Question 1 1.2 / -0
Which number will replace '?' in the given series?
Solution
The series is as follows:
Question 2 1.2 / -0
If in a certain code, COLD is written as OCDL, then KEPT will be written as
Solution
COLD = OCDL
Question 3 1.2 / -0
Which of the following numbers will replace the question mark (?) in the first figure of triangle?
Solution
In the 2nd figure, rd figure, st figure,
Question 4 1.2 / -0
Paul starts from point A and walks 200 m towards right, and takes a left turn and walks another 600 m. From that point, he again turns left and walks another 800 m. Paul's wife Candida starts from point A and walks 100 m towards west. From that point, she turns right and walks another 600 m. What is the distance between both of them?
Solution
Path travelled by Paul is marked with Black and path travelled by Candida is marked with Green.
So, 800 m - 300 m = 500 m
Question 5 1.2 / -0
Choose the alternative that closely resembles the water image of the given combination of letters and numbers.
Solution
Hence, answer option (1) is correct.
Question 6 1.2 / -0
Find out the total number of triangles in the figure given below.
Solution
The triangles are BPN, PNE, ABM, EFG, MLK, GHI, QRO, RSO, STO, QTO, BPE, TQR, QRS, RST, STQ, MPO, GPO, LPJ, HPJ, MPG, PCB, PDE and LPH.
Question 7 1.2 / -0
If in a certain language, 'how' means '+' , 'you' means '-' , 'are' means '÷', and 'today' means '×' , then what will be the answer of the equation given below?
Solution
'how' means '+' , 'you' means '-' , 'are' means '÷' , and 'today' means '×'. (10 ÷ 5) - 4 × 2 = 20 + 2 - (4 × 2) = 20 + 2 - 8 = 14
Question 8 1.2 / -0
Which of the following will give you the eighth letter from the left, if the letters of the given word are arranged in reverse alphabetical order?
Solution
When the letters of the given word ENCOURAGE are arranged in reverse alphabetical order, then the result will be:C
Question 9 1.2 / -0
Which of the following numbers will logically replace the question mark in the given number series?
Solution
The series is as follows: 2 = 43 = 272 = 163 = 1252 = 363 = 343
Question 10 1.2 / -0
What would be the next combination in the given series?
Solution
Hence, next combination = (I + 4)(6 + 2)(K + 4) = M8O
Question 11 1.2 / -0
Which of the following Venn diagrams shows the relationship between scanners, input devices, and output devices?
Solution
Input and output devices are different, and scanners are the input devices. So, the following Venn diagram is made.
Question 12 1.2 / -0
Which number lies in the circle and triangle but not in the rectangle in the figure given below?
Solution
This is the correct option. The number which lies in the circle and triangle but not in the rectangle is 6.
Question 13 1.2 / -0
Thomas was ranked 5th from the top and 40th from the bottom in a class. How many students are there in the class?
Solution
He was ranked 5th from the top and 40th from the bottom.
Question 14 1.2 / -0
Arrange the words given below in a meaningful sequence:
Solution
First, we dig the soil and put the seed in the soil, so 1 comes first.
Question 15 1.2 / -0
If '÷' means '+' , '×' means '-' , '-' means '÷' , and '+' means '×' , then what will be the value of the following expression?
Solution
48 - 6 + 8 × 2 ÷ 10 = ?
Question 16 1.2 / -0
What will be the 45th term, if an A.P. consists of 73 terms, and the first and the last terms be 9 and 297?
Solution
Given: n = 73, a = 9 and a73 = 297n = a + (n - 1)d45 = a + 44d = 9 + 44(4) = 9 + 176 = 185
Question 17 1.2 / -0
In a flower bed, there are 40 roses in the first row, 38 roses in the second row, 36 roses in the third row, and so on. If there are 12 roses in the last row, how many rows are there in the flower bed?
Solution
The numbers of flowers in the flower bed rows form an AP.
