Question 1 1.2 / -0
Directions:
Solution
Three numbers 3, 4 and 9 are immediately followed by a vowel and immediately preceded by a consonant.
Question 2 1.2 / -0
Choose a box that is similar to the box formed when the given sheet of paper is folded.
Solution
Here, three, one and two dots are opposite to the four, five and six dots respectively.
The box given in option (3) is similar to the box formed when the given sheet of paper is folded.
Question 3 1.2 / -0
Starting from a point P, Aryan walked 40 metres towards North. Then he turned right and walked 60 metres. He then turned right and walked 40 metres. At last he turned right and walked 40 metres and reached a point Q. How far and in which direction is he now from the starting point?
Solution
Now, PQ = 60 - 40 = 20 m
Aryan is 20 metres far and in the East direction from the starting point.
Question 4 1.2 / -0
Select a figure from the options which does not satisfy the same conditions of placement of the dots as in the given figure.
Solution
Check and compare the placement of dots in all the options with the given figure.
Question 5 1.2 / -0
Directions: Two rows of numbers are given. The resultant number in each row is to be worked out separately based on the following rules and the question below the rows of numbers is to be answered. The operations on numbers progress from left to right.
Rules: (i) If an even number is followed by an even number, then they are to be added.
(ii) If an odd number is followed by an even number, then the odd number is to be multiplied by the even number.
(iii) If an even number is followed by an odd number which is a perfect square, then they are to be added.
(iv) If an even number is followed by a prime number, then the first number is to be divided by the second number.
(v) If an odd number is followed by a prime number, then the prime number is subtracted from the odd number.
If P is the resultant of the first row, then what is the resultant of the second row?
Solution
First row:
So, P = 66
Second row:
Question 6 1.2 / -0
Select a figure from the options in which the given figure is exactly embedded as one of its parts.
Question 7 1.2 / -0
In a certain code language, if 'CONFIDENCE' is coded as 'FGPEGEQPHK', then how will 'PERFECTION' be coded in the same language?
Question 8 1.2 / -0
Select a figure from the options which satisfies the same conditions of placement of the dots as in the given figure.
Solution
Check and compare the placement of dots in option 4 with the given figure.
Question 9 1.2 / -0
Seven students P, Q, R, S, T, U and V are standing in a line facing north. V is to the immediate right of S and to the immediate left of Q. P and S have one student between them. P is to the immediate right of R. U and S have two students between them. Who is standing in the middle of the line?
Solution
The correct arrangement is:
So, S is standing in the middle of the line.
Question 10 1.2 / -0
Pointing to a man in a photograph, a woman says, ''This man's son's sister is my mother-in-law''. How is the woman's daughter's father related to the man?
Solution
Man's son's sister is man's daughter. So, man's daughter is woman's mother-in-law. Also, woman's daughter's father is her husband. So, women's husband is the grandson of the man in the photograph.
Question 11 1.2 / -0
There is a certain relationship between figures 1 and 2. Establish the same relationship between figures 3 and 4 by selecting a suitable figure from the options which will replace (?) in figure 4.
Solution
From figure 1 to figure 2, the outer element rotates 180°, circle is increased by 1 and the inner element becomes its water image.
Question 12 1.2 / -0
Select a figure from the options which will complete the given figure pattern.
Question 13 1.2 / -0
Which of the following Venn diagrams best represents the relationship among Shirts, Trousers and Skirts?
Solution
There is no relation between three different types of clothing.
Question 14 1.2 / -0
Find the missing number, if a certain rule is followed either row-wise or column-wise.
3 2 5 4 5 7 1 3 2 26 38 ?
Solution
The rule followed is:
3
2 + 4
2 + 1
2 = 26
2
2 + 5
2 + 3
2 = 38
Similarly, 5
2 + 7
2 + 2
2 =
Question 15 1.2 / -0
If 'A - B' means 'B is younger than A', 'A * B' means 'A is younger than B' and 'A
B' means 'A and B are of the same age, then which of the following is definitely true for P
Q - R * S?
