Question 1 1.2 / -0
Directions: Select a figure from the options, which will continue the same series as established by the Problem Figures.
Solution
Figure rotates 45° clockwise in every next step.
Question 2 1.2 / -0
In a certain code language, the word PATIENCE is written as TPNIEECA. How will the word SPACIOUS be written in that language?
Solution
The letters of the word are arranged in the reverse alphabetical order. Hence, SPACIOUS will be written as USSPOICA.
Question 3 1.2 / -0
Find the mirror-image of the given combination of letters, if the mirror is placed vertically to the right.
Question 4 1.2 / -0
Find the missing number, if the same rule is followed in all the three figures.
Solution
The rule followed is:
(35 + 28) ÷ 7
= 63 ÷
7 = 9
(45 + 39) ÷ 7
= 84
7 = 12
Similarly, (51 + 68) ÷ 7
= 119 ÷ 7 =
Question 5 1.2 / -0
Directions: There is a certain relationship between figures (P) and (Q). Establish a similar relation between figures (R) and (S) by selecting a suitable figure from the given options that will replace (?) in figure (S).
Solution
The outer element gets divided into equal parts by horizontal line of symmetry and then two parts get vertically inverted. The inner element gets rotated by 90°.
Question 6 1.2 / -0
The following question is based on the information given below :
Solution
(A) M × R ÷ Q means M is the brother of R who is the father of Q. So, M is the uncle of Q.
Question 7 1.2 / -0
Select a figure, from the options, which satisfies the same condition of placement of dots as in Fig. (X).
Question 8 1.2 / -0
Seven boys are standing in a circle facing to the centre. B is standing to the right of A after two boys. C is standing left side of B after four boys. C is standing between D and F. B is standing beside F. G is standing to the immediate right of E. E is standing to the immediate right of A.
Solution
The correct arrangement is as follows:
So, G is standing to the immediate left of B.
Question 9 1.2 / -0
Directions: The given question consists of a set of three figures X, Y and Z showing a sequence of folding of a piece of paper. Fig. Z shows the manner in which the folded paper has been cut. Choose a figure from the options which would most closely resemble the unfolded form of piece of paper.
Question 10 1.2 / -0
Select a figure from the options which is exactly embedded in Fig. (X) as one of its parts.
Question 11 1.2 / -0
If '+' is written as '÷', '÷' is written as '-', '-' is written as '×' and '×' is written as '+', then 110 + 11 - 10 ÷ 100 × 96 = ?
Solution
After interchanging the signs, the given equation becomes 110 ÷ 11 × 10 - 100 + 96
Question 12 1.2 / -0
Two positions of a dice are shown here. When 4 dots are at the bottom, the number of dots at the top will be __________.
Solution
The number of dots on opposite faces are given in pairs as, (1, 6), (2, 3) and (4, 5).
Question 13 1.2 / -0
Which of the following Venn diagrams best represents the relationship among ''Diseases, Typhoid, Pneumonia''?
Question 14 1.2 / -0
Amit, Raj, Varun, Shivam and Ali go into a shop.
Only Shivam buys a samosa.
Only Raj, Varun and Ali buy a chocolate.
Everyone except Raj buy an ice cream.
Raj is the only one who buys toffees.
Nobody except Amit and Varun chooses a burger.
Each of the boys buy a packet of chips.
Who among the following buys the maximum number of items?
Solution
Amit, Raj, Varun, Shivam and Ali go into a shop.
Only Shivam buys a samosa.
Only Raj, Varun and Ali buy a chocolate.
Everyone except Raj buy an ice cream.
Names/Items Samosa Chocolate Ice cream Toffees Burger Packet of chips Shivam √ χ √ Raj χ √ χ Varun χ √ √ Ali χ √ √ Amit χ χ √
Raj is the only one who buys toffees.
Nobody except Amit and Varun chooses a burger.
Each of the boys buy a packet of chips.
