Question 1 1.2 / -0
Select the correct water image of the given figure.
Question 2 1.2 / -0
The question consists of a set of three figures P, Q and R showing a sequence of folding a piece of paper. Figure (R) shows the manner in which the folded paper has been cut. Select the figure from the options which would most closely resemble the unfolded form of figure (R).
Question 3 1.2 / -0
Select a letter which replaces the question mark (?), if the same rule is followed either row-wise or column-wise.
Solution
The rule followed is:
Question 4 1.2 / -0
In a certain code language, the word CONFUSED is written as EMNBEFTV. How will the word SECLUDED be written in that language?
Solution
Firstly, the letters in the first half and the second half of the given word are written in the reverse order.
We get
Similarly,
Question 5 1.2 / -0
lf 'P + Q' means 'P is the mother of Q', 'P
Q' means 'P is the brother of Q', 'P # Q' means 'P is the father of Q' and 'P * Q' means 'P is the sister of Q', then how is L related to O in 'K
L + M # N * O'?
Solution
'K
L + M # N * O' means K is the brother of L, who is the mother of M. Also, M is the father of N, who is the sister of O. So, L is the grandmother of O.
Question 6 1.2 / -0
Which of the following Venn diagrams best represents the relationship among Women, Boys and Students?
Solution
Some women can be students and some boys can be students, so we get the following Venn diagram:
Question 7 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 '?' in figure (iv).
Solution
From figure (i) to figure (ii), the figure rotates 90° anticlockwise and the shaded circle becomes unshaded and vice versa. Also, the middle line flips vertically to the opposite side and then the triangle attached to it gets vertically flipped.
Question 8 1.2 / -0
Directions : 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 on numbers progress from left to right.
Rules: (i) If a 2-digit even number is followed by another even number, then the first one is to be divided by the second one.
(ii) If an even number is followed by a prime number, then the two are to be multiplied.
(iii) If an odd number is followed by another odd number, then the two are to be added.
(iv) If a 3-digit number is followed by a 2-digit number which is a perfect square, then the second number is to be subtracted from the first number.
(v) If a 3-digit number is followed by another 3-digit number which is not a perfect square, then the first number is to be divided by the second one.
If m is the resultant of the first row, then what will be the resultant of the second row?
Solution
First row: 150 81 43
Question 9 1.2 / -0
Select a figure from the options which is exactly embedded in Fig. (X) as one of its parts.
Solution
Option (3) is the correct answer.
Question 10 1.2 / -0
Three figures (X), (Y) and (Z) show a sequence of folding of a sheet of paper. Figure (Z) shows the manner in which the folded paper has been cut. Select a figure from the options which represents the unfolded form of figure (Z).
Solution
Hence, option (1) is the correct answer.
Question 11 1.2 / -0
Sonali walks 20 m North. Then she turns right and walks 30 m. Then she again turns right and walks 35 m. In which direction and how many metres away is she from her original position?
Solution
AE
2 = DE
2 + AD
2 AE
2 = (35 - 20)
2 + (30)
2 AE
2 = (15)
2 + (30)
2 AE =
So, she is 15
m away and in the South-East direction from the original position.
Question 12 1.2 / -0
If the interchange of signs '×' and '-' is made in each of the following options, then which of the following is correct?
Solution
After interchanging the signs, we get
Question 13 1.2 / -0
Find the minimum number of straight lines required to make the given figure.
Solution
Number of red lines = 5
Number of blue lines = 1
Number of yellow lines = 14
The minimum number of straight lines required to make the given figure is 20.
Question 14 1.2 / -0
Directions:
Solution
A is the immediate neighbour of B and C. We gets two cases:
G, who is second to the left of D, is the immediate neighbour of E and F. D is not the immediate neighbour of C and E.
Hence, Case-2 is not valid and we get the final arrangement as shown below:
Hence, C is second to the right of B.
Question 15 1.2 / -0
Select a figure from the options which satisfies the same conditions of placement of the dots as in Fig. (X).
Solution
According to the figure given in the question, we can conclude that :
(1) One dot is common between circle and square.
(2) One dot is common between triangle and square.
