Question 1 1.2 / -0
Fill the missing number in the following pattern.
Solution
In every triangle, the number inside the triangle is double the sum of the numbers outside the triangle.
Question 2 1.2 / -0
12 76 16 32 97 21 45 107 ?
Find out the missing number from the given options.
Solution
See horizontally. Add all the digits of the numbers in the first two boxes to get the number in the third box.
Question 3 1.2 / -0
Directions: In the following problem, a square transparent sheet with a pattern is given. Figure out from amongst the four alternatives, how the pattern will appear when the transparent sheet is folded along the dotted line.
Solution
When the square transparent sheet
is folded along the dotted line, we get
pattern.
Thus, option 4 or figure D is the correct answer.
Question 4 1.2 / -0
Directions: The first figure in the first unit of the Problem Figures bears a certain relationship to the second figure. Similarly one of the figures in the Answer Figures bears the same relationship to the second figure. Locate the figure which would fit in the question mark.
Solution
In each step, inner square is rotated 90° clockwise and dot is on the corner which is empty.
Question 5 1.2 / -0
Directions: A group of pieces, out of the four figures (a), (b), (c) and (d), when joined together form the shape given on the left side. Identify the group.
Solution
Figure (c) consists of all the pieces which join together to form the given figure. Figure (c) consists of 2 squares, 2 trapeziums (1st normal trapezium and 2nd consisting of 1 triangle and 1 rectangle).
Question 6 1.2 / -0
Directions : In the question given below, there are four statements followed by three conclusions numbered I, II, and III. You have to take the given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusions logically follow(s) from the given statements. Statements: Conclusions:
Solution
Only III applies as some shirts are belts.
Question 7 1.2 / -0
Directions: Study the following arrangement carefully and answer the question given below.
B M % R 3 J @ K © D F 6 9 W 4
N E P 2 $ A Y 5 I Q Z # 7 U G
How many such consonants are there in the above arrangement, each of which is immediately preceded by a symbol and immediately followed by a number?
Solution
B M % R 3 J @ K © D F 6 9 W 4 N E P 2 $ A Y 5 I Q Z # 7 U G
Question 8 1.2 / -0
Which of the following options can be the top view of the below funnel lying on a table?
Solution
The top view of the given object will be as below:
In the above figure, the shaded portion with crosses represents the smaller diameter cylindrical tube of the funnel, and the shaded portion with lines represents the larger diameter conical part of the funnel.
Question 9 1.2 / -0
In the diagram above, the circle represents Milky Bar, the triangle represents Five Star, the rectangle represents Bar One, and the square represents Snickers packing areas. Study the diagram carefully and answer the question given below.
In which area are Snickers, Five Star and Milky Bar packed?
Solution
6 is the area in which Snickers, Five Star and Milky Bar are packed.
Question 10 1.2 / -0
Find out the missing number in the given figure.
Solution
The mathematical operation applied in the two vertically opposite sectors of the circle is as: 2 + 5 = 302 + 6 = 422 + 11 = 1322 + 14 = 210
Question 11 1.2 / -0
Complete the below series:
Solution
There are two series: 89 + 9 = 98 + 18 = 116 + 27 = 143 Another series = 56 +7 = 63 + 14 = 77 + 21 = 98
Question 12 1.2 / -0
What is the number of vertices in the solid figure given below?
Solution
Vertex typically means a corner or a point where lines meet. For example a square has four corners, each is called a vertex. The plural form of vertex is vertices.
The vertices are shown by numbers in the given figure.
From the above labelled figure, it is clear that the solid figure has 8 vertices clearly shown.
Hence, option (1) is the correct option.
Question 13 1.2 / -0
Which number will replace the question mark?
Solution
Pattern followed here is:
Question 14 1.2 / -0
Rohit started his journey from his house and walked 50 metres towards north. Then, he turned to the right and walked 15 metres. He then turned to the left and walked 15 metres again. And then, he took a final left turn and walked 10 metres. In which direction was he with respect to the starting position?
Solution
It can be seen from the figure that he was in northeast direction with respect to the starting position.
Question 15 1.2 / -0
Find the number which will replace the question mark, if the same rule is followed in three figures.