Names/Items Samosa Chocolate Ice cream Toffees Burger Packet of chips Shivam √ χ √ χ χ √ Raj χ √ χ √ χ √ Varun χ √ √ χ √ √ Ali χ √ √ χ χ √ Amit χ χ √ χ √ √
So, Varun buys the maximum number of items.
Question 15 1.2 / -0
If 1 is added to the middle digit and 1 is subtracted from the last digit of each of the following numbers, then what will be the sum of the digits of the highest number so formed?
Solution
The new numbers formed are 257, 644, 441, 790, 614.
Question 16 1.2 / -0
Which of the following is true about a triangular prism?
Solution
A triangular prism has 6 vertices and 5 faces, out of which 2 are triangular faces and 3 are rectangular faces.
Question 17 1.2 / -0
Simplify: (12 + 22 + 32 + 42 )1/3 × (13 + 23 + 33 + 43 )1/3 × (22 + 32 - 5 × 2)2/3
Solution
We have,2 + 22 + 32 + 42 )1/3 × (13 + 23 + 33 + 43 )1/3 × (22 + 32 - 5 × 2)2/3 1/3 × (1 + 8 + 27 + 64)1/3 × (4 + 9 - 10)2/3 1/3 × (100)1/3 × (3)2/3 1/3 × (10)1/3 × (10)2/3 × (3)2/3 ( 2/3) + (1/3) × (10)( 1/3) + (2/3) 3/3 × (10)3/3 = 3 × 10 = 30
Question 18 1.2 / -0
The value of
is _____.
Solution
We have,
=
Question 19 1.2 / -0
If x
2 + y
2 = 47 and xy =
, then the value of 2(x + y)
2 + (x - y)
2 is
Solution
We have, x
2 + y
2 = 47 ...(i)
And xy =
Now, (x + y)
2 = x
2 + y
2 + 2xy
= 47 + 2 ×
[Using (i) and (ii)]
= 47 + 19 = 66
Also, (x - y)
2 = x
2 + y
2 - 2xy = 47 - 2 ×
[Using (i) and (ii)]
= 47 - 19 = 28
So, 2(x + y)
2 + (x - y)
2 = 2 × 66 + 28
= 132 + 28 = 160
Question 20 1.2 / -0
In the given figure, EB is the diagonal of square EDBA. Find
CEF and
ECD.
Solution
We have, EDBA is a square and EB is the diagonal.
So,
BEA =
BED = 45°
In ΔACE,
CAE +
ACE +
CEA = 180°
63° + 53° +
AEB +
CEF = 180°
116° + 45° +
CEF = 180°
CEF = 180° – 161° = 19°
So,
CED =
BED –
CEF = 45° – 19° = 26°
Now, in ΔCED,
CED +
EDC +
DCE = 180°
DCE = 180° – 90° – 26° = 64°
Question 21 1.2 / -0
If x
2 +
= 16, then find the value of x +
.
Question 22 1.2 / -0
The given figure shows 3 different views of a three-dimensional figure constructed using cubes. Which could be the correct option?
Question 23 1.2 / -0
Find the probability of getting 'A' from the word ATTACHES.
Solution
Total number of letters in the word = 8
Number of 'A' in the word = 2
∴
Required probability =
Question 24 1.2 / -0
When the interest is compounded quarterly, the amount (A) is calculated by:
Solution
When interest is compounded quarterly, the amount (A) is calculated by A = P
.
Question 25 1.2 / -0
If x : y = 2 : 3 and 2 : x = 1 : 2, then find the value of y.
Solution
We have, 2 : x = 1 : 2
Now, x : y = 2 : 3
Question 26 1.2 / -0
If 35% of a number is 12 less than 50% of that number, then the number is ______.
Solution
Let the number be x.
According to question,
35% of x = 50% of x - 12
35x = 50x - 1200
15x = 1200
x = 80
Question 27 1.2 / -0
The approximate value of
is
Question 28 1.2 / -0
Given below are the steps of construction of a quadrilateral ABCD, where AB = 5.6 cm, BC = 4.1 cm, CD = 4.4 cm, AD = 3.3 cm and
= 75°. Which of the following is INCORRECT step?
