Question 1 1.2 / -0
In a certain code language, INTRODUCED is written as EFDVEPSUOJ. How will INNOVATIVE be written in that language?
Solution
First arrange the letters of the word INTRODUCED in reverse order. We get DECUDORTNI.
Then,
Similarly, arrange the letters of the word INNOVATIVE in reverse order. We get EVITAVONNI.
So,
Question 2 1.2 / -0
Find the correct mirror image of the given figure.
Question 3 1.2 / -0
Aadi and Zoya start walking from the same point in opposite directions. Aadi walks 4 m west and Zoya walks 3 m. Then Aadi turns to his right and walks 3 m, and Zoya also turns to her right and walks 4 m. In which direction is Zoya with respect to Aadi?
Solution
So, Zoya is in the south-east direction with respect to Aadi.
Question 4 1.2 / -0
If it is possible to make only one meaningful word with the 2nd , 4th , 6th and 11th letters of the word 'INTELLIGENT' (using each letter only once), then the third letter of the word formed would be your answer. If more than one such words can be formed, then give Z as the answer. If no such word can be formed, then choose Y as your answer.
Solution
The 2nd , 4th , 6th and 11th letters of the word 'INTELLIGENT' are N, E, L and T, respectively.
Question 5 1.2 / -0
Select a figure from the options in which Fig. (X) is exactly embedded as one of its parts.
Question 6 1.2 / -0
Select the odd one out.
Question 7 1.2 / -0
Which of the following Venn diagrams best illustrates the relationship among Flute, Musical Instruments and Violin?
Question 8 1.2 / -0
Find the missing number, if same rule is followed in all the three figures.
Solution
The rule followed is:
and
Similarly,
Question 9 1.2 / -0
Pointing to a person, Puneet said, ''His only brother is the father of my daughter's father.'' How is the person related to Puneet?
Solution
The father of Puneet's daughter's father is Puneet's father. So, the person is the brother of Puneet's father. Hence, the person is the uncle of Puneet.
Question 10 1.2 / -0
In a certain code language, 'nro bsi mit' means 'help people everyday', 'bsi nro zpi' means 'themselves people help' and 'sti kti nro' means 'people love everyone'. Which of the following does mean 'everyday themselves love everyone' in the same language?
Solution
We have
nro bsi mit
help people everyday ... (i)
bsi nro zpi
themselves people help ... (ii)
sti kti nro
people love everyone ... (iii)
From (i), (ii) and (iii), we have
nro
people ... (iv)
From (i), (ii) and (iv), we have
bsi
help
So, from (i) and (ii), we get
mit
everyday and zpi
themselves
From (iii), we get
sti kti
love everyone
So, 'zpi mit sti kti' means 'everyday themselves love everyone'.
Question 11 1.2 / -0
How many triangles are there in the given figure?
Solution
The triangles formed in the given figure are: A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A', B', C', BC, KL, PQ, TU, A'B', ..., and so on.
There are more than 29 triangles.
Question 12 1.2 / -0
Two positions of a dice are shown here. When 4 is at the bottom, which number will be on the top?
Solution
1 is common in both dice, move in clockwise
Question 13 1.2 / -0
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 of numbers progress from left to right.
Rules: (i) If a two-digit even number is followed by another even number, the first one is to be divided by the second one.
(ii) If an even number is followed by a prime number, the two are to be multiplied.
(iii) If an odd number is followed by another odd number, the two are to be added.
(iv) If a three-digit number is followed by a two-digit number which is a perfect square, the second number is to be subtracted from the first number.
(v) If a three-digit number is followed by a two-digit number which is not a perfect square, the first number is to be divided by the second number.
Rows: What is the difference between the resultants of the first row and the second row?
Solution
First row: 84 14 13
Second row: 360 24 17
Required difference = 78 - 32 = 46
Question 14 1.2 / -0
A square transparent sheet with a pattern and a dotted line on it is given. Select a figure from the options as to how the pattern would appear when the transparent sheet is folded along the dotted line.
Question 15 1.2 / -0
Select a figure from the options which will replace the question mark (?) to complete the pattern in Fig. (X).
