Question 1 1.2 / -0
Select a figure from the options which will continue the same series as established by the Problem Figures.
Solution
Symbols
and symbols
interchange alternatively.
Question 2 1.2 / -0
Select the correct mirror image of the given figure.
Question 3 1.2 / -0
Reema is the sister of Vipin. Sudha is the mother of Vipin. Jagdish is the father-in-law of Sudha. How is Reema related to Jagdish?
Solution
Jagdish is the father-in-law of Sudha and Sudha is the mother of Vipin and Reema.
Question 4 1.2 / -0
Which of the following Venn diagrams best represents the relationship among "Red", "Rose", and "Clothes"?
Question 5 1.2 / -0
Town X is towards west of town Y. Town Z is towards south of town X. Town B is towards south of town Z. In which direction is town X with respect to town B?
Solution
So, town X towards the north of town B.
Question 6 1.2 / -0
If it is possible to make a meaningful word with the first, second, seventh and eighth letters of the word DIAGONAL, then the third letter of the word thus formed is the answer. If no such meaningful word is formed, then give 'N' as your answer. If more than one such word is formed, then give 'M' as your answer.
Solution
First, second, seventh and eighth letters of the word DIAGONAL are D, I, A and L, respectively. The meaningful words formed are DIAL and LAID.
Question 7 1.2 / -0
If in a certain code language, MEDICATE is written as GVCEKFGO, then how will VALIDATE be written in the same code language?
Solution
After reversing the letters of MEDICATE, we get:
Similarly, after reversing the letters of VALIDATE, we get:
Question 8 1.2 / -0
If each of the odd digits in the number 147832 is increased by 1 and each of the even digits is decreased by 1, then find the sum of the digits of the new number formed.
Solution
Given number = 147832
Question 9 1.2 / -0
The sheet of paper shown in Fig. (X) is folded to form a box. Choose the box from the options that will not be formed.
Solution
The opposite faces of the box formed are (A, E), (C, F) and (B, D).
Question 10 1.2 / -0
Count the number of triangles in the given figure.
Solution
Triangles formed are as follows:
A, B, C, D, E, F, H, J, K, L, M, N, O, P, R, AB, AC, CD, DB, LM, OP
∴ Number of triangles formed in the given figure = 21
Question 11 1.2 / -0
Select the option which has exactly the same components as those in the given figure.
Solution
The red highlighted portions in the above mentioned options are missing.
Only the figure in option (2) has exactly the same components as those in the given figure.
Question 12 1.2 / -0
Find the missing number if the same rule is followed in all the three figures.
Solution
The rule followed is:
Question 13 1.2 / -0
A square transparent sheet (X) with a pattern and a dotted line on it is shown here. Find the figure from the options as to how the pattern would appear when the transparent sheet is folded along the dotted line.
Question 14 1.2 / -0
Select a term from the options which will continue the given series.? __
Solution
The pattern followed is:
∴ Required term is J15Q.
Question 15 1.2 / -0
Select a figure from the options which will complete the pattern given in Fig. (X).
Question 16 1.2 / -0
In the given figure (not drawn to scale), ABC and DBE are straight lines. Find the value of y.
Solution
ABC and DBE are straight lines.
∴
ABE =
DBC (Vertically opposite angles)
ABF +
FBE = 142°
90° + y = 142°
y = 142° - 90° = 52°
Question 17 1.2 / -0
In the given figure, state whether the triangles are congruent and choose the correct order.
Solution
Given triangles are not congruent to each other.
Question 18 1.2 / -0
In the given figure, ACD is a straight line. AC = CB and BF || DE. Find
BAE.
Solution
We have,
AC = CB
CAB =
CBA [Angles opposite to equal sides of a triangle are equal]
In ΔABC,
ACB +
BAC +
CBA = 180° [Angle sum property]
2
CAB + 106° = 180°
CAB = 37°
Also,
FCD =
BCA = 106° [Vertically opposite angles]
BF || DE and AD is the transversal.
FCD +
ADE = 180°
ADE = 180° – 106° = 74°
Now, in ΔADE,
ADE +
DEA +
EAD = 180° [Angle sum property]
74° + 59° +
EAD = 180°
EAD = 180° – 133° = 47°
So,
BAD =
BAC +
EAD = 37° + 47° = 84°
Question 19 1.2 / -0
In the given figure (not drawn to scale), if EFA is a right-angled triangle with
EFA = 90° and FGB is an equilateral triangle, then find the value of y - 2x.
Solution
FGB is an equilateral triangle.