Step-I: Draw AB = 5.6 cm and construct
BAX = 75°.
Step-II: With A as centre and radius = 3.3 cm, cut off AD = 3.3 cm along AX.
Step-III: Join BD. With D as centre and radius = 4.1 cm, draw an arc.
Step-IV: With B as centre and radius = 4.1 cm, draw an arc to cut the arc drawn in above step at C. Join BC, CD to obtain the required quadrilateral ABCD.
Solution
The correct step is:
Question 29 1.2 / -0
A spinner is made from a regular octagon. What is the probability of getting the number 2?
Solution
Total possible outcomes = 8
Number of favourable outcomes = 2
∴ Probability of getting the number 2 =
Question 30 1.2 / -0
The radius of a wheel is 0.25 metres. Find the number of revolutions it will make to travel a distance of 11 km.
Solution
Radius of the wheel = 0.25 m
Circumference of the wheel = 2
r
=
∴ Number of revolutions to cover
So, number of revolutions to cover 11 km, i.e. 11,000 m
=
Question 31 1.2 / -0
Which of the following conditions vary directly?
Solution
The number of subjects with the time taken to complete the homework vary directly.
Question 32 1.2 / -0
In the following figure, ABDH and CEFG are two parallelograms. Find the value of x.
Solution
Since ABDH is a parallelogram,
AHD =
ABD = 130°
(Opposite angles of a ||gm are equal.)
Also,
GHD +
AHD = 180° (Linear pair)
GHD = 180° - 130° = 50° ...(i)
Since, CEFG is a parallelogram.
So,
CGF +
GFE =180° (Adjacent angles of a || gm)
CGF = 180° - 30° = 150°
Also,
FGC +
HGC = 180° (Linear pair)
HGC = 180° - 150 = 30° ...(ii)
In ΔHGM,
HGM +
GHM +
HMG = 180° (Angle sum property of a triangle)
30° + 50° + x = 180° (Using (i) and (ii))
x = 180° - 80° = 100°
Question 33 1.2 / -0
In two triangles ABC and DEF, if AB = BC,
B =
E, DE = EF and BC = EF, then which of the following statements is CORRECT?
Solution
As, AB = BC, DE = EF and BC = EF
AB = BC = DE = EF
Now,
In ΔABC and ΔDEF,
AB = DE (Given)
ABC =
DEF (Given)
BC = EF (Given)
∴ ΔABC ≌ ΔDEF (By SAS congruence criteria)
So, both the triangles are congruent and isosceles.
Question 34 1.2 / -0
If
= 0.004 × 0.4 ×
, then a/b is equal to
Solution
We have,
= 0.004 × 0.4 ×
On squaring both sides, we get:
0.04 × 0.4 × a = (0.004)
2 × (0.4)
2 × b
= 16 × 10
-5
Question 35 1.2 / -0
Simplify:
Solution
We have,
=
+
[Using identity a
2 - b
2 = (a - b) (a + b)]
=
+
=
=
Question 36 1.2 / -0
A train 270 m long is moving with a speed of 25 km/hr. In what time will it cross a man coming from the opposite direction with a speed of 2 km/hr in which the train is moving?
Solution
Speed of train relative to man = (25 + 2) km/hr
= 27 km/hr = 27 ×
m/sec
Time taken by the train to cross the man
= Time taken by it to cover 270 m at
m/sec
= 270 ×
= 36 sec
Question 37 1.2 / -0
An urn contains 2 red, 3 green and 2 blue balls. If a ball is drawn at random, then find the probability that the ball is not blue.
Solution
Total number of balls = 2 + 3 + 2 = 7
∴ Probability of getting the ball that is not blue
=
Question 38 1.2 / -0
A shopkeeper offers 3.5% discount on cash purchases. What cash amount would Trishi pay for a dress, if the marked price of the dress is Rs. 1250?
Solution
Marked price of the dress = Rs. 1250
Discount = 3.5%
So, amount paid by Trishi = Rs. (1250 - 3.5% of 1250)
= Rs.