(3) One dot is only in square.
By using the above conclusions we get option (3) is the correct answer.
Question 16 1.2 / -0
In the given figure, line RT is drawn parallel to SQ. If
QPS = 100°,
PQS = 40°,
PSR = 85° and
QRS = 70°, then
QRT = _______.
Solution
In △PQS, we have,
100° + 40° +
PSQ = 180° (Angle sum property)
PSQ = 40°
Also,
PSR = 85° (Given)
PSQ +
QSR = 85°
QSR = 85° - 40° = 45°
In
SQR, we have,
45° + 70° +
SQR = 180° (Angle sum property)
SQR = 180° - 115° = 65°
Now, PT || SQ and QR is a transversal.
QRT =
SQR = 65°.
Question 17 1.2 / -0
If a number 54x49y is divisible by 90, then what is the value of
?
Solution
Since a number is divisible by 90, it is divisible by both 9 and 10.
So, 54x49y is divisible by 10, if and only if y = 0
Now, 54x490 is divisible by 9, if sum of its digits is divisible by 9.
i.e., 5 + 4 + x + 4 + 9 + 0 is divisible by 9
22 + x is divisible by 9
x = 5
Hence,
= 0
Question 18 1.2 / -0
Which of the following is equal to 25?
Question 19 1.2 / -0
If 540 is 10% of y and z% of y is 16,200, then find the value of y and z respectively.
Solution
We have, 540 = 10% of y
y = 5400
Also, z% of y = 16,200
= 16,200
z = 300
Question 20 1.2 / -0
In a rectangle, if the difference between the sum of adjacent sides and the diagonal is one-fourth the length of longer side, then 7 times the length of longer side is ______ times the length of shorter side.
Solution
Let l and b be the length and breadth of the rectangle.
By Pythagoras theorem,
AC =
According to question,
(l + b) -
On squaring both sides, we get,
So, 7 times the length of longer side is 24 times the length of shorter side.
Question 21 1.2 / -0
Which of the following statements is/are incorrect?
Solution
Statement 1: The length of a side of a square and its area do not vary directly with each other. For example, let 'a' be the length of each side of a square. So, area of the square = Side = a
2 So, if we increase the length of the side of a square, then its area increases but not directly. Hence, this statement is false.
Statement 2: If one angle of a triangle is kept fixed, then the measures of the remaining two angles can't vary inversely with each other.
E.g. In ΔABC,
= 180°[Sum of all angles of a triangle is 180°]
If
= 50°, then
= 180° - 50° = 130°
So, it is not dependent on any proportion by applying angle sum properties of a triangle.
Hence, this statement is false.
Statement 3: The area of a circle and its diameter vary directly with each other.
Area of a circle = π(d/2)
2 So, The area of a circle vary directly with the square of the radius.
Hence, all of the given statements are incorrect.
Question 22 1.2 / -0
Find the smallest whole number that must be subtracted from 899 to make it a perfect cube.
Solution
Since 93 = 729 and 103 = 1000
Question 23 1.2 / -0
The numerator and the denominator of a rational number are in the ratio 5 : 7. When 6 is added to both the numerator and denominator, the ratio becomes 4 : 5. What is the rational number?
Solution
Let numerator and denominator be 5x and 7x respectively.
According to question,
25x + 30 = 28x + 24
3x = 6
x = 2
∴ Required rational number =
Question 24 1.2 / -0
Factorise: 25(x + y)2 - 36(x - 2y)2
Solution
25(x + y)2 - 36(x - 2y)2 2 + 25y2 + 50xy - 36x2 - 144y2 + 144xy2 + 194xy - 119y2 2 + 187xy + 7xy - 119y2
Question 25 1.2 / -0
To construct a unique parallelogram, the minimum number of measurements required is ________.
Solution
To construct a parallelogram uniquely, we require the measure of any two non-parallel sides and the measure of an angle. Hence, the minimum number of measurements required to draw a unique parallelogram is 3.
Question 26 1.2 / -0
Which of the following rational numbers does not lie between
and
?
Solution
We have,
L.C.M. of 4, 3 = 12
Rational numbers between
and
,
,
,
So,
does not lie between
.