Question 16 1.2 / -0
A 3-digit number 93a is added to another 3-digit number 365 to give a 4-digit number 1b98, which is a divisible by 11. Find the value of
.
Solution
As, 1b98 is divisible by 11.
So, (1 + 9) - (b + 8) = 2 - b is either zero or a multiple of 11.
b = 2
Now,
So, a = 3
Question 17 1.2 / -0
Which of the following graphs cannot be a time-temperature graph?
Solution
Since only one temperature exists at a particular time, the graph given in option 2 cannot be a time-temperature graph.
Question 18 1.2 / -0
If x
2 + y
2 = 47 and xy =
, then the value of 2(x + y)
2 + (x - y)
2 is _______.
Solution
x
2 + y
2 = 47 and xy =
2xy = 19
2(x + y)
2 + (x - y)
2 = 2[x
2 + y
2 + 2xy] + [x
2 + y
2 - 2xy]
= 2[47 + 19] + [47 - 19] = 2 × 66 + 28 = 160
Question 19 1.2 / -0
Mohit invests a sum of Rs. 41,250 at the rate of 6% per annum. What approximate compound interest will he obtain at the end of 3 years?
Solution
Principal = Rs. 41,250
Rate = 6% p.a.
Time = 3 years
Compound interest = P
- P
= 41,250
- 41,250
= 41,250 ×
- 41,250
= 41,250
= 7879.41 ≈ Rs. 7879
Question 20 1.2 / -0
If ABCD is a parallelogram, and
ADN and
ABC are isosceles triangles, find
BAC.
Solution
In
[Exterior angle property]
In
ADN, AD = AN
= 66°
Now, in
ABC,
AC = AB
Now,
[Angle sum property]
[
Opposite angles of a ||
gm are equal]
Question 21 1.2 / -0
Given below are the steps of construction of a parallelogram ABCD, where AB = 7 cm, BC = 9 cm and
B = 80°. Which of these steps is incorrect?
Step-1: Draw AB = 7 cm.
Step-2: With B as centre, draw
ABX = 80°.
Step-3: Mark a point C on
such that BC = 9 cm.
Step-4: With C and A as centres and 7 cm and 9 cm as respective radii, draw arcs intersecting at point B.
Step-5: Join CD and AD. ABCD is the required parallelogram.
Solution
Step-4 is incorrect.
The correct step is:
With C and A as centres and 7 cm and 9 cm as respective radii, draw arcs intersecting at point D.
Question 22 1.2 / -0
If A : B = 5 : 6 and B : C = 7 : 8, then approximately by what percentage is C more than A?
Solution
We have
A : B = 5 : 6 and B : C = 7 : 8
A : B = 35 : 42 and B : C = 42 : 48
A : B : C = 35 : 42 : 48
Thus, required percentage =
= 37.14%
Question 23 1.2 / -0
When a dice is thrown, find the probability of not getting a prime number.
Solution
Total number of outcomes = 6
Prime numbers are 2, 3 and 5.
Numbers which are not prime are 1, 4 and 6.
Required probability =
Question 24 1.2 / -0
x and y vary inversely. When x is 12, y is 3. Which of the following is not a possible pair of corresponding values of x and y?
Solution
For inverse proportion, xy = constant or x
1 y
1 = x
2 y
2 x
1 y
1 = 12 × 3 = 36
(1) As, x
1 y
1 = 36; x
2 y
2 = 4 × 9 = 36
x
1 y
1 = x
2 y
2 (2) As, x
1 y
1 = 36; x
2 y
2 = 10 × 3.6 = 36
x
1 y
1 = x
2 y
2 (3) As, x
1 y
1 = 36; x
2 y
2 = 72 × 0.5 = 36
x
1 y
1 = x
2 y
2 (4) As, x
1 y
1 = 36; x
2 y
2 = 5 × 6 = 30
x
1 y
1 x
2 y
2
Question 25 1.2 / -0
If a four-digit number ccdd is divisible by 55, then the possible value of d is
Solution
In option, d = 2
Question 26 1.2 / -0
Match the following:
(1) Rectangle (p) A quadrilateral having its opposite sides equal and parallel (2) Square (q) A parallelogram having its opposite sides equal with each of the angles being a right angle (3) Parallelogram (r) A parallelogram having all sides equal with each of the angles being a right angle (4) Rhombus (s) A quadrilateral in which a pair of opposite sides is parallel (5) Trapezium (t) A parallelogram having all the sides equal
Solution
(1) Rectangle is a parallelogram having its opposite sides equal with each of the angles being a right angle.
