Question 1 1.2 / -0
There is a certain relationship between figures (i) and (ii). Establish a similar relationship between figures (iii) and (iv) by selecting a suitable figure from the options which will replace the (?) in figure (iv).
Solution
From figure (i) to (ii), the element in the upper left corner turns 90° anticlockwise and moves to the upper right corner. The element in the lower right corner turns 90° anticlockwise and moves to the lower left corner. The element in the middle turns 45° clockwise.
Question 2 1.2 / -0
Select the correct mirror image of the given figure.
Question 3 1.2 / -0
Pointing to a photograph, Manish said, "He is the son of the only daughter of the father of my brother." How is Manish related to the man in the photograph?
Solution
The father of Manish's brother would also be Manish's father. The only daughter of Manish's father would be Manish's sister. So, Manish is the maternal uncle of his sister's son.
Question 4 1.2 / -0
Which of the following Venn diagrams correctly describes the relationship among "scientists", "car owners" and "females"?
Solution
As some scientists are car owners, some scientists are also females and some females are also car owners, the above given Venn diagram is the correct answer.
Question 5 1.2 / -0
A man walks 6 km to the east, and then turns towards south and walks 5 km. Again, he turns towards east and walks 6 km. Next, he turns northwards and walks 10 km. How far is he now from his starting point?
Solution
AF = AB + BF = AB + CD = 6 + 6 = 12 km
Also,
EF = ED - BC = 10 - 5 = 5 km
By using Pythagoras theorem,
AE
2 = AF
2 + EF
2 = 12
2 + 5
2 = 144 + 25 = 169
AE = 13 km
∴ The man is 13 km far from the starting point.
Question 6 1.2 / -0
Arrange the given words as they occur in the dictionary.
Solution
The correct order of words according to dictionary is:
Question 7 1.2 / -0
In a certain code language, 'EMPLOYEES' is written as 'DLOKOXDDR'. How will 'FURNITURE' be written in the same language?
Solution
We have:
Similarly,
Question 8 1.2 / -0
If we interchange '÷' with '+', and '-' with '×' in each of the following options, then which option becomes correct?
Solution
On interchanging the signs, we get:
Question 9 1.2 / -0
Three positions of a die are shown below. How many dots will be there on the face opposite to the face having 6 dots?
Solution
Taking cubes 1 and 3,2 4 3 6
Question 10 1.2 / -0
How many squares are there in the given figure?
Solution
The squares formed are ABCD, EFGH, AEOF, EBGO, FOHD, OGCH, FIOL, IEJO, OJGK, and LOKH.
Thus, the number of squares formed is 10.
Question 11 1.2 / -0
Select a figure from the options which will complete the given figure matrix.
Solution
In each row, the second figure is made by the combination of the first figure and the third figure.
Question 12 1.2 / -0
Find the missing number.
Solution
The rule followed is:
Question 13 1.2 / -0
Select a figure from the options which will complete the given figure pattern.
Question 14 1.2 / -0
A square transparent sheet with a pattern and a dotted line on it is shown below. Select a figure from the options which shows how the pattern would appear when the transparent sheet is folded along the dotted line.
Question 15 1.2 / -0
Select the odd one out.
Question 16 1.2 / -0
In the given figure, CD || AB. Find the value of y.
Solution
In ΔABC,
A +
B +
ACB = 180° (Angle sum property)
2x + 3x + 4x = 180°
9x = 180°
x = 20°
AB || CD and AC is transversal.
A =
ACD (Alternate interior angles)
∴
ACD = 2x = 2 × 20° = 40°
Now,
ACB +
ACD + y = 180° (Linear pair)
4x + 40° + y = 180°
80° + 40° + y = 180°
y = 180° - 120° = 60°
Question 17 1.2 / -0
In the given figure, if
A = 2
B and
ACD = 2
DCB, then find the measure of
DCB +
B.
Solution
Let
B = x and
DCB = y.
Then,
A = 2x and
ACD = 2y
In ΔCAB,
CAB +
ABC +
BCA = 180° [Angle sum property]
2x + x + 3y = 180°
3x + 3y = 180°
y + x = 60°
Hence,
DCB +
B = y + x = 60°
Question 18 1.2 / -0
In the given figure (not drawn to scale), ABC is a triangle and BC = BD. Find the value of y.