= Rs. (1250 - 43.75) = Rs. 1206.25
Question 39 1.2 / -0
15 litres of mixture contains 20% alcohol and the rest water. If 3 litres of water be mixed with it, the percentage of alcohol in the new mixture would be:
Solution
Quantity of alcohol in the mixture of 15 litres
= 20% of 15 =
× 15 = 3 litres
New quantity of mixture = 15 + 3 = 18 litres
Now, percentage of alcohol in 18 litres mixture
=
Question 40 1.2 / -0
In a garden, there are as many trees in a row as there are number of rows in the garden. If there are 576 trees in the garden, find the number of trees in a row.
Solution
Let the number of rows be n.
So, the number of trees in each row = n
∴ Total number of trees = n × n = 576
n
2 = 576
n = 24
Question 41 1.2 / -0
A rectangular garden 200 m long and 150 m wide has a path all around it, on the inner side, having a width of 3 m. In the centre of this plot, there is a circular pond of radius 7 m. What area of the land is left for the lawn and the flower beds?
Solution
Let ABCD be the rectangular garden.
Area of land left for the lawn and the flower beds = Area of PQRS - Area of circle
= [(200 - 3 - 3) × (150 - 3 - 3)] -
× (7)
2 = (194 × 144) -
= (27936 - 154) m
2 = 27782 m
2
Question 42 1.2 / -0
Present ages of Sunita and Anand are in the ratio of 5 : 4, respectively. Three years hence, the ratio of their ages will become 11 : 9, respectively. What is Anand's present age (in years)?
Solution
Let the present age of Sunita be 5x years and present age of Anand be 4x years.
According to the question,
45x + 27 = 44x + 33
x = 6
∴ Present age of Anand = (6 × 4) years = 24 years
Question 43 1.2 / -0
A shopkeeper offers 2.5% discount on cash purchases. What cash amount would Rohan pay for a cycle whose marked price is Rs. 650?
Solution
Marked price of cycle = Rs. 650
∴ Amount that Rohan has to pay = 650 - 2.5% of 650
= 650 -
× 650 = 650 - 16.25 = Rs. 633.75
Question 44 1.2 / -0
A house is purchased by Mohit, Arun and Armaan. Arun contributes
of Mohit's contribution, while Armaan contributes
of Mohit's contribution. If Mohit's contribution is Rs. 15,00,000, then find the contribution of Armaan and Arun.
Solution
Contribution of Mohit = Rs. 15,00,000
∴ Contribution of Armaan =
× 15,00,000 = Rs. 5,00,000
And contribution of Arun =
×
15,00,000 = Rs. 5,75,000
Question 45 1.2 / -0
A wall is 5 times as high as it is broad and 8 times as long as it is high. If the volume of the wall is 12.8 m3 , then find the breadth of the wall.
Solution
Let the breadth of wall be x m.
∴ Height of wall = 5x m
Length of wall = (8 × 5x) m = 40x m
Volume of the wall = length × breadth × height
x × 5x × 40x = 12.8
200x
3 = 12.8
∴ Breadth of the wall = 0.4 m = 40 cm
Question 46 1.2 / -0
Select the CORRECT option. In the options, T and F stand for true and false, respectively
(i) Compound interest is calculated by using the formula, C.I. = P
.
(ii) The simple interest and the compound interest on the same principal for same time period (> 1 year) and at the same rate of interest are not equal.
(iii) If a sum of Rs. 2000 becomes Rs. 2600 after three years, then rate of simple interest is 10% per annum.
(iv) In case of compound interest, the principal remains constant throughout the time period.
Solution
(i) False; C.I. =
(ii) True; In simple interest, principal is same for every year. But in compound interest, principal varies every year. Here, new principal = old principal + interest
(iii) True; Principal (P) = Rs. 2000, Amount = Rs. 2600, Time (T) = 3 years
S.I. = Amount - Principal = Rs. (2600 - 2000) = Rs. 600
Also, S.I. =
(iv) False; In case of compound interest, the principal changes as the time period changes.