Solution
In all the three figures, the pattern which is being followed is:st number multiplied by 3rd at the bottom = 1st digit (From the left, inside the circle)nd number at the top multiplied by 2nd at the bottom = 2nd digit (inside the circle)rd number at the top multiplied by 1st number at the bottom = 3rd digit (inside the circle)
Question 16 1.2 / -0
A dice is rolled twice. What will be the probability of getting a multiple of 3 in the first roll, and a prime number in the second roll?
Solution
Multiples of 3 on the dice are 3 and 6.Prime numbers on the dice are 2,3 and 5.Probability of getting a multiple of 3 =
Probability of getting a prime number =
Total probability =
Question 17 1.2 / -0
What is the value of IJ?
Solution
Look at the diagram: Find the unknown segment lengths. MN and IN are tangents to the inscribed circle from N.
Question 18 1.2 / -0
How many terms are there in the given series?
Solution
63 + 61 + 59 + 57 + .....+25n = 25 n
Question 19 1.2 / -0
If sin x =
and cos x =
, then find out the value of
.
Question 20 1.2 / -0
If
, then find out the value of sin x cos x.
Solution
(sin x + cos x)
2 = 2
sin
2 x + cos
2 x + 2sinx cosx = 2
1 + 2 sin x cos x = 2
2 sin x cos x = 1
Question 21 1.2 / -0
Following is the pie chart showing the percentages of pets in a pet shop,
What is the number of dogs in the shop, if the total number of pets is 160?
Solution
Number of pets = 160
Percentage of dogs in the shop = 55%
So, number of dogs =
× 160 = 88
Question 22 1.2 / -0
The sum of the first four consecutive even numbers is 60. Find out the 2nd consecutive even number.
Solution
2a + 2a + 2 + 2a + 4 + 2a + 6 = 60
8a + 12 = 60
8a = 60 – 12
8a = 48
a =
= 6
2
nd consecutive even number = 2a + 2
= 2 × 6 + 2 = 14
Question 23 1.2 / -0
If 3a
2 = b
2 ≠ 0, then the value of
is
Question 24 1.2 / -0
Find the area of triangle KLM. Write the answer as a decimal rounded to the nearest tenth.
Solution
Area of triangle KLM =
, where K, L, M are the side lengths of triangle KLM.
s =
s =
= 26.5
Area of triangle KLM =
=
=
=
= 76.5061
To the nearest tenth, the area of triangle KLM = 76.5 m
2
Question 25 1.2 / -0
Find the length OR.
Solution
Given,
PR = QR = 5 cm
Radius, OP = 13 cm
From the right triangle PRO (Since radius is perpendicular to chord at the mid-point of the chord)
OP
2 = OR
2 + PR
2 OR
2 = OP
2 – PR
2 OR
2 = (13)
2 – (5)
2 OR
2 = 169 - 25
OR =
OR = 12 cm
Question 26 1.2 / -0
The sum of two equal sides of an isosceles triangle is 5 times the third side. If the perimeter is 60 cm, then find the biggest side of the triangle.
Solution
Let two equal sides be x.
Question 27 1.2 / -0
J is the centre of the circle. In triangle JMN, angle JMN = 55°. Find out the measure of
L.
Solution
In triangle JMN, JM = JN
So,
JMN =
JNM = 55°
JMN +
JNM +
MJN = 180°
55° + 55° +
MJN = 180°
110° +
MJN = 180°
MJN = 180 – 110
MJN = 70°
L =
of
MJN (Note: An inscribed angle at the circumference is half of the central angle made by the chord)
L =
× 70 = 35°
Question 28 1.2 / -0
If z = x, y = w and u = v, then which of the following relationships is true?
Solution
z = x (Given) --1
Question 29 1.2 / -0
In a pack of 52 cards, what is the probability of getting an ace and a jack without replacement?
Solution
Number of aces in a pack = 4
The probability of getting an ace =
Probability of getting a jack out of 51 =
Now, the probability of getting an ace and a jack =
=
Question 30 1.2 / -0
(sin θ + cosec θ)2 + (cot θ + tan θ)2 = ?