Question 27 1.2 / -0
Simplify:
Solution
We have,
Question 28 1.2 / -0
The difference between compound interest and simple interest on a sum for 2 years at 8% p.a. is Rs. 768. Find the sum.
Solution
Let P be the principal.
According to question, C.I. - S.I. = Rs. 768
64P = 76,80,000
∴ P = 1,20,000
Question 29 1.2 / -0
Which of the following equations have x = 12, as its solution?
Question 30 1.2 / -0
Directions For Questions
Directions:
...view full instructions
How much more does the family spend on clothing than on savings?
Solution
Let the total expenditure be Rs. x.
Amount spent on miscellaneous items = Rs. 520
Angle for miscellaneous items = 104°
x = 1800
Now, amount spent on clothing =
= Rs. 725
Savings amount =
= Rs. 210
Required difference = Rs. (725 - 210) = Rs. 515
Question 31 1.2 / -0
Directions For Questions
Directions:
...view full instructions
How much does the family spend on rent, food and clothing in a year, if the expenditure is same throughout the year?
Solution
Let the total expenditure be Rs. x.
Amount spent on miscellaneous items = Rs. 520
Angle for miscellaneous items = 104°
x = 1800
The amount spent on rent =
× 1800 = Rs. 195
The amount spent on food =
× 1800 = Rs. 150
The amount spent on clothing = Rs. 725
Amount spent on rent, food and clothing in a month = Rs. (195 + 150 + 725) = Rs. 1070
Amount spent on rent, food and clothing in a year = Rs. (1070 × 12) = Rs. 12,840
Question 32 1.2 / -0
If (a
2 + b
2 )
3 = (a
3 + b
3 )
2 and ab
0, then
is equal to ______.
Solution
We have, (a
2 + b
2 )
3 = (a
3 + b
3 )
2 (a
2 )
3 + (b
2 )
3 + 3a
2 b
2 (a
2 + b
2 ) = (a
3 )
2 + (b
3 )
2 + 2a
3 b
3 3a
2 b
2 (a
2 + b
2 ) = 2a
3 b
3 (a
2 + b
2 ) =
ab ...(i)
Now,
(using (i))
Question 33 1.2 / -0
Using Euler's formula, find the value of P, Q and R.
Faces 8 5 Q Vertices P 6 13 Edges 12 R 30
Solution
We know that,
Faces + Vertices = Edges + 2
∴
8 + P = 12 + 2
P = 14 - 8 = 6 and 5 + 6 = R + 2
R = 11 - 2 = 9
Also, Q + 13 = 30 + 2
Q = 32 - 13 = 19
Question 34 1.2 / -0
Three cuboids of dimensions 20 cm × 30 cm × 130 cm, 50 cm × 60 cm × 70 cm and 40 cm × 70 cm × 80 cm are melted to form a cube. Find the side of the cube formed.
Solution
Let the side of the cube formed be 'a' cm.
Volume of cube formed = a
3 cm
3 So, volume of cube formed = Sum of volumes of three cuboids
a
3 = (20 × 30 × 130) + (50 × 60 × 70) + (40 × 70 × 80)
= 78,000 + 2,10,000 + 2,24,000 = 5,12,000 cm
3 a = 80 cm = 0.8 m
Question 35 1.2 / -0
Solve for x: 2 + (3x - 2)2 = (6x + 5) (3x - 2) + 12
Solution
(i) 2(x + 5) - (x - 6) = 3(x + 7) - 3
2x + 10 - x + 6 = 3x + 21 - 3
x + 16 = 3x + 18
2x = -2
x = - 1
(ii) (3x + 4)
2 + (3x - 2)
2 = (6x + 5) (3x - 2) + 12
9x
2 + 16 + 24x + 9x
2 + 4 - 12x = 18x
2 + 15x -12x - 10 + 12
18x
2 + 12x + 20 = 18x
2 + 3x + 2
9x = - 18
x = -2
Question 36 1.2 / -0
A farmer has a field in the shape of an isosceles trapezium whose perimeter is 215 m. One of its non-parallel sides is 50 m. What is the sum of its parallel sides?