So,
GBF =
BFG =
FGB = 60°
In ΔBCF,
CBF +
BFC =
GCF (Exterior angle property)
60° +
BFC = 92°
BFC = 92° - 60° = 32°
Now,
BFG =
BFC + x
60° = 32° + x
x = 60° - 32° = 28°
Also,
EFA =
BFA + y
90° = 32° + y
y = 90° - 32° = 58°
∴
y - 2x = 58° - 2 × 28° = 58° - 56° = 2°
Question 20 1.2 / -0
By which congruency criterion are the two triangles in the given figure congruent?
Solution
In ΔABE and ΔACE,
Question 21 1.2 / -0
Directions For Questions
Directions:
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In which year was the difference of number of copies of both the newspapers sold maximum?
Solution
In 2015,
Question 22 1.2 / -0
Directions For Questions
Directions:
...view full instructions
What is the ratio of newspapers sold in the years 2016 and 2017 together to the total number of newspapers sold in 2018?
Solution
Newspapers sold in year 2016 = 80 + 55 = 135
Newspapers sold in year 2017 = 60 + 40 = 100
Newspapers sold in year 2016 and 2017 together = 135 + 100 = 235
Total number of newspapers sold in 2018 = 70 + 30 = 100
Required ratio =
, i.e. 47 : 20
Question 23 1.2 / -0
The sum of two rational numbers is -7. If one of the rational numbers is
, then find the additive inverse of the other rational number.
Solution
Let the other rational number be x.
According to question,
x = -7 +
x =
∴ Additive inverse of
is
.
Question 24 1.2 / -0
A sum of money at simple interest doubles itself in 5 years 6 months. In how much time will it triple itself at the same rate?
Solution
Let the principal be Rs. x.
According to the question,
Amount = Rs. 2x
S.I. = Amount - Principal = Rs. (2x - x) = Rs. x
∴ S.I. =
x =
Also, if sum of money triples, i.e.
Amount = Rs. 3x
S.I. = Amount - Principal = Rs. (3x - x) = Rs. 2x
∴ 2x =
T = 11 years
Question 25 1.2 / -0
Study the given figure (not drawn to scale) carefully and select the correct option.
(i) Perimeter of the complete figure is 198 cm.
(ii) Total area of figures II and III is 4 cm
2 less than the total area of figures I and IV.
Solution
(i) Perimeter of the figure = AB + BC + CD + DE + EF + FI + IJ + JK + KL + LM + MA
= (AB + BC + DE) + (CD + EF) + FI + (IJ + KL + AM) + JK + LM
= (44 + 40 + 44 + 40 + 18 + 18) cm = 204 cm
So, (i) is false.
(ii) Area of figure II = 18 × 10 = 180 cm
2 Area of figure III = 40 × 14 = 560 cm
2 Total area of figures II and III = (560 + 180) cm
2 = 740 cm
2 Area of figure I = 20 × 18 = 360 cm
2 Area of figure IV = 32 × 12 = 384 cm
2 Total area of figures I and IV = (360 + 384) cm
2 = 744 cm
2 ∴ Required difference = (744 - 740) cm
2 = 4 cm
2 So, (ii) is true.
Question 26 1.2 / -0
If a =
, b =
and c =
, then which of the following statements is CORRECT?
Solution
We have, a =
and c =
L.C.M. of 100, 5, and 10 = 100
a =
, b =
and c =
So, a < c < b.
Question 27 1.2 / -0
The following are the steps involved in finding the value of x : y, if
. Arrange them in sequential order from the first to the last.
1. 9x + 12y = 8x + 20y
2. Given,
3.
4. 3(3x + 4y) = 4(2x + 5y)
5. x = 8y
Solution
3(3x + 4y) = 4(2x + 5y)
9x + 12y = 8x + 20y
x = 8y
The sequential order from first to last is:(2)
(4)
(1)
(5)
(3)
Question 28 1.2 / -0
What rational number should be added to
to get the greatest negative integer?
Solution
Let the required rational number be x.
Greatest negative integer = -1
According to question,
x = -1 +
x =
Question 29 1.2 / -0
The ratio of number of 10 rupee notes to 20 rupee notes in a purse is 3 : 4. If there are total 84 notes in the purse, then how much money is there in the purse?
Solution
Let the number of 10 rupee notes and 20 rupee notes be 3x and 4x, respectively.
According to question,
3x + 4x = 84
7x = 84
x =
= 12
So,
Number of 10 rupee notes = 3 × 12 = 36
And,
Number of 20 rupee notes = 4 × 12 = 48
∴ Total amount of money in the purse = 36 × 10 + 48 × 20
= 360 + 960 = Rs. 1320
Question 30 1.2 / -0
Read the following statements carefully.
1. 48.95 - 32.006 = 16.944
2. 4 + 4.44 + 0.4 + 44.04 = 52.87
3. 101
= 101.00027
Which of the given statements is/are CORRECT?
