Question 1 1.2 / -0
Which of the following numbers comes next in the series?
Solution
This is a simple alternating addition and subtraction series.
Question 2 1.2 / -0
In the morning, Tom started walking in the direction opposite to the Sun. After covering a distance of 10 km, he took right turn and covered a distance of 5 km. Then, he took a right turn and covered another 10 km. In which direction is Tom now from the starting point?
Solution
Tom is in North direction from his starting point.
Question 3 1.2 / -0
Find the missing pair of letters in the given question.
Solution
D = (+2) = F
Question 4 1.2 / -0
Complete the series.
Solution
13 = 1, 23 = 8, 33 = 27, 43 = 64, 53 = 125, 63 = 216
Question 5 1.2 / -0
If PREPARE is coded as RPGNCPG, then REMEMBER should be coded as
Solution
P + 2 = R
Question 6 1.2 / -0
Directions:
Solution
By rearranging the letters, we get BANANA and Banana belongs to fruit category.
Question 7 1.2 / -0
Directions: Find the number to replace the question mark, if the same rule is followed in the three figures.
Solution
The following pattern has been followed,st term = 1st term on the top + 1st term on the bottomnd term = 2nd term on the top + 2nd term on the bottomrd term = 3rd term on the top + 3rd term at the bottom
Question 8 1.2 / -0
Complete the pattern.
Solution
7 is subtracted from the previous number every time.
Question 9 1.2 / -0
'Able' is related to lbea and Dust is 'sutd'. Base is related to 'saeb' in the same way as 'Feet' is related to
Solution
The first letter becomes the fourth, the second letter remains second, the third becomes the first and the last becomes the third.
Question 10 1.2 / -0
How many lines are required to make this shape?
Solution
14 lines are required to make this shape.
Question 11 1.2 / -0
The following Venn diagram represents the number of students who scored grades A, B and C in the first semester of their college.
How many students scored grade A and grade B, altogether?
Solution
Grade A is pentagon, grade B is rectangle and grade C is circle.
Question 12 1.2 / -0
Directions:
Solution
The correct sequence of the words according to the dictionary is
Question 13 1.2 / -0
Which of the following statements is true if '%' stands for 'x' , '@' stands for '÷', '$' stands for '-' and '&' stands for '+'?
Solution
% = x
Question 14 1.2 / -0
A man walks 30 m towards South, turns right and walks 20 m. He then turns left and walks 30 m. How far is he from the starting point?
Solution
In
By Pythagoras theorem,
AD
2 = AC
2 + DC
2 AD
2 = (AB + BC)
2 + BE
2 [AC = AB + BC], [DC = EB]
AD
2 = (30 m + 30 m)
2 + (20 m)
2 AD
2 = (60 m)
2 + (20 m)
2 AD
2 = 3600 m
2 + 400 m
2 AD
2 = 4000 m
2 AD
2 = (20 × 20 × 10)m
2 AD =
AD =
m
Question 15 1.2 / -0
Directions:
Solution
A, B, C, D and E are facing South but not necessarily in same order, whereas M, N, O, P and Q are facing towards North direction but not necessarily in same order. C, N and A are sitting on the extreme ends of their respective rows. E is sitting third to the right of A. E is sitting opposite O.
P is sitting second to the left of N. B and Q are sitting opposite each other. D is sitting exactly between E and B.
O is sitting second to the left of Q.
Question 16 1.2 / -0
Which of the following are the coordinates of mid-point of line segment joining A(4, 6) and B(8, 4)?
Solution
The mid-point of line segment joining (x
1 , y
1 ) and (x
2 , y
2 )
=
=
=
= (6,5)
= Mid-point = (6, 5)
Question 17 1.2 / -0
Directions: th and 6th term of the series.
Solution
The first term of the series is a = 20th term of the series = a + (n - 1)d = a + 7d = 20 + 35 = 55
Question 18 1.2 / -0
Find the first term of the series whose seventh term is 75 and whose tenth term is 111.
Solution
The nth term of the series is a + (n - 1)d.
Question 19 1.2 / -0
Find the common root for the quadratic equations x2 + 7x + 12 = 0 and 2x2 + 7x + 3 = 0.
Solution
x2 + 7x + 122 + 4x + 3x + 12 = x(x + 4) + 3(x + 4)2 + 7x + 3 = 0x 2 + 6x + 1x + 3 = 0
Question 20 1.2 / -0
Solve the equation for rootsx 2 + 3x + 1 = 0
Solution
x
2 + 3
x + 1 = 0
x
2 + 3
x = -1
x
2 + 3
x +
= -1 +
x +
=
x =
Question 21 1.2 / -0
Simplify
.