Solution
Let ABCD be the field which is in the form of an isosceles trapezium.
AD = 50 m [Given]
BC = 50 m [Non-parallel sides of an isosceles trapezium are of equal length]
Perimeter of trapezium ABCD = AB + BC + CD + DA
215 = AB + CD + 50 + 50
215 = 100 + AB + CD
AB + CD = 215 - 100 = 115 m
Sum of parallel sides = 115 m
Question 37 1.2 / -0
Shalini tosses a biased coin 98 times, and head is obtained 56 times. If the coin is tossed at random, then what is the probability of getting a tail?
Solution
Total number of times the coin is tossed = 98
Number of times head obtained = 56
Number of times tail obtained = 98 - 56 = 42
Probability of getting a tail =
Question 38 1.2 / -0
A sugar factory has annual sales of 3,72,00,00,000 kg of sugar. Express this quantity in the standard form.
Solution
Quantity of sugar sold = 3,72,00,00,000 kg7 ) kg9 ) kg
Question 39 1.2 / -0
A shopkeeper fixes the marked price of a pair of shoes 45% above its cost price. What is the percentage of discount allowed to gain 16%?
Solution
Let C.P. be Rs. 100.
M.P. = 100 + 100 ×
= Rs. 145
= Rs. 116
Discount = M.P. - S.P. = (145 - 116) = Rs. 29
Discount % =
= 20%
Question 40 1.2 / -0
A group of students decided to collect as many paise from each member of the group as is the number of members. If the total collection amounts to Rs. 59.29, then the number of members in the group is ________
Solution
Let the number of members in the group be x.
Then, the amount received from each member = x paise
Now, total collection = x
2 paise
(59.29 × 100) paise = x
2 paise
5929 = x
2 x = 77
So, number of members in the group = 77
Question 41 1.2 / -0
A water pump pumps out 14
L of water per minute from a reservoir. How many litres of water will be pumped out in 1
of an hour?
Solution
Quantity of water pumped out in 1 minute =
L
As, 1
of an hour =
× 60 = 72 minutes
Quantity of water pumped out in 72 minutes
=
× 72 = 1020 L
Question 42 1.2 / -0
Present ages of Trishika and Sanchi are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Sanchi's present age?
Solution
Let present age of Trishika be 5x years and present age of Sanchi be 4x years.
Three years hence,
Age of Trishika = (5x + 3) years
Age of Sanchi = (4x + 3) years
According to question,
45x + 27 = 44x + 33
x = 6
Present age of Sanchi = 24 years
Question 43 1.2 / -0
The circumference of the base of a circular cylinder is 8
cm. The height of the cylinder is same as the diameter of the base. How much water can the cylinder hold?
Solution
Circumference = 2
r
According to question,
2
r = 8
r = 4 cm
Since the height of the cylinder = Diameter of the base
h = 2r = 8 cm
Volume of cylinder =
r
2 h
=
× 4 × 4 × 8 = 128
cm
3 =
litres = 0.128
litres
Question 44 1.2 / -0
A loan was repaid in two annual instalments of Rs. 3630 each. If the rate of interest be 10% per annum compounded annually, then find the sum that was borrowed.
Solution
For n = 1, 3630 = P
= Rs. 3300
For n = 2,
= Rs. 3000
Total sum borrowed = Rs. (3300 + 3000) = Rs. 6300
Question 45 1.2 / -0
Mr Hooda sets up a business and invests Rs. 80,000. During the first three successive years, his profits were 20%, 30% and 40% respectively. Find his total profit, if each year the profit was on previous year's capital.
Solution
Amount of money invested = Rs. 80,000
For 1
st year:
Profit = Rs.
= Rs. 16,000
So, new capital = Rs. [80,000 + 16,000] = Rs. 96,000
For II
nd year:
Profit = Rs.
= Rs. 28,800
So, new capital = Rs. [96,000 + 28,800] = Rs. 1,24,800
For III
rd year:
Profit = Rs.
= Rs. 49,920
Thus, total profit earned = Rs. [16,000 + 28,800 + 49,920]
= Rs. 94,720
Question 46 1.2 / -0
State 'T' for true and 'F' for false and select the correct option.
