies the given conditions is option 4.
Question 16 1.2 / -0
By which congruency criterion,
QPR
QPS, if QR = QS, PR
QA and PS
QC.
Solution
In
QPR and
QPS
QRP =
QSP = 90°
QR = QS (given)
QP = QP (Common)
QPR
QPS [By RHS congruence criterion]
Question 17 1.2 / -0
In the given figure (not drawn to scale), QS is the bisector of
PQR. Find the value of 2
QSP.
Solution
In
PQR,
PQR +
QRP +
RPQ = 180° (Angle sum property)
PQR + 50° + 60° = 180°
PQR = 180° - 110° = 70°
As, QS is the bisector of
PQR;
So,
PQS =
SQR =
PQR =
= 35°
Now, in
PQS,
PQS +
QSP +
SPQ = 180° (Angle sum property)
35° +
QSP + 60° = 180°
QSP = 180° - 95° = 85°
2
QSP = 2 × 85° = 170°
Question 18 1.2 / -0
Which of the following angles can be used to construct a right angled triangle?
Solution
In a right angled triangle, one angle must be of 90°. So, option (1) is correct as in other options 90° angle is not possible.
Question 19 1.2 / -0
In the given figure (not drawn to scale), AB and AC are the bisectors of
DBC and
DCB, respectively. Which of the following options is incorrect?
Solution
(1) In
BDC,
DCB +
CBD +
BDC = 180° (Angle sum property)
70° + 60° +
BDC = 180°
BDC = 180° - 70° - 60°
BDC = 50°
(2)
ABC =
DBC =
× 60° = 30°
ACB =
DCB =
× 70° = 35°
In
BAC,
BAC +
ACB +
ABC = 180°
BAC + 35° + 30° = 180°
BAC = 180° - 35° - 30°
BAC = 115°
(3)
ABC = 30°
(4)
ACB = 35°
33°
Option 4 is not correct.
Hence, option 4 is the answer.
Question 20 1.2 / -0
Which of the following figures have at least 2 lines of symmetry?
Solution
Only figures P, Q and R have at least 2 lines of symmetry.
Question 21 1.2 / -0
Which of the following data has the median as 16?
Solution
1. Arranging the given data in ascending order,
1, 7, 11, 12, 16, 18, 22
Number of observations n = 7
Median =
term
= 4
th term = 12
2. Arranging the given data in ascending order,
1, 11, 15, 16, 17, 19, 21
Here, n = 7
Median =
term = 4
th term = 16
3. Arranging the given data in ascending order,
2, 9, 10, 13, 14, 16, 21.
Here n = 7
Median =
term = 4
th term = 13
4. Arranging the given data in ascending order,
8, 16, 17, 19, 20, 22, 25
Here n = 7
Median =
term = 4
th term = 19
Question 22 1.2 / -0
Which of the following rational numbers satisfy the given property?
Question 23 1.2 / -0
Find the sum which will earn a simple interest of Rs. 156 in 4 years at 12% per annum.
Solution
Let the sum be Rs. x.
S.I. =
156 =
x =
x = 325
The sum is Rs. 325.
Question 24 1.2 / -0
In the given figure (not drawn to scale), ABCD is a rectangle. ED = 16 cm, FG = FC = 8 cm, BF = 20 cm and FG is perpendicular to BC. If CD is half of AD, then find the area of the shaded region (in cm
2 ).
Solution
Draw a line GH perpendicular to CD. So, GFCH is a square.
Area of square GFCH = (8
2 ) cm
2 = 64 cm
2 Since ABCD is a rectangle and BC = AD
28 = AE + ED
AE = (28 - 16) cm = 12 cm
As CD is half of AD
CD =
AD =
cm = 14 cm
CH + HD = 14 cm
HD = (14 - 8) cm = 6 cm
Now, area of
GHD =
× 8 × 6 = 24 cm
2 Area of
AEB =
× 12 × 14 = 84 cm
2 Area of rectangle ABCD = (28 × 14) cm
2 = 392 cm
2 Area of the shaded region = Area of rectangle ABCD - (Area of
AEB + Area of
GHD + Area of square GFCH)
= {392 - (84 + 24 + 64)} cm
2 = 220 cm
2
Question 25 1.2 / -0
The ratio of the length of Rope A to the length of Rope B is 3 : 4. The ratio of the length of Rope C to the length of Rope B is 7 : 6. If the length of the longest rope is 84 cm, then find the total length of the three ropes.
Solution
Let the length of Rope A be 3x and length of Rope B be 4x.
Given that,
Length of Rope C =
× Length of Rope B
=
× 4x =
As, Rope C is the longest rope.
= 84
x = 18
Length of Rope A = 3 × 18 = 54 cm
Length of Rope B = 4 × 18 = 72 cm
Hence, the total length of three ropes = 84 + 54 + 72 = 210 cm
Question 26 1.2 / -0
Which of the following statements is incorrect?
Solution
(1) Every negative rational number is less than 0 and every positive rational number is greater than 0.th term of the number pattern: 11, 21, 31, 41, ..... is 10n + 1.