Solution
By using identity:
(a + b)
2 = a
2 + b
2 + 2ab
(sin θ + cosec θ)
2 - (cot θ + tan θ)
2 = (sin
2 θ + cosec
2 θ + 2 sin θ cosec θ) - (cot
2 θ + tan
2 θ + 2cot θ tan θ)
= sin
2 θ + cosec
2 θ + 2 × sin θ ×
- cot
2 θ - tan
2 θ - 2 × tan θ ×
= sin
2 θ + cosec
2 θ + 2 - cot
2 θ - tan
2 θ - 2
= sin
2 θ + (1 + cot
2 θ) - cot
2 θ - tan
2 θ
= sin
2 θ + 1 - tan
2 θ
= sin
2 θ - tan
2 θ + 1
Question 31 1.2 / -0
What will be the 45th term of an A.P., if it consists of 73 terms and the first and the last terms are 1 and 145, respectively?
Solution
Given: n = 73, a
1 = 1
So, a
1 + 72d = 145
1 + 72d = 145
72d = 144
d =
d = 2
a
45 = a
1 + 44d
= 1 + 44(2)
= 1 + 88
= 89
So, a
45 = 89
Question 32 1.2 / -0
In a car-bazaar, the total number of cars is 79. The percentage of white cars is 29.65%. How many cars in the car-bazaar are white?
Solution
29.65% = 0.2965
Question 33 1.2 / -0
What would be the height of a triangle ABC, if the base of the triangle is 8 cm and the area of the triangle is equal to the area of a square whose side is equal to the base of the triangle ABC?
Solution
Area of square = (Side)
2 = (8)
2 = 64 cm
2 Area of a triangle = 64 cm
2 Area of triangle =
× base × height
64 =
× 8 × height
Height =
= 16 cm
Question 34 1.2 / -0
In a triangle ABC,
A is twice of
B. Find the measurement of angle C if
A = 68°.
Solution
In a triangle ABC,
A = 2
B
68° = 2
B
B = 34°
As
A +
B +
C = 180° (Sum of angles of a triangle)
68° + 34°
+
C = 180°
C = 180° - 102°
C = 78°
Question 35 1.2 / -0
If an A.P. consists of 55 terms and if the first and last terms are 13 and 175, respectively, then determine the 49th term.
Solution
Given: n = 55, a
1 = 13
and a
55 = 175
So, a
1 + 54d = 175
13 + 54d = 175
54d = 162
d =
d = 3
a
49 = a
1 + 48d = 13 + 48(3) = 13 + 144 = 157
So, a
49 = 157
Question 36 1.2 / -0
In a shop, 20% of the fruits are apples, 50% of the remaining are bananas and 30% of the remaining are grapes. The remaining 6,300 fruits are of different types. What is the total number of fruits in the shop?
Solution
Let the total number of fruits in the shop be x.
20% of these fruits are apples = 0.2x apples
Therefore the remaining fruits = x − 0.2x = 0.8x fruits
50% of these remaining fruits are bananas = 50% of 0.8x = 0.4x fruits
Therefore, the remaining fruits = 0.8x − 0.4x = 0.4x fruits
30% of these remaining fruits are grapes = 30% of 0.4x = 0.12x fruits
Now the remaining fruits = 0.4x − 0.12x = 0.28x fruits
According to the question, the number of remaining fruits = 6300
0.28x = 6300
x =
x = 22,500 fruits
Therefore, the total number of fruits in the shop = 22,500
Question 37 1.2 / -0
In triangle DEF, DE = 5 cm, EF is twice of DE, and DF = 13 cm. Find out the area of triangle DEF using Heron's formula.
Solution
Let DE = a cm, EF = b cm and DF = c cm
S =
cm
S =
cm
S =
cm
S = 14 cm
Area =
Area =
cm
2 Area =
cm
2 Area =
cm
2 = 22.45 cm
2
Question 38 1.2 / -0
The area of a rectangular box is 212 cm2 . The ratio of the perimeter to the width of the rectangular box is 6 : 2. What is the length of the box?
Solution
4l + 4b = 6b
b =
l × b = 212
l × 2l = 212
l
2 = 106
l = 10.3 cm
Question 39 1.2 / -0
In an Art and Craft class, Aman creates 2 triangles with a cardboard. The base of one of the triangles is 15 cm and its height is 12 cm. What will be the height of the other triangle if its area is double the area of the first triangle and its base is 20 cm?