Question 18 1.2 / -0
Find the value of: tan2 45° cos2 30° + cos2 45° sin2 30°.
Solution
tan
2 45°
×
cos
2 30°
+ cos
2 45°
×
sin
2 30°
...(i)
We know,
tan45°
= 1, cos30°
=
, cos45°
=
, sin30°
=
Putting the values in (i),
=
+
=
Question 19 1.2 / -0
What is the measure of ∠I, if IJ is the diameter of the given circle?
Solution
If IJ is a diameter of a circle, then the inscribed angle ∠JKI is a right angle.
So,
IJK is a right triangle, and ∠J and ∠I are complementary.
Write an equation setting the sum of their measures equal to 90°, and solve for ∠I.
∠J + ∠I = 90°
54° + ∠I = 90°
∠I = 36°
Question 20 1.2 / -0
Find x, if
= 5.
Solution
= 5
On cubing both the sides, we get
2x + 1 = 125
Or 2x = 124
Or x = 62
Question 21 1.2 / -0
Find the sum (S) and the product (P) of the roots of the quadratic equation x2 + 4x + 3 = 0.
Solution
Solving the equation: 2 + 4x + 3 = 02 + 3x + x + 3 = 0
Question 22 1.2 / -0
Find the sum of all numbers between 100 and 500 which are divisible by 8.
Solution
The first number bigger than 100 which is divisible by 8 is 104 and the last number smaller than 500 which is divisible by 8 is 496.
⇒ 496 = 104 + (n - 1)8 (where, n is the number of terms)⇒ n = 50So, n = 50
Sum of 50 terms:
S =
(where, l = last term)
=
= 25(104 + 496)
= 25 × 600 = 15,000
Hence, there are 50 numbers between 100 and 500 which are divisible by 8 and their sum is 15,000.
Question 23 1.2 / -0
If the mean of first 5 observations is 7 and the mean of first 6 observations is also 7, then the 6th observation is:
Solution
Mean of 5 observations = 7
Question 24 1.2 / -0
One end of a line is (3, 4). Find the other end, if its midpoint is (4, 5).
Solution
Let the coordinates of other point be (x, y).
Using midpoint formula,
4 =
and 5 =
8 = 3 + x and 10 = 4 + y
Or x = 5 and y = 6
The coordinates of other point are (5, 6).
Question 25 1.2 / -0
When a certain positive number is increased by 16 and squared, then the resulting number is 368 more than twice the square of the number. Which of the following is the possible value of the number?
Solution
According to the question,2 = 2x2 + 3682 + 256 + 32x = 2x2 + 3682 - 32x + 112 = 0
Question 26 1.2 / -0
In the figure given below, if PA = PB, then find ∠AOB.
Solution
PA = PB (Tangents drawn from external point are equal)
So, ∠PBA = ∠PAB = 65°
In
ABP,
∠PBA + ∠PAB + ∠APB = 180° (Angle sum property)
65° + 65° + ∠APB = 180°
∠APB = 180° - 65° - 65°
∠APB = 50°
Now in quadrilateral OAPB,
∠AOB + ∠APB = 180° [As, ∠OAP = ∠OBP = 90°]
∠AOB + 50° = 180°
∠AOB = 130°
Question 27 1.2 / -0
The sides of a triangle have lengths 6 units, 8 units, and 12 units. What kind of triangle is it?
Solution
Let a = 6, b = 8, c = 122 = 62 = 362 = 82 = 642 = 122 = 1442 + b2 = 1002 + b2 < c2 Hence, it is an obtuse-angled triangle.
Question 28 1.2 / -0
Which of the following options is the same as (x + 7)2 – 6(x + 7) + 9?
Solution
(x + 7)2 – 6(x + 7) + 92 – 6a + 9 = (a – 3)2 2 = [x + 7 – 3]2 = (x + 4)2 = (x + 4)(x + 4)
Question 29 1.2 / -0
What is the greatest integer 'k' for which the roots of the equation x2 – kx + 20 = 0 are imaginary?