Solution
As we know, Sin (90
- X) = Cos X and Cos (90 - X) = Sin X
Question 22 1.2 / -0
Amin has a right angled triangular garden as shown in the picture.
What is the length of side m (in feet)?
Solution
Using Pythagoras theorem,
12
2 + m
2 = 13
2 144 + m
2 = 169
m
2 = 169 - 144
m
2 = 25
m =
m = 5 ft
Question 23 1.2 / -0
If x = 3, then find y.
Solution
6 + 15 -
y + 27 - 1y = 0
48 - 8y = 0
y = 6
Question 24 1.2 / -0
What is the value of the given expression?4 x - cosec4 x + cot2 x + cosec2 x)
Solution
Given expression is (cot4 x + cot2 x) - (cosec4 x - cosec2 x) 2 x(cot2 x + 1) - cosec2 x(cosec2 x - 1) 2 x cosec2 x - cosec2 x cot2 x = 0
Question 25 1.2 / -0
If cos
4 x - sin
4 x =
, then the value of (2cos
2 x - 1) is
Solution
cos
4 x - sin
4 x =
(cos
2 x + sin
2 x)(cos
2 x - sin
2 x) =
(cos
2 x - sin
2 x) =
(cos
2 x + sin
2 x = 1)
cos
2 x - (1 - cos
2 x) =
2cos
2 x - 1 =
Question 26 1.2 / -0
A jar contains 48 marbles, some are red and others are yellow. If a marble is drawn at random from the jar, the probability of getting a red marble is
. Find the number of yellow marbles in the jar.
Solution
Total number of marbles = 48
Probability of getting a red marble =
Number of red marbles =
= 40
So, number of yellow marbles = 48 - 40 = 8
Question 27 1.2 / -0
A dice is thrown once. What is the probability of getting a prime number?
Solution
Prime numbers are 2, 3 and 5.
So, probability of getting a prime number is
or
.
Question 28 1.2 / -0
The angles of a quadrilateral are in ratio 5 : 8 : 4 : 7. Find all the angles of the quadrilateral.
Solution
We will assume common ratio between angles to be 'x' and then see the total of all internal angles in a quadrilateral is 360°.
Using that, we can find the value of 'x' and then angles accordingly.
5x + 8x + 4x + 7x = 360°
24x = 360
x =
= 15
5x = 5 × 15 = 75°
8x = 8 × 15 = 120°
4x = 4 × 15 = 60°
7x = 7 × 15 = 105°
Question 29 1.2 / -0
What is the measure of ∠G?
Solution
Since FG is a diameter of the circle, ∠E is a right angle.
Question 30 1.2 / -0
If mode = 90 and median = 110, then mean is
Solution
Mode = 3 Median - 2 Mean
Question 31 1.2 / -0
In a shop, 20% of the fruits are apples. 50% of the remaining fruits are bananas and 30% of the remaining fruits are grapes. The remaining 6300 fruits are of a different type. 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 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 total remaining fruits = 6300
0.28x = 6300
x =
x = 22,500 fruits
Therefore, the total number of fruits in the shop = 22,500
Question 32 1.2 / -0
If the area of a rectangle and that of a square are equal and the length of the rectangle is bigger than its width by 6 cm, then what is the length of the side of the square if the width of the rectangle is 30 cm?
Solution
Let s be the side of the square.2 2 2
Question 33 1.2 / -0
What is the value of
?
Question 34 1.2 / -0
In the figure, O is the centre of the circle, AB is the chord of the circle, EF is the diameter of the circle and angle ACB = 40°. If angle OBA measures 40°, find the value of angle OAB.
Question 35 1.2 / -0
Find the number if the difference between the number and
rd of the number is 80.
Solution
Let, the number be x
x -
1x = 80 × 3
So, x = 240
Question 36 1.2 / -0
At Downtown Burger, cheese burgers and chicken burgers are available. 6 of the last 12 customers wanted cheese burgers. What is the probability that the next customer will also want a cheese burger?
Solution
The experimental probability is the number of times an event occurs out of the total number of trials. Write the experimental probability as a fraction in its simplest form.
Question 37 1.2 / -0
Months ago, a store purchased a chalkboard and priced it at Rs. 8000. The store needed to clear out space, so the manager decided to sell the chalkboard at 45% of the marked price. If Ellie, who earns a 7% commission on the sale price, sold the chalkboard, then how much commission did she make?
Solution
First find the discount price. Write 45% as the decimal 0.45 before using it in the equation.
Question 38 1.2 / -0
There are 247 men and 156 women in HDFC bank headquarters. The bank's Chairman wants to divide employees in two sections such that a section can have only men bankers or only women bankers. If each section has same number of bankers in a row and the Chairman wants to have as few rows in each section as possible, then find the number of rows in HDFC bank headquarters.