Solution
'P
Q - R * S' means 'P and Q are of the same age and R is younger than Q'. R is younger than S. Also, R is younger than P.
Thus, R is the youngest.
Question 16 1.2 / -0
The expenditure incurred on various things during the construction of a house is given below:
Items Expenditure (Rs. in thousand) Bricks 180 Cement 80 Timber 90 Steel 55 Wood 45 Total 450
Which of the following pie charts exhibits the given information?
Solution
Expenditure incurred on Bricks =
× 360°
= 144°
Expenditure incurred on Cement =
× 360° = 64°
Expenditure incurred on Timber
× 360° = 72°
Expenditure incurred on Steel =
× 360° = 44°
Expenditure incurred on Wood
× 360° = 36°
Question 17 1.2 / -0
One card is drawn from a well-shuffled deck of 52 cards. Find the probability that the number on the card drawn is a multiple of 5.
Solution
Total number of cards = 52
Number of multiples of 5 are 5, 10 i.e. 2
In a deck, there are 4 red and 4 black cards which are multiples of 5.
Required probability =
Question 18 1.2 / -0
What is the least number which should be subtracted from 0.000326 to make it a perfect square?
Solution
0.000326 can be written as:
Now, subtract 2 from 326 to make it a perfect square.
326 - 2 = 324, which is a perfect square.
So,
= 0.000002 is subtracted from 0.000326 to make it a perfect square.
Question 19 1.2 / -0
In the given quadrilateral ABCD (not drawn to scale), BC = AC = AD. Find the sum of
DAC and
ACB.
Solution
In △ABC,
AC = BC (Given)
ABC =
BAC = 62° (Angles opposite to equal sides are equal.)
Also,
ABC +
BAC +
ACB = 180° (Angle sum property)
2
ABC +
ACB = 180°
ACB = 180° - 2(62°) = 56° ... (i)
Now, in
ADC, AD = AC
ADC =
ACD = 52° (Angles opposite to equal sides are equal.)
Also,
ACD +
ACD +
DAC = 180° (Angle sum property)
2
ACD +
DAC = 180°
DAC = 180° - 2(52°) = 76° ... (ii)
So,
DAC +
ACB = 76° + 56° = 132° (Using (i) and (ii))
Question 20 1.2 / -0
Arman sold an article offering a discount of 15% and earning a profit of 25.5%. What would have been the percentage of profit earned if no discount was offered?
Solution
Let the marked price of the article be Rs. x.
After discount of 15%,
Selling price (S.P.) = Rs.
Profit = 25.5%
Since C.P. =
If no discount was offered, then
S.P. = Rs. x
So, profit % =
Question 21 1.2 / -0
If one member of a pythagorean triplet is 2 m, then the other two members are:
Solution
(2m)2 + (m2 - 1)2 = 4m2 + m4 + 1 - 2m2 = (m2 + 1)2 2 + 1, m2 - 1.
Question 22 1.2 / -0
Find the total area of the shaded region in the given figure.
Solution
Area of two shaded triangles = ar(
ABC) + ar(
CDE)
=
=
=
= 400 cm
2 Area of the shaded square = (2 × 2) cm
2 = 4 cm
2 Total area of the shaded region = (400 + 4) cm
2 = 404 cm
2
Question 23 1.2 / -0
What is the approximate value of (15.01)
2 ×
?
Question 24 1.2 / -0
Sam cut out 6 identical circles from a rectangular piece of paper. Find the shaded area.
Solution
Diameter of each circle =
cm = 7 cm
Radius of each circle =
cm
Area of 1 circle =
cm
2 Area of 6 circles =
cm
2 = 231 cm
2 Area of the rectangle = 14 cm × 21 cm = 294 cm
2 Shaded area = (294 - 231) cm
2 = 63 cm
2
Question 25 1.2 / -0
There are two boxes shown in the figure. Which box requires more amount of material to be made?
Solution
Volume of box (i) = 40 × 30 × 25 = 30,000 cm3 3 = 42,875 cm3
Question 26 1.2 / -0
Which of the following is the net of a hexagonal prism?