Solution
x2 – kx + 20 = 02 + bx + c = 0, we get2 – 4ac < 0. 2 – 80 < 0 2 < 80
Question 30 1.2 / -0
If two complementary angles are in the ratio 6 : 9, then the measure of the largest angle is
Solution
Since, angles are in ratio 6 : 9, measure of the first angle will be 6x.
Question 31 1.2 / -0
Find the value of x and y from the following equations:
Solution
Given that x - 3y = 8 ------------------ (1)
Question 32 1.2 / -0
If degree of p(x) = 4, and degree of q(x) = 4, then what can be the sum of the possible values of degree of p(x) + q(x)?
Solution
Possible values of degree are: 0, 1, 2, 3 or 4.
Question 33 1.2 / -0
Find the value of k, if x - 1 is a factor of 4x3 + 3x2 - 4x + k.
Solution
As x - 1 is a factor of p(x) = 4x3 + 3x2 - 4x + k3 + 3(1)2 - 4(1) + k = 0
Question 34 1.2 / -0
Deepika has 27 coins. She finds p more coins from her drawer. Priyanka has double the number of coins Deepika has now. Choose the expression that shows the total number of coins they both have altogether?
Solution
Initially, Deepika had 27 coins.
Question 35 1.2 / -0
A certain number of elephants and an equal number of men are going somewhere. Half of the owners are on their elephant's back while the remaining are walking along leading their elephants. If the number of legs walking on the ground is 80, how many elephants are there?
Solution
Let the number of elephants = Number of men = x
Then, number of legs = 4x + 2 × (
) = 5x
So, 5x = 80, or x = 16
Correct answer - 16 elephants
Question 36 1.2 / -0
A gold ornament is of cylindrical shape. Its diameter is 16 cm and height is 2 cm. A goldsmith decides to melt that cylindrical ornament and make 12 spherical ornaments of same size. What will be the diameter of each of the spherical ornaments thus formed?
Solution
Volume of cylinder = π(r
c )
2 h
Radius of cylinder = r
c = 8
Volume of sphere =
πr
3 Volume of 12 spherical ornaments = Volume of one cylindrical ornament
= 12 ×
πr
3 = π(r
c )
2 h
= 12 ×
πr
3 = π × 8 × 8 × 2
r
3 =
r
3 = 8
r = 2 cm
Diameter = 2 × 2 = 4 cm
Question 37 1.2 / -0
In a box, there are red, blue, green and black balls. The number of blue balls is 15, number of black balls is 17 and number of red balls is 19. If the total number of balls in the box is 72 and one ball is drawn at random, then what is the probability that it is the green ball?
Solution
Total number of balls n(S) = (red + green + blue + black) balls = 72
Number of green balls n(E) = 72 - 51 = 21
Required probability P(E) =
Question 38 1.2 / -0
Arnav purchased an article for Rs. 5,000 and he decided to raise its price by 50%. After one month, he decided to sell it for 30% off. What was the price after discount?
Solution
Cost price of the article = Rs. 5,000
Question 39 1.2 / -0
An electronics vendor purchases the electric bulbs at a cost of Rs. 10 and sells them at a price of Rs. 32. What is percentage increase?
Solution
The percentage change formula can be used to find percent of increase.
Percentage increase =
Plug Rs. 10 and Rs. 32 into the formula and simplify:
Percentage increase =
=
=
= 220%
The percentage increase is 220%.
Question 40 1.2 / -0
A lot consists of 100 ball pens out of which 10 are defective and the others are good. Harry will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to him. What is the probability that he will buy it?
Solution
Total ball pens = 100
Question 41 1.2 / -0
From the information counter, I get to know that flight to Delhi leaves every 6 hours. Also, I learn that the last flight took off 50 minutes before. If the time now is 11:15 a.m, then what time will be the next flight?
Solution
Current time = 11:15 am
Question 42 1.2 / -0
A store pays Rs. 488 for a sewing kit. The store marks-up the price by 35%. What will be the new price?