Question 27 1.2 / -0
Which of the following statements is INCORRECT?
Solution
(1) Let two consecutive natural numbers be a and b (= a + 1). Then, product = a(a + 1)
Case 1: If a is even, then (a + 1) is odd.
We know that even x odd = even.
So, the product is even,
Case 2: If a is odd, then (a + 1) is even.
Now, odd x even = even
So, the product is even,
So, 1 is correct.
(2) Put x = 2 and y = 3.
(x + y)/2 = 2.5
2.5 lies between 2 and 3.
So, 2 is correct.
(3) Let three rational numbers be
.
Now,
So, rational numbers are not associative under subtraction.
(4) Since one number is positive and the other number is negative, they must be lying on the opposite sides of '0' on the number line.
Question 28 1.2 / -0
If 5x - 1 + 5x + 5x + 1 = 775, then the value of x, where x is a positive integer, is _______.
Solution
We have 5
x + 5
x - 1 + 5
x + 1 = 775
+ 5
x + 5 × 5
x = 775
= 5
x = 775
= 775
5
x = 125
5
x = 5
3 x = 3
Question 29 1.2 / -0
Find the value of p from
+ p = 3, when
.
Solution
We have
35x + 25 - 23 = 3
35x + 2 = 39 - 4x + 2
39x = 39
x = 1
Now,
+ p = 3 (Given)
2 + p = 3
p = 1
Question 30 1.2 / -0
Study the given graph carefully. Complete the table and find the value of P + Q – R – S.
Solution
According to the graph, we have,
So, P = 4, Q = 4, R = 2 and S = 5
P + Q - R - S = 4 + 4 - 2 - 5 = 1
Question 31 1.2 / -0
The following pie chart gives the marks scored in an examination by a student in English, Hindi, Science and Technology, Social Science, and Mathematics. If the total marks obtained by the student were 540, then the subject in which he scored 105 marks would be _________.
Solution
Total marks scored by the student = 540
Marks scored in English =
× 540 = 82.5
Marks scored in Mathematics =
× 540 = 135
Marks scored in Social Science =
× 540 = 97.5
Marks scored in Science and Technology =
× 540 = 120
Marks scored in Hindi =
× 540 = 105
Question 32 1.2 / -0
One of the factors of 2(b2 - a2 + 2ac - c2 ) is _________.
Solution
We have 2(b2 - a2 + 2ac - c2 )2 - (a2 - 2ac + c2 )) = 2(b2 - (a - c)2 )
Question 33 1.2 / -0
Which of the following is NOT a polyhedron?
Solution
Since the figure in option 4 has a curved face, it is not a polyhedron.
Question 34 1.2 / -0
The volumes of two cubes are in the ratio 1 : 64. If the volume of the larger cube is 504 cm3 more than that of the smaller cube, then:
Solution
Let the volume of the smaller cube be x cm
3 .
Volume of the larger cube = 64x cm
3 According to the question,
64x - x = 504
63x = 504
x = 8
(a) Volume of the smaller cube = x cm
3 = 8 cm
3 (b) Volume of the larger cube = 64x cm
3 = 512 cm
3 Side of the larger cube =
cm = 8 cm
Question 35 1.2 / -0
What must be subtracted from x4 + 2x2 - 3x + 7 to get x3 + x2 + x - 1?
Solution
Let P be subtracted from x
4 + 2x
2 - 3x + 7 to get x
3 + x
2 + x - 1.
x
4 + 2x
2 - 3x + 7 - P = x
3 + x
2 + x - 1
P = x
4 + 2x
2 - 3x + 7 - x
3 - x
2 - x + 1
= x
4 - x
3 + x
2 - 4x + 8
Question 36 1.2 / -0
Ritesh selected a card from a deck of 52 playing cards. Find the probability that the selected card is a red queen.