Solution
The net of hexagonal prism is:
Question 27 1.2 / -0
Which of the following statements is always true?
Solution
The rational number between x and y is
.
Question 28 1.2 / -0
It
, then what is the value of 2b?
Solution
We have
a
2b - 3 + 2b + 2 + 12 = a
9 + 18 4b + 11 = 27
4b = 16
b = 4
Thus, 2b = 2(4) = 8
Question 29 1.2 / -0
Solve for x:
= 4
Solution
We have
= 4
36x - 6 - 4x + 1 - x = 48
31x - 5 = 48
31x = 53
Question 30 1.2 / -0
Directions For Questions
Directions: In the given pie-chart, percentage of students studying in six different schools A, B, C, D, E and F has been shown. Use this information to answer the question asked.
Total number of students = 75,000
...view full instructions
What is the average number of students studying in schools B, D and E?
Solution
Total number of students = 75,000
Question 31 1.2 / -0
Directions For Questions
Directions: In the given pie-chart, percentage of students studying in six different schools A, B, C, D, E and F has been shown. Use this information to answer the question asked.
Total number of students = 75,000
...view full instructions
The ratio of the number of students studying in school C to that in school E is _______.
Solution
Number of students studying in school C = 24% of 75,000 = 18,000
Question 32 1.2 / -0
If
, find the value of
.
Question 33 1.2 / -0
Which of the following CANNOT be true for any polyhedron?
Solution
Euler's formula for polyhedron is F + V - E = 2.
Question 34 1.2 / -0
How many cubes of volume 216 cm3 can be obtained from a cube whose side is 36 cm?
Solution
Side of the cube = 36 cm
Volume of the cube = 36 × 36 × 36 cm
3 ∴ Required number of cubes =
= 216
Question 35 1.2 / -0
If p =
and q =
, find the value of
.
Question 36 1.2 / -0
Three years ago, the average age of wife, husband and their child was 27 years. Five years ago, the average age of wife and child was 20 years. The present age of husband is
Solution
Let x, y and z be the ages (three years ago) of wife, husband and their child, respectively.
Now,
x + y + z = 81 ... (i)
Also,
= 20
x + z - 4 = 40
x + z = 44 ...(ii)
From (i) and (ii), we get
y + 44 = 81
y = 81 - 44 = 37
So, present age of husband = (y + 3) years = 40 years
Question 37 1.2 / -0
Riya started a business investing Rs. 25,000. After 3 months, Sneha joined her with a capital of Rs. 30,000. At the end of the year, they made a profit of Rs. 19,000. What will be Riya's share in the profit?
Solution
Monthly investment by Riya = Rs. 25,000
Total investment by Riya = Rs. (25,000 × 12) = Rs. 3,00,000
Investment by Sneha for 9 months = Rs. (30,000 × 9)
= Rs. 2,70,000
Let the share of Riya in the profit be Rs. x, then the share of Sneha in the profit be Rs. (19,000 - x).
Now, 3,00,000 : 2,70,000 = x : (19,000 - x)
30/27 = x/(19,000 - x)
10/9 = x/(19,000 - x)
1,90,000 - 10x = 9x
1,90,000 = 19x
x = 10,000
Question 38 1.2 / -0
In a simultaneous throw of two dice, what is the probability of getting a doublet?
Solution
Total number of possible outcomes = 36
Favourable outcomes: (1, 1), (2, 2), (3, 3), (4, 4), (5, 5) and (6, 6), i.e. 6 in number
∴ Required probability =
Question 39 1.2 / -0
The mean weight of 120 students in a class is 56 kg. If the mean weight of boys and that of girls in the class respectively are 60 kg and 50 kg, then the number of boys in the class is ______.
Solution
Total number of students in the class = 120
Let the number of boys in the class be x.
Number of girls in the class = 120 - x
According to the question,
6x + 5 (120 - x) = 56 × 12
6x + 600 - 5x = 672
x = 672 - 600 = 72
Question 40 1.2 / -0
4096 soldiers are arranged in an auditorium in such a manner that there are as many soldiers in a row as there are rows in the auditorium. How many rows are there in the auditorium?