Question 27 1.2 / -0
Which of the following can be the net of the given solid?
Question 28 1.2 / -0
Which of the following number lines correctly represents 'p' if, p - (2p + 5) - 5(1 - 2p) = 2(3 + 4p) - 3(p - 4)?
Solution
We have,
p - (2p + 5) - 5(1 - 2p) = 2(3 + 4p) - 3(p - 4)
p - 2p - 5 - 5 + 10p = 6 + 8p - 3p + 12
9p - 10 = 5p + 18
9p - 5p = 10 + 18
4p = 28
p = 7
So, the number line which represents '7' is
Question 29 1.2 / -0
Solve for x:
Question 30 1.2 / -0
If
of 64% of
is 1,280, then the value of x is _______.
Solution
We have,
of 64% of
= 1,280
= 1,280
x =
= 98,000
Question 31 1.2 / -0
Simplify
Solution
We have,
= 2
(p - 8 - p + 11) × 8
(q - 4 - q + 5) = 2
3 × 8
1 = 2
6
Question 32 1.2 / -0
Select a pair of integers whose sum is - 51.
Solution
(1) - 42 + 93 = 51
- 51
(2) 1 + (- 50) = - 49
- 51
(3) - 93 + 42 = -51
(4) - 1 + (- 52) = -53
- 51
Question 33 1.2 / -0
A circle with centre at O and radius 5 cm is given. A right angled triangle AOB is inscribed in the circle. Find the area of the shaded region.
Solution
Area of
AOB =
× OB × OA =
× 5 × 5 =
cm
2 Now, area of circle =
r
2 =
× 5 × 5 =
cm
2 Area of shaded region = Area of circle - area of
AOB
=
cm
2
Question 34 1.2 / -0
By how much is -12x + 2y greater than the sum of -18x + 6y and 5x - 25y?
Solution
Sum = (- 18x + 6y) + (5x - 25y) = - 13x - 19y
Required expression = (- 12x + 2y) - (- 13x - 19y)
= - 12x + 2y + 13x + 19y = x + 21y
Question 35 1.2 / -0
If a : b = 2
: 1
and b : c = 1
: 3
, then find a : b : c.
Solution
a : b =
And b : c =
So, a : b : c = 15 : 10 : 28
Question 36 1.2 / -0
Shubh and Naksh donate some money in a relief fund. The amount donated by Naksh is Rs. 125 more than the amount donated by Shubh. If the total money paid by them is Rs. 975, find the amount of money donated by Shubh.
Solution
Let the amount of money donated by Shubh be Rs. x.
So, the amount of money donated by Naksh = Rs. (125 + x)
Total amount of money donated by them = Rs. 975
x + 125 + x = 975
2x = 975 - 125
x =
= 425
Question 37 1.2 / -0
A shopkeeper sells two televisions for Rs. 1955 each, gaining 15% on one and losing 15% on other. Find his gain or loss per cent in the whole transaction.
Solution
For first television: S.P. = Rs. 1955
Gain % = 15%
C.P. =
For second television: S.P. = Rs. 1955
Loss % = 15%
C.P. =
× 1955 = Rs. 2300
Now, total C.P. = Rs. (1700 + 2300) = Rs. 4000
Total S.P. = Rs. (1955 × 2) = Rs. 3910
Loss = C.P. - S.P. = Rs. (4000 - 3910) = Rs. 90
Loss% =
=
%
Question 38 1.2 / -0
A floor measuring 2 m by 1.5 m is to be covered with tiles measuring 25 cm by 25 cm. Find the number of tiles required to cover the floor and the cost of the tiles at Rs. 420 per dozen.
Solution
Number of tiles required =
=
= 48
Cost of 12 tiles = Rs. 420
So, cost of 1 tile = Rs.
= Rs. 35
Cost of 48 tiles = Rs. (35 × 48) = Rs. 1680
Question 39 1.2 / -0
Alisha has to score 40% of the maximum marks to pass. Alisha scored 255 marks and failed by 45 marks. Calculate the maximum marks.
Solution
Let the maximum marks be x.
Number of marks required to pass = 40% of x =
According to the question, we have
Question 40 1.2 / -0
An 80 m long ladder is placed against a wall in such a way that the foot of the ladder is 64 m away from the wall. Up to what height does the ladder reach the wall?
Solution
Let AB be the length of the ladder, AC be the height of the wall up to the ladder reaches and BC be the distance between the foot of the ladder and the wall.
By using Pythagoras theorem, we get
AB
2 = AC
2 + BC
2 80
2 = AC
2 + 64
2 AC
2 = 80
2 - 64
2 AC
2 = 6400 - 4096
AC
2 = 2304
AC
2 = 48
2 AC = 48 m
Question 41 1.2 / -0
A certain freezing process requires room temperature be lowered from 50°C at the rate of 6°C every hour. What will be the room temperature 12 hours after the process begins?