Solution
Total number of cards = 52
Number of red queen cards = 2
∴ Required probability =
Question 37 1.2 / -0
Two years ago, Mohit was three times as old as his son and two years hence, twice of Mohit's age will be equal to five times that of his son. The present age of Mohit is ________.
Solution
Let the present age of Mohit be y years and the present age of his son be x years.
According to the question, y - 2 = 3(x - 2)
y - 2 = 3x - 6
y = 3x - 4 ... (i)
And 2(y + 2) = 5(x + 2)
2y + 4 = 5x + 10
2y - 5x - 6 = 0
2(3x - 4) - 5x - 6 = 0 (using (i))
6x - 8 - 5x - 6 = 0
x = 14
∴ y = 3 × 14 - 4 = 38
So, present age of Mohit = 38 years
Question 38 1.2 / -0
A sells his motorcycle to B at a profit of 7%. B sells it to C at a profit of 8%. If C pays Rs. 14,445 for it, then what was the cost price of motorcycle for A?
Solution
Let the cost price of motorcycle for A be x.
Cost price of motorcycle for B = Selling price of motorcycle for A
=
Also, cost price of motorcycle for C = Selling price of motorcycle for B =
= Rs. 12,500
Question 39 1.2 / -0
Anshu and Ashu together can do a piece of work in 9 days. Ashu alone can complete the same work in 45 days. How many days will Anshu alone take to complete the same work?
Solution
(Anshu + Ashu)'s 1-day work =
Ashu's 1-day work =
Anshu's 1-day work =
Anshu alone will take
days to complete the work.
Question 40 1.2 / -0
A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup does the hospital have to prepare daily to serve 250 patients?
Solution
Quantity of soup filled in a cylindrical bowl =
r
2 h
=
Quantity of soup prepared daily to serve 250 patients
= 154 × 250 = 38,500 cm
3 = 38.5 L
Question 41 1.2 / -0
There are few adults and children in a restaurant. If
of the people in the restaurant are adults and there are 90 more children than adults, then how many children are there in the restaurant?
Solution
Let the total number of people in the restaurant be x.
Then, number of adults =
x
Number of children =
According to the question,
Number of children =
+ 90 = 135 + 90 = 225
Question 42 1.2 / -0
The perimeter of a rectangular garden is 420 cm. If its length is increased by 20% and breadth is decreased by 40%, we get the same perimeter. What are the new respective length and breadth of the rectangular garden?
Solution
Let the length and the breadth of the garden be I and b.
Perimeter of the rectangular garden = 420 cm (Given)
2(I + b) = 420
l + b = 210 .. .(i)
New length of the garden = I + 20% of l
New breadth of the garden = b - 40% of b
=
According to the question,
= 420
12I + 6b =
2l + b = 350 ... (ii)
Subtracting (i) from (ii), we get
l = 140 cm
Now, 140 + b = 210 (From (i))
b = 70 cm
New length of the garden =
= 168 cm
New breadth of the garden =
= 42 cm
Question 43 1.2 / -0
Vidhushi is 8 times as old as her grandson. Four years ago, Vidhushi was 12 times as old as her grandson. Find the difference between their present ages.
Solution
Let the present age of Vidhushi's grandson be x years.
So, present age of Vidhushi = 8x years
According to the question,
8x - 4 = 12(x - 4)
8x - 4 = 12x - 48
4x = 44
x = 11
So, difference between their present ages = 8x - x = 7x
= 7 × 11 = 77 years
Question 44 1.2 / -0
A swimming pool is 24 m long and 15 m breadth. When a certain number of men dive into the pool, the height of water rises by 1 cm. If the average amount of water displaced by one of the men be 0.1 cu. m, how many men are there in the pool?