Solution
Total number of soldiers = 4096
Let the number of rows be x.
∴ Number of soldiers in each row = x
∴ According to the question,
x × x = 4096
x =
= 64
Hence, number of rows = 64
Question 41 1.2 / -0
A man sells a book at a profit of 20%. If he had bought it at 20% less and sold it for Rs. 18 less, he would have gained 25%. The cost price of the book is.
Solution
Let the cost price of the book be Rs. x.
Profit % = 20%
Selling price =
× Cost price
= Rs.
x
New cost price = x - 20%x
=
New selling price = Rs.
Profit % = 25%
40x - 1800 = 20x
20x = 1800
x = 90
∴ Cost price = Rs. 90
Question 42 1.2 / -0
In a half-yearly examination, Sushma scores 50% and gets 20 marks more than the minimum passing marks, while her friend Preeti scores 40% and fails by 40 marks. Find the minimum passing marks.
Solution
Let the minimum passing marks be x.
Number of marks obtained by Sushma = 50% of total marks
Number of marks obtained by Preeti = 40% of total marks
According to the question,
[Total marks] = x + 20
Total marks = 2(x + 20) ... (i)
And
[Total marks] = x - 40
Total marks =
(x - 40) ... (ii)
From (i) and (ii), we get
2(x + 20) =
(x - 40)
4x + 80 = 5x - 200
x = 280
Question 43 1.2 / -0
The capacity of a rectangular tank is 600 kL. If the length and breadth of the tank respectively are 12 m and 5 m, then the depth of the tank is _________.
Solution
Since the tank is in a cuboidal shape;
Volume of the tank = length × breadth × depth
600 m
3 = 12 m × 5m × depth (∵ 1 kL = 1 m
3 )
Depth of the tank =
= 10 m
Question 44 1.2 / -0
Vikas's garden is in the form of a parallelogram whose one side is 4.8 cm and the other side is 1
times this side. He wants to fence his garden four times by a wire. Find the length of the wire required.
Solution
Let ABCD be the garden in which AB = CD = 4.8 cm.
[∵ Opposite sides of a parallelogram are equal]
Now, BC =
cm
=
cm = 7.2 cm
∴ BC = DA = 7.2 cm
Now, length of the wire required = 4 × perimeter of ||
gm ABCD = 4 × (4.8 + 7.2 + 4.8 + 7.2) cm = 96 cm
Question 45 1.2 / -0
The cost of a vehicle is Rs. 1,75,000. If its value depreciates at the rate of 20% per annum, then the total depreciation for 3 years is _______.
Solution
Cost of the vehicle = Rs. 1,75,000
Rate of depreciation = 20% p.a.
∴ Depreciated value after 3 years
= 1,75,000
= 1,75,000
= Rs. 89,600
∴ Total depreciation = Rs. (1,75,000 - 89,600) = Rs. 85,400
Question 46 1.2 / -0
Find the values of P, Q, R and S, respectively.
Principal (in Rs.) Time (in Year) Rate (in %) S.I. (in Rs.) C.I. (in Rs.) (i) 12,500 3 P 4500 5061.6 (ii) 8800 2 Q 1559.58 (iii) R 3 5 180 S
Solution
(i) S.I. =
P = 12%
(ii) S.I. =
= Rs. 1496
Q = Rs. 1496
(iii) S.I. =
=
S = Rs. 189.15
Question 47 1.2 / -0
PQRS is a rectangle of dimensions 12 cm and 5 cm. PMNR is a rectangle drawn in such a way that the diagonal PR of the first rectangle is one of its sides and the side opposite to it is touching the first rectangle at S as shown in the figure. What is the ratio of the area of rectangle PQRS to that of PMNR?
Solution
Draw a line ST perpendicular to PR.
PQRS is a rectangle.