Solution
1. 48.95 - 32.006 = 16.944 (Correct)
2. 4 + 4.44 + 0.4 + 44.04 = 52.88
52.87 (Incorrect)
3. 101
=
= 101.00027 (Correct)
∴ Both statements 1 and 3 are correct.
Question 31 1.2 / -0
The value of x in
(7x - 1) -
= x +
is ________.
Question 32 1.2 / -0
Given that LM || NQ,
LMP = 135° and
QNP = 120°. Find the value of x.
Solution
Draw a line PR || NQ, such that PR || NQ || LM.
NQ || PR and NP is transversal.
∴
QNP +
NPR = 180° (Co-interior angles)
120° +
NPR = 180°
NPR = 60°
Also, LM || PR and MP is transversal.
∴
LMP =
MPR (Alternate interior angles)
135° = x +
NPR
x = 135° – 60° = 75°
Question 33 1.2 / -0
Which of the following number lines represents -3 - 4?
Solution
– 3 – 4 is represented by:
Question 34 1.2 / -0
How many more unit squares in the figure must be shaded so that the fraction of unshaded squares becomes
?
Solution
Total number of equal squares = 25
Required fraction of unshaded squares =
∴ Required number of unshaded squares =
× 25 = 10
And, number of unshaded squares in the figure = 16
∴ Required number of squares that must be shaded = 16 - 10 = 6
Question 35 1.2 / -0
The following are the margins of victory in the matches of a football league:
Solution
Sum of all observations = 60
Total number of observations = 20
∴ Mean =
= 3
Question 36 1.2 / -0
Tani decides to spend Rs. 900 for distributing food items to poor children. But, she has only Rs. 420. So, she decides to do a typing job that can earn her Rs. 60 per hour. Form an equation in terms of x, if she works for x hours.
Solution
Amount of money Tani decides to spend = Rs. 900
Question 37 1.2 / -0
A rice company earns a profit of Rs. 15 per bag of Type I rice sold and a loss of Rs. 10 per bag of Type II rice sold. If the company sells 2000 bags of Type I rice and 1000 bags of Type II rice in a month, then find the overall profit or loss.
Solution
Profit on 1 bag of Type I rice sold = Rs. 15
Question 38 1.2 / -0
A rectangular grassy land is 65 m long and 50 m broad. It is surrounded by 3 m wide path. Find the cost of gravelling the path at Rs. 2.50 per m2 .
Solution
Area of EFGH = 65 m × 50 m = 3250 m
2 Area of ABCD = 71 m × 56 m = 3976 m
2 Area of path = (3976 - 3250) m
2 = 726 m
2 ∴ Cost of gravelling the path = Rs. (2.50 × 726) = Rs. 1815
Question 39 1.2 / -0
The number of students in a school increased by 8% annually. If there are 71,280 students in the school, then how many students were there last year?
Solution
Let number of students in last year = x
Number of students in the current year = x + 8% of x
=
According to question,
Question 40 1.2 / -0
A certain sum was divided between Priya and Yashika in the ratio 5 : 6. If Yashika's share was Rs. 2400, find the total sum.
Solution
Let the share of Priya and Yashka be Rs. 5x and Rs. 6x, respectively.
Now, 6x = 2400
x =
= 400
So, share of Priya = Rs. 5x = (5 × 400) = Rs. 2000
∴ Total sum = Rs. 2000 + Rs. 2400 = Rs. 4400
Question 41 1.2 / -0
In a hall,
of the people were females and
of those females were school girls. If the total number of people were 600, then how many school girls were there in the hall?
Solution
Total number of people = 600
Number of females =
of 600 =
× 600 = 200
Number of school girls =
× 200 = 100
Question 42 1.2 / -0
A man gave Rs. 5489.38 to his daughter and Rs. 12,364.57 to his wife from his total savings. He still had Rs. 20,000 left with him. Find his total savings.
Solution
Man's total savings
Question 43 1.2 / -0
Find the sum of the mode and the median of the given data.
Solution
Arranging the given data in ascending order:
1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 6
2 occurs most number of times.
Mode = 2
Number of observations, n = 11
∴ Median =
term =
term =
term
= 6
th term = 3
Hence, required sum = 2 + 3 = 5
Question 44 1.2 / -0
Kanika lent Rs. 6400 to Richa and Renuka each at 15% per annum for 5 years and
years, respectively. Find the difference between the simple interests paid by them.
Solution
Simple interest paid by Richa =
= Rs. 4800
Simple interest paid by Renuka =
=
= Rs. 3360
∴ Required difference = Rs. 4800 - Rs. 3360 = Rs. 1440
Question 45 1.2 / -0
Shivam rolled a die once. What is the probability of getting a number multiple of 3?