(i) If Sunil bought a laptop for Rs. 44,000 including a tax of 10%, then price of the laptop before the tax was added was Rs. 40,000.
(ii) x % of y is equal to y % of x.
(iii) The compound interest on Rs. 12,000 for 1
years at 10 % per annum compounded half yearly is Rs. 13,891.50.
(iv) lf a retailer sells an alarm clock for Rs. 350 and gains
of its cost price, then the cost price is Rs. 250.
Solution
(i) True; let x be the price of laptop before adding tax.
According to question,
x + 10% of x = 44,000
= 44,000
= 44,000
= Rs. 40,000
(ii) True; x % of y =
and y % of x =
(iii) False; Principal (P) = Rs. 12,000, Time (n) = 1
years,
Rate (R) = 10% compounded half yearly
= 12,000
= 12,000
= Rs. 1891.50
(iv) False; let the cost price of clock be Rs. x.
Gain = Selling price - Cost price
= Rs. 300
Question 47 1.2 / -0
Solution
(P)
In quadrilateral ABCD,
ABC +
BCD +
CDA +
DAB = 360°
90° + a + 90° + 50° = 360°
a = 360° - 230° = 130°
Also, b +
CDA = 180° (Linear pair)
b = 180° - 90° = 90°
So, a + b = 130° + 90° = 220°
(Q)
As, b + 85° = 180° (Linear pair)
b = 180° - 85° = 95°
Also,
TAB +
DAB = 180°
DAB = 180° - 50° = 130°
Also,
ADN +
ADC = 180°
ADC = 180° - 115° = 65°
In quadrilateral ABCD,
65° + 130° + 95° +
BCD = 360°
BCD = 360° - 290° = 70°
Since, a +
BCD = 180° (Linear pair)
a = 180° - 70° = 110°
So, a + b = 110° + 95° = 205°
(R) Since the given figure is a regular pentagon.
So, measure of each angle =
= 108°
a + b = 108° + 108° = 216°
(S)
Since AB = AC
ABC =
ACB = 60° (Angles opposite to equal sides are equal)
Since b +
ACB = 180° (Linear pair)
b = 180° - 60° = 120°
Also, a =
ABC +
ACB (Exterior angle property)
a = 60° + 60° = 120°
a + b = 120° + 120° = 240°
Question 48 1.2 / -0
Arrange the following steps in the correct order while constructing a trapezium PQRS in which SR II PQ, PQ = 11 cm, QR = 9 cm, PS = 9.5 cm and
Q = 70°.
Step 1: With Q as centre, draw
PQY = 70°.
Step 2: With R as centre, draw
QRZ = 110°.
Step 3: Draw PQ = 11 cm.
Step 4: With P as centre, draw an arc of radius 9.5 cm which meets RZ at point S.
Step 5: With Q as centre, draw an arc of radius 9 cm on
and mark the point as R.
Step 6: Join PS.
Solution
The correct sequence of steps is: 3, 1, 5, 2, 4, 6.
Hence we get the following diagram
Question 49 1.2 / -0
If seven slips of paper are labelled as 1, 2, 3, 4, 6, 7, 8 and one is drawn out of it, then
Solution
Numbers on slips are 1, 2, 3, 4, 6, 7, 8
Total number of slips = 7
(i) P(3) =
(ii) Numbers greater than 5 are 6, 7 and 8.
Required probability =
(iii) Even numbers are 2, 4, 6, 8.
Required probability =
Question 50 1.2 / -0
In the given figure (not drawn to scale), find the value of (b + d) - (a + c).
Solution
Draw a line UW such that SW ||RT.
Now, SR||VT and SW is a transversal.
SWV =
RSW = 90° (Alternate interior angles)
In △UVW,
a = 90° + 25° = 115° [Exterior angle property]
Now, RT||SW and TW is transversal.
d =
SWV = 90°
b =
RSW = 90°
Now, in △PQR,
b = 50° + c
90° = 50° + c
c = 40°
(b + d) - (a + c) = (90° + 90°) - (115° + 40°)
= 180° - 155° = 25°
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