In
PQR, we have:
PR
2 = PQ
2 + QR
2 (By Pythagoras theorem)
PR
2 = (12)
2 + (5)
2 = 169
PR = 13 cm
Now, area of
PSR =
× base × height
Also, PM = ST =
cm
Area of rectangle PQRS = PQ × QR = (12 × 5) cm
2 = 60 cm
2 Area of rectangle PMNR = MN x PM
=
cm
2 = 60 cm
2 ∴ Required ratio =
, i.e. 1 : 1
Question 48 1.2 / -0
Match the following:
Column I Column II (P) A cylindrical roller is of length 2 m and diameter 84 cm. The number of revolutions it has to make to cover an area of 7920 m2 is (i) 17,600 (Q) The circumference of the base of a right circular cylinder is 176 cm. If the height of the cylinder is 1 m, the lateral surface area (in sq. cm) of the cylinder is (ii) 1500 (R) The dimensions of a cuboid are in the ratio 5 : 2 : 1. Its volume is 1250 cubic metres. Its total surface area (in sq. m) is (iii) 9 (S) If the total surface area of a cubical tank is 486 sq. m, the length (in m) of one side is (iv) 850
Solution
(P) Length of the cylinder, i.e. height (h) of the cylinder = 2 m
Diameter of the cylinder = 84 cm
∴ Radius (r) of the cylinder =
cm = 42 cm = 0.42 m
Curved surface area of the cylinder = 2
rh
= 2 ×
× 0.42 × 2 = 5.28 m
2 Number of revolutions the cylinder has to make to cover 5.28 m
2 area = 1
So, number of revolutions it has to make to cover 1 m
2 area =
Hence, number of revolutions it has to make to cover 7920 m
2 area
=
× 7920 = 1500
(Q) Circumference of the base of cylinder = 176 cm
∴ Radius (r) of the cylinder = 28 cm
Height (h) of the cylinder = 1 m = 100 cm
Lateral surface area of the cylinder = 2
rh
= 2 ×
× 28 × 100 = 17,600 cm
2 (R) Let sides of the cuboid be 5x, 2x and x.
Volume = 5x × 2x × x = 10x
3 But 10x
3 = 1250
x
3 = 125
x = 5
Sides of the cuboid are 25 m, 10 m and 5 m.
Total surface area of the cuboid
= 2(25 × 10 +10 × 5 + 25 × 5)
2(250 + 50 + 125) 2 × 425 = 850 m
2 (S) Let side of the cubical tank be x m.
Total surface area = 6x
2 But 6x
2 = 486
x
2 = 81
x = 9
Side of the cubical tank = 9 m
Question 49 1.2 / -0
Which of the following statements is/are true?Statement 1: The value of a car depreciates at the rate of 10% per year. A car which was bought three years ago is now worth Rs. 4,73,850. Its original price was Rs. 6,50,000.Statement 2: In fixed deposit, a bank gives 10% interest compounded annually for senior citizens. In 6 years, it will double a sum of money.
Solution
Statement 1:
Let the original price of the car be Rs. x.
Price of the car after one year = x - 10% of x
=
Price of the car after two years
=
Price of the car after three years
=
So, current price of the car = Rs.
According to the question,
= 4,73,850
x = 6,50,000
Hence, original price of the car = Rs. 6,50,000
So, Statement 1 is true.
Statement 2:
Let sum = Rs. P, Rate = 10%, Time = 6 years
Amount =
= P(1.1)
6 = (1.771561)P ≠ 2P
∴ So, Statement 2 is false.
Question 50 1.2 / -0
Fill in the blanks and select the correct option.
(i) A number ending in __
(P) __ number of zeros is never a perfect square.
(ii) The square of an __
(Q) __ natural number can always be written as the sum of two consecutive positive integers.
(iii) The sum of the first n odd natural numbers is ___
(R) ___.
(iv) If (3 × 3 × 7)
2 = 3969, then
= __
(S) __.
Solution
(i) A number ending in odd number of zeros is never a perfect square.
Examples: 1000, 2000, 34500000
(ii) The square of an odd natural number can always be written as the sum of two consecutive positive integers.
(iii) The sum of the first n odd natural numbers is n
2 .
(iv) Since (3 × 3 × 7)
2 = 3969,
= 3 × 3 × 7 = 63
×
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