Solution
Total number of outcomes (1, 2, 3, 4, 5, 6) = 6
∴ Number of possible outcomes (3, 6) = 2
Hence, required probability =
Question 46 1.2 / -0
Given that
ACD is 4° more than
CDE and
CDE is 22° more than
DAC. Also, the sum of
BCE and
BDE is 26° and
EBF = 80°. Find the value of x.
Solution
ACD = 4° +
CDE
CDE = 22° +
DAC
Let
DAC = y
∴
CDE = 22° + y.
And,
ACD = 4° + 22° + y
= 26° + y
In ΔACD,
ACD +
CDE +
DAC = 180° (Angle sum property)
26° + y + 22° + y + y = 180°
3y + 48° = 180°
3y = 180° – 48° = 132°
∴ y = 44°
DAC = 44°
ACD = 26° + 44° = 70°
And,
CDE = 22° + 44° = 66°
Now,
ACD +
ADC = 70° + 66° = 136°
ACE +
ECD +
ADB +
BDC = 136°
(
ECD +
BDC) + (
ACE +
ADB) = 136°
ECD +
BDC + 26° = 136° [∵
BCE +
BDE = 26° (given)]
ECD +
BDC = 110° … (i)
In ΔFCD,
FCD +
FDC +
CFD = 180° (Angle sum property)
110° +
CFD = 180° (Using (i))
CFD = 70°
As,
BFE =
CFD (Vertically opposite angles)
∴
BFE = 70°
In ΔBEF,
BEF +
BFE +
EBF = 180° (Angle sum property)
x + 70° + 80° = 180°
x = 30°
Question 47 1.2 / -0
Match the following.
Column-I Column-Il P. A number is as much greater than 52 as it is less than 82. The number is (a) 6 Q. Two-fifth of a number is less than three-fifth of a number by 2. The number is (b) 216 R. If 50 is subtracted from two third of a number, the result is the sum of 40 and one-fourth of that number. The number is (c) 67 S. Adding 8 to double of a number gives 20. The number is (d) 10
Solution
P: A - 52 = 82 - A
By solving the given conditions, we get the number 67.
Q: Let the number be x.
Two-fifth of x =
x
Three-fifth of x =
x
According to question, we have:
R: Let the number be x.
Two-third of x =
x
One-fourth of x =
x
According to question, we have:
x = 216
S: Let the number be x.
Twice of x = 2x
According to question, we have:
2x + 8 = 20
2x = 12
x = 6
Question 48 1.2 / -0
Read the given statements carefully and select the CORRECT option.
Statement-1: A person lent certain sum of money at 4% simple interest. In 5 years, the interest amounted to Rs. 520 less than the sum lent. Then, the sum lent was Rs. 650.
Statement-2: If an investment triples itself in 30 years, then the rate of simple interest is 7
%.
Solution
Let the sum be Rs. x.
Interest =
According to question, we have:
x -
= 520
= 520
x =
= 650
∴ Statement-1 is true.
Let the amount of investment be Rs. x.
Amount = 3x
∴ Simple interest = 3x - x = 2x
Now,
R =
∴ Statement-2 is false.
Question 49 1.2 / -0
Read the statements carefully and state 'T' for true and 'F' for false.
(i) The percentage decrease in the price of a shirt when the price decreases from Rs. 100 to Rs. 80 is 20%.
(ii) The mode of the data 6, 7, 7, 4, 2, 7, 6, 4 is 6.
(iii) If length of the side of a square table is x units, then its perimeter is (4 + x) units.
(iv) If the angles of a triangle are
, (x - 20°) and (x - 40°), then the value of x is 44°.
Solution
(i) True
Decrease in price = Rs. (100 - 80) = Rs. 20
∴ Percentage decrease in price =
× 100 = 20%
(ii) False
7 occurs most number of times.
∴ Mode = 7
(iii) False
Length of side of a square table = x units
∴ Perimeter of the square table = 4x units
(iv) False
Sum of all angles of a triangle = 180°
x - 10° + x - 20° + x - 40° = 180°
x + x + x = 180° + 70°
= 250°
5x = 500°
x = 100°
Question 50 1.2 / -0
The given bar graph represents Demand and Production for five companies A, B, C, D and E. On the basis of the graph, answer the following question.
(a) If x% of demand for company C equals demand for company B, then x equals ________.
(b) The ratio of the number of companies having more demand than production to those having more production than demand is___________.
Solution
(a) Demand for company C = 2500
Demand for company B = 500
Now, x% of 2500 = 500
× 2500 = 500
x = 20
(b) Companies having more demand than production are A, C, and E, i.e. 3 in number.
Companies having more production than demand are B and D, i.e. 2 in number.
∴ Required ratio =
or 3 : 2
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