Solution
Write the percentage as a decimal
35% = 0.35
The mark-up price is:
488
0.35 = 170.80
The new price will be
170.80 + 488.00 = 658.80
Hence, the new price after mark-up will be Rs. 658.80.
Question 43 1.2 / -0
If 10 pencils and 8 pens together cost Rs. 90, while 8 pencils and 7 pens together cost Rs. 78, then find the cost of one pen.
Solution
Let the cost of one pen = Rs. x
Question 44 1.2 / -0
Profit obtained on selling a mixer for Rs. 56 is the same as the loss incurred on selling it for Rs. 42. What is the cost (in Rs.) of the mixer?
Solution
Let CP of the mixer be Rs. x.
Question 45 1.2 / -0
Peter bought a total of 20 thumb pins, some of which cost $0.25 each and some of which cost $0.15 each. If Peter spent $4.20 to buy these pins, how many pins of each type did he buy?
Solution
Let X be the number of pins that cost $0.25 each, and Y be the number of pins that cost $0.15 each. The total number of pins is 20. Hence
X + Y = 20.... (1)
If X is the number of pins that cost $0.25, then the cost of X pins will be 0.25 X.
If Y is the number of pins at $0.15, then the cost of Y pins will be 0.15 Y.
The total cost of X pins and Y pins is known to be $4.20, and is also given by
0.25 X + 0.15 Y = 4.2 ....(2)
Solve (1) and (2), we get
X + Y = 20
0.25 X + 0.15 Y = 4.2
The first equation gives Y = 20 - X.
Substitute value of (Y) in the second equation and solve
0.25 X + 0.15 (20 - X) = 4.2
X(0.25 - 0.15) + 3 = 4.2
0.1 X = 1.2
X = 12 and Y = 20 - 12 = 8
Question 46 1.2 / -0
Directions: ABCD be a quadrilateral with area 18 sq. units with side AB parallel to side CD, and AB = 2CD . Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius will be
Question 47 1.2 / -0
Weights of 8 students of a class are: 36.5 kg, 34.5 kg, 42.8 kg, 40.6 kg, 38.6 kg, 36.9 kg, 40.5 kg and 39.0 kg
Solution
If we arrange the data in ascending order:- 34.5, 36.5, 36.9, 38.6, 39.0, 40.5, 40.6, 42.8
Median =
= 38.8 kg
Thus, statement I is not true.
Range of data = 42.8 – 34.5 = 8.3 kg
Thus, statement II is true.
Hence, option 2 is the correct answer.
Question 48 1.2 / -0
Fill in the blanks:
Solution
1. An arc is a s emi- circle chord three
Question 49 1.2 / -0
The area of triangle LMN is 120 square units. The shaded and unshaded regions have equal areas. If the area of triangle MVU is 1/3
rd the area of triangle LMN, and the area of triangle LWX is 1/4
th the area of triangle LMN, then find the area of quadrilateral ABCD. (Note: The figure is not drawn as per the scale.)
Solution
Area of
MUV = (1/3)
Area of ΔLMN = 40 sq. units
Similarly, area of
LWX = (1/4)
120 sq. units = 30 sq. units
Let the area of ABCD be x sq. units.
Then, area of the shaded region = 30 sq. units – x + 40 sq. units – x + x = 70 sq. units – x = Area of the unshaded region
70 sq. units – x = (½) × 120 sq. units = 60 sq.units
x = 10 sq. units
Question 50 1.2 / -0
The number of real roots of
= 9 is
Solution
= 9
= 3
2 On comparing the powers, we get
2x
2 – 7x + 7 = 2
Or, 2x
2 – 7x + 5 = 0
Or, 2x
2 – 5x – 2x + 5 = 0
Or, x(2x – 5) – 1(2x – 5) = 0
Or, (x – 1)(2x – 5) = 0
Or, x = 1, 5/2
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