Solution
In ΔADB,
DAB +
ABD +
BDA = 180° (Angle sum property)
28° + 48° +
BDA = 180°
BDA = 180° - 28° - 48° = 104°
BC = BD
So,
BDC =
BCD = y (Angles opposite to equal sides are equal)
Now,
BDA +
BDC = 180° (Linear pair)
104° + y = 180°
y = 180° - 104° = 76°
Question 19 1.2 / -0
In ΔABC and ΔLMN, AB = LM and BC = MN. Which of the following conditions can make the two triangles congruent?
Solution
If two corresponding sides and one included angle are equal in two triangles, then the two triangles are congruent by SAS congruence criteria.
So,
B =
M can make the given triangles congruent.
Question 20 1.2 / -0
Evaluate:
Question 21 1.2 / -0
Which of the following options is CORRECT?
Solution
(1)
Incorrect : Two rational numbers with different denominators can be equal. Ex: 1/2 and 2/4
(2)
Incorrect : The rational number
lies towards the left of 0 on the number line.
(3)
Correct: Difference between two rational numbers is always a rational number.
(4)
Incorrect: The standard from of
is
.
Question 22 1.2 / -0
The following number line shows the temperature in degree celsius (°C) at different places (P to T) on a particular day.
What is the difference in temperature between the hottest and coldest places as shown on the number line?
Solution
Temperature of the hottest place, i.e. T = 24°C
Question 23 1.2 / -0
In which of the following cases, a triangle CANNOT be drawn?
Solution
In the case of option (2), a triangle cannot be drawn as
B = 90°,
C = 120°.
B +
C = 90° + 120° = 210° > 180°
Whereas, in the other options, the sum of the angles in triangle does not exceed 180°.
Question 24 1.2 / -0
Find the mean of the first 7 odd natural numbers.
Solution
First 7 odd natural numbers are 1, 3, 5, 7, 9, 11 and 13.
Sum = 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49
∴ Mean =
= 7
Question 25 1.2 / -0
In the given magic square, if each row, column and diagonal has the same sum, then the values of A and B respectively are ______.
Solution
We have, 1 + (-10) + 0 = -9
∴ 1 + A + (-6) = -9
A - 5 = -9
A = -9 + 5 = -4
Also, 1 + (-3) + B = -9
B - 2 = -9
B = -9 + 2 = -7
Question 26 1.2 / -0
What fraction of the given square is shaded?
Solution
Total number of equal parts = 18 × 4 = 72
Number of shaded parts = 7 + 7 + 10 + 9 = 33
∴ Required fraction =
Question 27 1.2 / -0
Solve for x:
Solution
We have,
(x - 4)(x + 4) = 54 + (x - 5)(x - 10)
x
2 + 4x - 4x - 16 = 54 + x
2 - 10x - 5x + 50
x
2 - x
2 - 16 - 54 - 50 = -15x
-120 = -15x
x =
= 8
Question 28 1.2 / -0
What is the order of rotational symmetry of the given figure?
Solution
If we rotate the given hexagon by 60° about a fixed point, it will look exactly the same.
So, order of rotational symmetry =
= 6
Question 29 1.2 / -0
A bag contains 5 blue gems, 8 red gems and 2 green gems. A gem is drawn at random. What is the probability of getting a blue gem?
Solution
Total number of gems = 5 + 8 + 2 = 15
So,
Probability of getting a blue gem =
Question 30 1.2 / -0
Find the area of the shaded portion of the given figure (not drawn to scale).
Solution
Area of rectangle ABCD = 18 × 10 = 180 cm
2 Area of ΔAFE =
× 6 × 10 = 30 cm
2 Area of ΔBCE =
× 8 × 10 = 40 cm
2 ∴ Area of shaded portion = Area of rectangle ABCD - (Area of ΔAFE + Area of ΔBCE)
= 180 - (30 + 40) = 180 - 70 = 110 cm
2
Question 31 1.2 / -0
If 30 shirts were bought for Rs. 9000 and out of those only 10 shirts were sold for Rs. 3500, find the profit/loss percent in transaction of 10 shirts.
Solution
C.P. of 30 shirts = Rs. 9000
C.P. of 1 shirt = Rs.
= Rs. 300
C.P. of 10 shirts = Rs. (300 × 10) = Rs. 3000
S.P. of 10 shirts = Rs. 3500
As C.P. < S.P, profit occurs.
Thus,
Profit = S.P. – C.P. = 3500 – 3000 = Rs. 500
∴ Profit% =
=
Question 32 1.2 / -0
Find the additive inverse of the number obtained by subtracting -9 from the additive inverse of -23.