Solution
Room temperature at the beginning = 50°C
Decrease in temperature in 1 hour = 6°C
Decrease in temperature in 12 hours = (12 × 6)°C = 72°C
Room temperature after 12 hours = (50 - 72)°C = -22°C
Question 42 1.2 / -0
Himani ate half of a cake on Monday. She ate half of the cake left on Tuesday and so on. She followed this pattern till Thursday. What fraction of the cake has she eaten till Thursday?
Solution
Let the total fraction of cake be x.
Fraction of cake eaten by Himani on Monday =
Fraction of remaining cake = x -
Fraction of cake eaten on Tuesday =
Fraction of remaining cake =
Fraction of cake eaten on Wednesday =
Fraction of remaining cake =
-
=
=
Fraction of cake eaten on Thursday =
Fraction of cake eaten by her till Thursday
Question 43 1.2 / -0
A bag contains red, white and blue pencils. The probability of selecting a red pencil is
and that of selecting a blue pencil is
. Find the probability of selecting a white pencil.
Solution
As probability (red pencil) + Probability (blue pencil) + Probability (white pencil) = 1
Probability (white pencil)
= 1 - [Probability (red pencil) + Probability (blue pencil)]
=
Question 44 1.2 / -0
In an examination, one should get 36% of the maximum marks to pass. A student obtained 113 marks and was declared fail by 85 marks. The maximum marks are ______.
Solution
Let the maximum marks be x.
Passing marks = 36% of x =
x
According to the question,
x = 113 + 85
x =
= 550
Question 45 1.2 / -0
The grades obtained by 30 students of class VII are as follows:- , B+ , A, B, A+ , B- , A- , B, B, B- , A, A, A+ , B, B+ , A, A+ , B, B, A, A, A- , A- , B, B+ , B, B+ , A- , A+ , A+ ?
Solution
Total number of students in class VII = 30
Number of students who got grade A
+ = 4
Required probability =
Question 46 1.2 / -0
In the given figure (not drawn to scale), if AB || CG || EF, then find
(i) 2z - x
(ii) x + 2y
Solution
AB || CG and BD is the transversal.
x = 80° [Corresponding angles]
BDG = x = 80° [Vertically opposite angles]
In
BDG,
40° + 80° + y = 180° [Angle sum property]
120° + y = 180°
y = 60°
CG || EF and DE is the transversal.
x = 20° + z [Alternate interior angles]
80° = 20° + z
z = 60°
(i) 2z - x = 2 × 60° - 80° = 40°
(ii) x + 2y = 80° + 2 × 60° = 200°
Question 47 1.2 / -0
Solution
(P):
(Q):
(R):
(S):
We have, (P)
(iii), (Q)
(iv), (R)
(i), (S)
(ii)
Question 48 1.2 / -0
Read the following statements carefully and select the correct option.Statement-1: Difference between the value of expression, 4x + 2(x + y) when x = 2; y = 3 and when x = 3; y = 2 is 10. Statement-2 : 4(a + 2b) + 3b2 + 9ab should be subtracted from 2a - 2b + b2 - 6ab to get - (2a + 10b + 8b2 + 5ab)
Solution
Statement - 1: Given expression = 4x + 2(x + y)
Putting x = 2, y = 3 in given expression, we get
4 × 2 + 2 (2 + 3) = 8 + 2 × 5 = 8 + 10 = 18
Also, putting x = 3 and y = 2 in given expression, we get
4 × 3 + 2 (3 + 2) = 12 + 2 × 5 = 12 + 10 = 22
Required difference = 22 - 18 = 4
10
Hence, Statement (1) is false.
Statement - 2: 2a - 2b + b
2 - 6ab - [4 (a + 2b) + 3b
2 + 9ab]
= 2a - 2b + b
2 - 6ab - [4a + 8b + 3b
2 + 9ab]
= 2a - 2b + b
2 - 6ab - 4a - 8b - 3b
2 - 9ab
= -2a - 10b - 2b
2 - 15ab
= -(2a + 10b + 2b
2 + 15ab)
- (2a + 10b + 8b
2 + 5ab)
Hence, Statement (2) is also false.
Question 49 1.2 / -0
Read the statements carefully and state 'T for true and 'F' for false.
Solution
(i) False, the difference between the lengths of any two sides of a triangle is less than the length of the third side.
Question 50 1.2 / -0
Study the double bar graph, which shows two different models of mobile phones, S
1 and S
7 produced in a factory from June to September.
(i) In which month was the production of mobile phones twice the production of mobile phones in September?
(ii) What is the mean of the S
7 mobile phone produced by the factory from June to September?
Solution
(i) Number of mobile phones produced in September
= 40000 + 30000 = 70000
Number of mobile phones produced in June
= 50000 + 70000 = 120000
Number of mobile phones produced in August
= 55000 + 75000 = 130000
Number of mobile phones produced in July
= 80000 + 60000 = 140000
= 2 × 70000
= 2 (Number of mobile phone produced in September)
(ii) Number of S
7 mobile phones produced from June to September = 70000 + 60000 + 75000 + 30000 = 235000
Mean =
= 58750
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