Solution
HCF of 247 and 156.
Question 39 1.2 / -0
The present ages of Virat and Rohit are in the ratio of 2 : 3 respectively. Four years from now, the ratio of their ages will be 3 : 4. What is Rohit's present age?
Solution
Let, the present ages of Virat and Rohit be 2x and 3x.
Then,
4(2x + 4) = 3(3x + 4)
8x + 16 = 9x + 12
x = 4
So, Rohit's present age = 3x = 12 years
Question 40 1.2 / -0
How many containers can be filled with cement having weight of
kg if the container has a capacity of
kg?
Solution
Total quantity of cement =
kg (Converting mixed numbers into fractions)
Capacity of one container =
kg
Number of containers that can fill in
kg of cement
= 33.10
That means, we require more than 30 containers.
Question 41 1.2 / -0
A pipe can fill a tank in 10 minutes, while a leak present in the tank can empty it in 25 minutes. Unaware of the leak, the owner opens the pipe to fill the tank. After a few minutes, he seals the leak and the pipe fills the rest of the tank in 6 minutes. Find the total time taken to fill the tank.
Solution
The portion of the tank filled when the pipe as well as the leak were open =
If x is the time taken to fill the tank when pipe and leak were open, then portion of the tank filled in x minutes =
Remaining portion to be filled when the leak was sealed =
Time taken to fill the remaining portion of the tank = 6 minutes
Solving the above equation, we get
x = 12 minutes
Total time taken to fill the tank = 6 minutes + 12 minutes = 18 minutes
Question 42 1.2 / -0
Chetan brought 150 chocolates and distributed them among his two best friends Mike and Peter. Mike got 16% more chocolates than Peter. The ratio of the chocolates present with Mike and Peter is
Solution
Assume that Mike got x% chocolates and Peter got (x - 16)% chocolates.
Question 43 1.2 / -0
Age of three brothers P, Q and R is in the ratio 3 : 1 : 5, respectively. After 5 years, P will be twice as old as Q. How many years was P younger to R five years ago?
Solution
The present ratio of P to Q is 3 : 1 and after 5 years, the ratio will be 2 : 1.
3x + 5 = 2x + 10
x = 5
The present age of P is 15 years and that of R is 25 years.
Five years back, age of P was 10 years and that of R was 20 years.
P was 10 years younger than R 5 years ago.
Question 44 1.2 / -0
A builder decides to fill the floor of a bed room using designer tiles costing Rs. 70 each. Each tile is a square and the dimension of the bed room is 6 m × 4.40 m. What was the minimum cost incurred while flooring the bed room?
Solution
Given that the tiles required for flooring are square. Hence, the length of the tile should be equal to the width of the tile.
Question 45 1.2 / -0
A crow comes and drinks water from a mud pot after every 30 minutes. It starts coming from 11 am onward till 5 pm. How many times will it come to drink water in a week?
Solution
Number of hours in a day = 24
Question 46 1.2 / -0
In the given figure, PA = PB. Find
APB.
Solution
PA = PB (Tangents drawn from external point are equal)
PBA =
PAB = 65°
In
ABP,
PBA +
PAB +
APB = 180° (Angle sum property)
65° + 65° +
APB = 180°
APB = 180° - 65° - 65°
APB = 50°
Question 47 1.2 / -0
In
ABC, DE || BC. What can be the possible value(s) of x?
Solution
By using B.P.T.
or
(x – 3)(x – 4) = 4(3x – 19)
x
2 – 7x + 12 = 12x – 76
x
2 – 19x + 88 = 0
(x – 8)(x – 11) = 0
Or, x = 8 or 11.
Question 48 1.2 / -0
Which of the following statements is true?Statement 1: A tangent to a circle is perpendicular to the radius at the point of tangency.Statement 2: The perpendicular from any point in the interior of the circle to the chord bisects the chord.
Solution
Statement 1 is correct by definition.
AB and AC are tangents and O is the circle's centre.
OAB =
OCB
AO = OC (Radii of the same circle)
OB = OB (Common)
AOB
COB
AB = BC (CPCT)
Statement 2 is false because the perpendicular from the centre of the circle to the chord bisects the chord.
Question 49 1.2 / -0
Fill in the blanks.
Solution
1. The centre of the circle lies in interior exterior d iameter
Question 50 1.2 / -0
In a cricket match, a batsman hits a boundary 8 times out of 40 balls he plays. Find the probability of not hitting a boundary.
Solution
Batsman played 40 balls.
Therefore, total number of trials (S) = 40 where, S is the sample space.
Let, E be the event of hitting the boundary = 8
The number of balls not hitting the boundary = E = 40 - 8 = 32
The probability of not hitting a boundary =
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