Question 47 1.2 / -0
Which of the following options is CORRECT?
Solution
1. Additive identity of any rational number is 0.
2. For rational numbers a, b and c,
a - (b - c) ≠ (a - b) - c.
3.
=
4. Reciprocal of
is x.
Question 48 1.2 / -0
Match the following:
Column-I Column-II (i) Sanchi is now 12 years old and Sam is two years old. In how many years will Sanchi be three times as old as Sam? P. 50 (ii) Two trains start at the same time from two towns 750 km apart and travel towards each other. The slower train travels at an average speed of 60 km/hour and the faster one at 90 km/hour. After how many hours will they pass each other? Q. 43 (iii) A truck travelling at a speed of 40 km/hour leaves Delhi. An hour later, a car leaves Delhi and catches up with the truck after four hours. What was the average speed (in km/hr) of the car? R. 5 (iv) The sum of the digits of a 2-digit number is 7. If the digit are reversed, then the number formed is 9 less than the original number. Find the number. S. 3
Solution
(i) Present age of Sanchi = 12 years
Present age of Sam = 2 years
Suppose, Sanchi becomes three times as old as Sam in x years.
So, 12 + x = 3(2 + x)
12 + x = 6 + 3x
6 = 2x
x = 3
(ii) Both trains are travelling towards each other.
So, relative speed = 90 + 60 = 150 km/hour
Distance = 750 km
∴ Time taken by the trains to pass each other =
= 5 hours
(iii) Speed of truck = 40 km/hr
So, distance covered by truck in 5 hours = 40 × 5 = 200 km
The car covered 200 km in 4 hours.
∴ Average speed of car =
= 50 km/hr
(iv) Sum of the digits is 7. Let the unit digit of the number be x.
So, tens digit of the number = 7 - x
∴ Number formed is 10(7 - x) + x = 70 - 9x
On reversing the digits, number formed is 10x + (7 - x) = 9x + 7
According to question, we have:
9x + 7 = 70 - 9x - 9
18x = 54
x = 3
So, the required number is 43.
Question 49 1.2 / -0
The given pie chart shows the number of students who like different subjects. If a student is selected at random, then which of the following options is correct?
Solution
Total number of students = 1440
1. Number of students who like Hindi
=
× 1440 = 400
∴ Probability of selecting a student who likes Hindi
=
2. Number of students who like Science
=
× 1440 = 200
∴ Probability of selecting a student who likes Science
=
3. Number of students who like Computers
=
× 1440 = 180
∴ Probability of selecting a student who likes Computers
=
4. Number of students who like English
=
× 1440 = 380
∴
Probability of selecting a student who likes English
=
Question 50 1.2 / -0
Which of the following statements is/are true?Statement 1: Gagan bought a plot of land for Rs. 2,35,000. If he built a boundary wall around the plot and leveled the land and sold it for Rs. 35,00,000, thus making a profit of 40% on his investment, then he spent Rs. 22,65,000 on the boundary wall and leveling the land.Statement 2: In a festive season, a retailer sells readymade clothes at a discount of 20% and still gains 20%. If the marked price for a pair of jeans is Rs. 4200, then the retailer's cost price is Rs. 4000.
Solution
Statement 1:
C.P. of land = Rs. 2,35,000
Let Rs. x be the amount spent on building the boundary wall and leveling the land.
So, total C.P. = Rs. (2,35,000 + x)
And S.P. = Rs. 35,00,000, Profit = 40%
2,35,000 + x =
× 35,00,000 = Rs. 25,00,000
x = 25,00,000 - 2,35,000
x = Rs. 22,65,000
∴ Statement 1 is true.
Statement 2:
Let C.P. of jeans for retailer = Rs. x
Since, M.P. of jeans = Rs. 4200
Discount = 4200 ×
= 840a
S.P. = 4200 - 840 = Rs. 3360
Profit = 20%
∴
∴ Statement-2 is false.
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