Solution
Length of the swimming pool = 24 m
Breadth = 15 m
Height of water raise = 1 cm = 0.01 m
Volume of water displaced = (24 × 15 × 0.01) m
3 = 3.6 m
3 Volume of water displaced by 1 man = 0.1 m
3 Let the number of men be n.
Volume of water displaced by n men = n × 0.1
So, n × 0.1 = 3.6
= 36
Question 45 1.2 / -0
The compound interest earned by Suresh on a certain amount at the end of 2 years at the rate of 8% per annum was Rs. 1414.40. What was the total amount that Suresh got back at the end of 2 years in the form of principal plus interest earned?
Solution
Let the principle amount be Rs. P.
Rate = 8% p.a, Time = 2 years
Compound interest = P
- P
= Rs. 8500
So,
Amount = Compound interest + Principal
= Rs. (1414.40 + 8500) = Rs. 9914.40
Question 46 1.2 / -0
A box has 30 balls with numbers 1 to 30 written on them. One ball is drawn at random. Find the value of (P + Q) ÷ R after completing the given table.
Event Probability (i) Getting a ball with a number less than 31 P (ii) Getting a ball with a number greater than 30 Q (iii) Getting a ball with an odd number R
Solution
Total number of balls = 30
(i) Number of balls with a number less than 31 = 30
(ii) Number of balls with a number greater than 30 = 0
(iii) Odd numbers: (1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29), i.e. total 15
Number of balls with an odd number = 15
(P + Q) ÷ R = (1 + 0) ÷
= 1 × 2 = 2
Question 47 1.2 / -0
State 'T for true and 'F' for false and select the correct option.
(i) The measure of each exterior angle of an n-sided regular polygon is
.
(ii) The adjacent angles in a parallelogram are supplementary.
(iii) In a quadrilateral PQRS, the bisectors of
P and
Q meet at point M. If
R = 120° and
S = 40°, then
PMQ = 80°.
Solution
(i) False; the measure of each exterior angle of an n-sided regular polygon is
.
(ii) True
(iii)
In a quadrilateral PQRS,
= 180° - 80° = 100°
Now, in
PQM,
MPQ +
MQP +
PMQ = 180°
= 180° - 100 = 80°
[As MP and MQ are the bisectors of
P and
Q, respectively]
Hence, the statement (iii) is true.
Question 48 1.2 / -0
Solution
(P) Area of the shaded region = Area of the big semicircle - Area of two small semicircles
=
=
= 134.75 m
2 (Q) Area of the shaded region = Area of the rectangle - Area of two semicircles
= (20 × 7) - 2 ×
= 140 -
= 101.5 m
2 (R) Area of the shaded region = Area of the rectangle - Area of the unshaded triangle
= (20 × 7) -
× 20 × 7
= 140 - 70 = 70 m
2 (S) Area of the shaded region = Area of the bigger circle - Area of the smaller circle
=
=
× (196 - 49) = 22 × 21 = 462 m
2
Question 49 1.2 / -0
Read the following statements carefully and select the correct option.Statement-I: An article marked at Rs. 800 is sold at successive discounts of 15% and 25%. If the buyer desires to sell it at a profit of 20% after allowing a 10% discount, then its marked price will be Rs. 680.Statement-II: If the amount of Rs. p at 10% per annum for 3 years compounded annually becomes Rs. q, then q : p is 125 : 216.
Solution
Statement-I: Marked price (M.P.) = Rs. 800
Price of the article after 15% discount = Rs.
= [800 – 120] = Rs. 680
Price of the article after another 25% discount = Rs.
= Rs. [680 – 170] = Rs. 510
So, cost price of the article for the buyer = Rs. 510
Let the marked price of the article be Rs. x.
Discount = 10%
Now, profit = 20%
Statement-I is true.
Statement-II: Principal (P) = Rs. p, Rate (R) = 10% p.a.
Time (T) = 3 years, Amount = Rs. q
q : p = 1331 : 1000
Statement-II is false.
Question 50 1.2 / -0
Fill in the blanks.
Solution
(i) Range = Highest observation - Lowest observation = 20 - 0 = 20
(ii) The probability of an impossible event is 0.
(iii) The number of times a particular observation occurs in a given data is called frequency.
(iv) Total number of outcomes = 36
Possible outcomes of getting a total of 11 = (6, 5), (5, 6), i.e. total 2
∴ Required probability =
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