Solution
Additive inverse of -23 = 23
Question 33 1.2 / -0
How many more unit squares in the figure must be shaded so that the fraction of shaded squares becomes
?
Solution
Total number of unit squares = 18
Let total number of shaded squares be x.
According to question,
Out of these 14 squares, 6 are shaded. So, we have to shade 8 more squares.
Question 34 1.2 / -0
Find the value of the resultant expression when xy + 2xy2 + x2 is added to y2 + 2x2 y + xy, for x = 1 and y = -1.
Solution
(xy + 2xy2 + x2 ) + (y2 + 2x2 y + xy)2 + y2 + 2xy2 + 2x2 y + 2xy2 + (-1)2 + 2(1)(-1)2 + 2(1)2 (-1) + 2(1)(-1)
Question 35 1.2 / -0
If
, then the value of
is ______.
Question 36 1.2 / -0
The teacher tells the class that the highest marks obtained by a student in her class are four times the lowest marks plus 6. The highest marks are 65. Form the equation which will calculate the lowest marks represented by m.
Solution
Four times the lowest marks = 4m
Question 37 1.2 / -0
Sushma sold an article at a loss of 12%. If she had sold it for Rs. 50.80 more, then she would have earned a profit of 8%. Find the cost price of the article.
Solution
Let the C.P. of the article be Rs. x.
According to question,
S.P. on 8% profit - S.P. on 12% loss = Rs. 50.80
= Rs. 50.80
108x - 88x = 5080
x =
= 254
∴ C.P. of the article = Rs. 254
Question 38 1.2 / -0
Divya wants to fence the rectangular garden in front of her house. The dimensions of the garden are 15 m and 25 m. Find the cost of fencing the garden at the rate of Rs. 12.25 per metre.
Solution
Length of rectangular garden = 25 m
Question 39 1.2 / -0
Sonali invests money in three different schemes for 6 years, 10 years and 12 years at 10% p.a. 12% p.a. and 15% p.a. at simple interest, respectively. At the completion of each scheme, she gets the same interest.
Solution
Let the amounts invested at 10%, 12% and 15% p.a. be x, y and z, respectively.
Now, according to question,
x = 2y = 3z
x = 2y and z =
y
∴ Required ratio is x : y : z = 2y : y :
y = 6 : 3 : 2
Question 40 1.2 / -0
Sahil is 15 years older than his nephew. Three years hence, his age will be twice the age of his nephew. Find the present age of Sahil's nephew.
Solution
Let the present age of Sahil's nephew be x years.
∴ Present age of Sahil = (x + 15) years
After three years,
Age of Sahil's nephew = (x + 3) years
And,
Age of Sahil = (x + 15 + 3) years
= (x + 18) years
According to question,
x + 18 = 2(x + 3)
x + 18 = 2x + 6
x = 12
∴ Present age of Sahil's nephew = 12 years
Question 41 1.2 / -0
A company's production department produces 6250 items in a day. After 30 days of regular work, these items are equally distributed to 50 dealers in different states. The number of items that each dealer gets is ____________.
Solution
Number of items produced in one day = 6250
Question 42 1.2 / -0
Mr. Sharma earns Rs. 64,000 per month. He gives
of his salary to his son,
of the remaining to his daughter and the rest to his wife. Find the share of his wife.
Solution
Amount of money that Mr Sharma earns in a month = Rs. 64,000
According to question,
Amount that he gives to his son =
× 64,000 = Rs. 25,600
Amount left with Mr Sharma = Rs. (64,000 - 25,600) = Rs. 38,400
Amount that he gives to his daughter =
× 38,400 = Rs. 24,000
So, the amount that he gives to his wife = Rs. (38,400 - 24,000) = Rs. 14,400
Question 43 1.2 / -0
A 120 m long ladder can reach a window 72 m from the ground on being placed against a wall. Find the distance of the foot of the ladder from the wall.
Solution
Let AB be the height of the window from the ground, AC be the length of the ladder and C be the foot of the ladder.
In right-angled triangle ABC,
AC
2 = AB
2 + BC
2 (120)
2 = (72)
2 + BC
2 BC
2 = 14,400 - 5184 = 9216
BC = 96 m
Hence, the distance of the foot of the ladder from the wall is 96 m.
Question 44 1.2 / -0
If 24 pairs of trousers of same size can be prepared with 66 m of cloth, then the length of cloth required for each pair of trousers is _____.