Solution
Area of the first triangle =
× base × height
=
× 15 × 12 = 90 cm
2 Area of the second triangle = 2 × area of the first triangle
180 =
× 20 × Height
Height = 18 cm
Question 40 1.2 / -0
The point which lies on X-axis at a distance of 6 units in the negative direction is
Solution
The point which lies on X-axis at a distance of 6 units in the negative direction is (-6), which is the x-coordinate.
Question 41 1.2 / -0
John builds a hall whose length, breadth and height are 11 m, 14 m and 12 m, respectively. What will be the total cost of painting the walls and the ceiling of the room if the cost of painting is Rs. 8.25 per m²?
Solution
Surface area = 2(lb + bh + lh)
Question 42 1.2 / -0
Two dice are thrown simultaneously. Find the sum of the probability of getting a prime number as the sum and probability of getting a doublet of prime numbers.
Solution
Total number of outcomes = 6 × 6 = 36
Outcomes for getting a prime numbers as the sum are:
(1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3), (5, 2), (5, 6), (6, 1) and (6, 5) = 15 outcomes
So, the probability of getting a prime number as the sum =
Further, prime doublets are (2, 2), (3, 3), (5, 5)
So, probability of getting a doublet of prime numbers =
Now, required probability =
Question 43 1.2 / -0
A Hula-Hoop with a radius of 35 cm is rolled on ground. To cover a distance of 110 m, how many revolutions should it make?
Solution
Radius = 35 cm
Diameter (d) = 35 × 2 = 70 cm
The circumference of the Hula-Hoop =
d
=
× 70 = 220 cm
The Hula-Hoop will cover a distance of 220 cm by revolving once.
The distance to be covered = 110 m = 11,000 cm
Therefore, number of times the hoop has to revolve to cover 110 m =
= 50
Question 44 1.2 / -0
In a parallelogram ABCD, the base is twice the height, and the area is 338 cm². Find out the height of the parallelogram.
Solution
Area of a parallelogram = Base × Height
Base = 2(Height)
2h × h = 338
2h
2 = 338
h
2 =
h
2 = 169
h =
h = 13 cm
Question 45 1.2 / -0
The marks scored by some students in their mathematics test are given below:
Marks 31 25 19 21 41 43 Number of students 4 5 6 2 3 1
Find the average marks scored by the students in their test.
Solution
Total number of students = 21
Total marks = (31 × 4 + 25 × 5 + 19 × 6 + 21 × 2 + 41 × 3 + 43) = 571
Average =
= 27.2
Question 46 1.2 / -0
If cos A =
, then find the value of
.
Solution
Since cos A =
52 = 42 + perpendicular
2 Perpendicluar =
So , sin A =
, tan A =
and sec A =
Now,
=
=
Question 47 1.2 / -0
Anuj picks a card from a deck of playing cards. If he chooses a black card, he goes to his job, and if he picks the other type, he does his own work for that day. What will be the probability that he goes to job by picking an 8?
Solution
There are, in total, 4 cards with number 8 (2 black, 2 red). So, he will go to his job only if he picks one of the two black cards with number 8, which is the favourable outcome here.
Thus,
P(of getting 8 among black colour) =
Question 48 1.2 / -0
Observe the linear equations given below and choose the correct option.
y =
+ 2 ...(i)
x = 2y + 6 ...(ii)
Solution
If we rewrite the equations provided, we get:
x + 2y - 4 = 0, and 2x + 4y - 12 = 0
Now, comparing their coefficients ,
i.e.,
.
Thus, the two equations have no solution.
Question 49 1.2 / -0
On plotting points (3, -6), (3, -4), (5, -3), (7, -4), (7, -6), (5, -7) and joining them together as a closed shape, which shape will be obtained?
Question 50 1.2 / -0
To construct a bullock cart, Ray takes 60 days, Gilly takes 30 days and Kyle takes 20 days. Kyle plans to construct a bullock cart. He gets help from Ray and Gilly every second day from the start of the construction of the bullock cart. How long will it take for the bullock cart to be constructed?
Solution
Kyle's one day's work =
Kyle, Gilly and Ray's one day's work =
Work done in 2 days =
So,
of work is done in 2 days.
Therefore, whole work will be done in
= 13.333 days
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