Solution
Length of cloth required to prepare 24 pairs of trousers = 66 m
Length of cloth required to prepare 1 pair of trousers =
= 2.75 m = 275 cm
Question 45 1.2 / -0
There are three places, i.e. A, B, and C in a straight line, as shown below. If the distance between places A and B is (2.4 × 10
6 ) m and the distance between places B and C is (5.2 × 10
5 ) m, then find the distance between places A and C in the standard form.
Solution
Distance between places A and B6 ) m = 24,00,000 m5 ) m6 + 5.2 × 105 ) m = (24,00,000 + 5,20,000) m4 ) m 4 ) m = (2.92 × 106 ) m
Question 46 1.2 / -0
There are 40 marbles in a box, which are numbered from 1 to 40. If a marble is drawn at random, then find the probability that the number on the marble drawn is:
Solution
(i) 5, 10, 15, 20, 25, 30, 35 and 40 are the multiples of 5.
So, number of favorable outcomes = 8
∴ Required probability =
(ii) 1, 2, 4, 5, 8, 10, 20 and 40 are the factors of 40.
So, number of favorable outcomes = 8
∴ Required probability =
Question 47 1.2 / -0
Study the following statements carefully and select the correct option.Statement-I: A hall is 36 m long and 24 m broad. If, allowing area of 40 m2 for doors and windows, the cost of papering the walls at Rs. 8.40 per square metre is Rs. 4704, then the height of the hall is 5 m.Statement-II: If the difference between the circumference and diameter of a circle is 154 cm, then the radius of the circle is 30.93 cm.
Solution
Statement-I: Cost of papering the wall = Rs. 4704
Rate of papering the walls = Rs. 8.40 per m
2 Papering area =
m
2 = 560 m
2 Area of doors and windows = 40 m
2 Total area of 4 walls = (560 + 40) m
2 = 600 m
2 Length of the hall = 36 m
Breadth of the hall = 24 m
Let the height of the hall be h m.
Then,
Area of 4 walls = {2(Length × Height) + 2(Breadth × Height)}
= 2(36 × h) + 2(24 × h) = 72h + 48h = (120h) m
2 ∴ 120h = 600
h =
= 5
Hence, the height of the hall is 5 m.
So, Statement-I is true.
Statement-II: Let 'r' be the radius of the circle.
According to question,
2
r - 2r = 154
2r
= 154
2r ×
= 154
r =
= 35.93 cm
So, Statement-II is false.
Question 48 1.2 / -0
State 'T' for true and 'F' for false and select the correct option.
(i) Every natural number is a rational number.
(ii) Every rational number is a fraction.
(iii) Zero is not a rational number.
(iv) The reciprocal of 0 is
.
Solution
(i) "Every natural number is a rational number." This is a
true statement as every natural number N can be written in the form of N/1, which is a rational number.
(ii) "Every rational number is a fraction." This is a
false statement. Every fraction is a rational number but vice-versa is not true.
(iii) "Zero is not a rational number." This is a
false statement. Zero is a rational number as it can be written in the form of 'p/q', where p and q are integers and q ≠ 0.
(iv) "The reciprocal of 0 is
." This is a
false statement. Zero does not have a reciprocal as 0 divided by 1 is undefined.
Question 49 1.2 / -0
The given double bar graph shows the sale of mobile phones and cars from 2005 to 2008.
(i) Find the ratio of the total number of mobile phones sold in 2006 and 2008 to the total number of cars sold in 2005 and 2007.
(ii) What is the average number of cars sold from 2005 to 2008?
Solution
(i) Number of mobile phones sold in 2006 and 2008 together = 40,000 + 40,000 = 80,000
Number of cars sold in 2005 and 2007 together = 80,000 + 50,000 = 1,30,000
∴ Required ratio =
, i.e. 8 : 13
(ii) Number of cars sold in 2005 = 80,000
Number of cars sold in 2006 = 70,000
Number of cars sold in 2007 = 50,000
Number of cars sold in 2008 = 90,000
∴ Required average =
=
= 72,500
Question 50 1.2 / -0
Arrange the following steps in the correct order, while constructing a triangle ABC (given AB = 6 cm, BC = 8 cm and
ABC = 60°).
Step-1: With B as a centre, draw an arc of radius 6 cm, which cuts BX at the point A.
Step-2: At B, draw a ray BX, making an angle of 60° with BC.
Step-3: Join AC,
ABC is the required triangle.
Step-4: Draw a line segment BC of length 8 cm.
Solution
The correct order of constructing the triangle is: 4, 2, 1, 3
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