Question 1 1.2 / -0
Select a Venn diagram from the options which best illustrates the relationship among ''Metal, Copper, Wood''.
Question 2 1.2 / -0
If '-' denotes '
', '+' denotes 'x', '
' denotes '-' and 'x' denotes '+', then what is the value of 43 × 7
5 + 8 - 4?
Solution
After changing the symbols, the given expression becomes:
43 + 7 - 5 × 8
4
= 43 + 7 - 5 × 2 = 43 + 7 - 10 = 40
Question 3 1.2 / -0
In a certain code language, 'Take Bath And Do Worship Of The Goddess' is coded as 'And Bath Do Goddess Of Take The Worship'. How will 'Then Why Did You Not Do Your Study' be coded using that language?
Solution
'Take Bath And Do Worship Of The Goddess' is coded as 'And Bath Do Goddess Of Take The Worship'.
Question 4 1.2 / -0
Which of the following is true about a triangular prism?
Solution
A triangular prism has 6 vertices and 5 faces, out of which 2 are triangular faces and 3 are rectangular faces.
Question 5 1.2 / -0
Select a figure from the options which will complete the pattern given in Fig. (X).
Question 6 1.2 / -0
Select a figure from the options which shows the correct mirror image of Fig. (X), if the mirror is placed vertically to the right.
Question 7 1.2 / -0
There is a certain relationship between the numbers on either sides of ::. Establish the same relationship in the other pair and find the missing number.
Solution
The pattern is,
5
2 : (5 + 1)
3 So, 4
2 : (4 + 1)
3 16 : 125
Question 8 1.2 / -0
If the following words are arranged in the alphabetical order, then which word will appear at the end?
Solution
The alphabetical order is:
Amassment, Amperes, Amplify,
Question 9 1.2 / -0
Ajay wants to go to the Management Institute. He starts from home, which is towards the east of a crossing. He walks towards the crossing. The road to the left ends in a school, straight ahead is a community hall. The road to the right leads to the Management Institute.
Solution
Management Institute is to the north of the crossing.
Question 10 1.2 / -0
Some children, A, B, C, D, E, F, and G, are standing in a line facing north. G is to the right of D and to the left of B. A is on the right of C. A and D have one child between them. E and B have two children between them. D and F have two children between them.
Solution
According to question, the correct arrangement is:
So, D is exactly in the middle.
Question 11 1.2 / -0
Select a figure from the options in which Fig. (X) is exactly embedded as one of its parts.
Question 12 1.2 / -0
Two different positions of a die has been shown below. If 1 is at the top, then what number will be at the bottom?
Solution
Numbers on the opposite faces are (1, 6); (2, 5); (3, 4).
So, 6 will be at the bottom, if 1 is at the top.
Question 13 1.2 / -0
Pointing towards a man in a photograph, Rohit said, ''His sister is the mother of Anuj, the son of my brother''. How is Rohit related to Anuj?
Solution
The son of Rohit's brother is Rohit's nephew. So, Rohit is the uncle of Anuj.
Question 14 1.2 / -0
If in the word 'ELECTROCARDIOGRAPH', the first half of the letters is reversed, second letter from the left end is then prefixed and finally 'S' is suffixed, then find the letter exactly in the middle.
Solution
The new word formed is,
CAORTCELE
DIOGRAPHS
So, the middle letter between C and S is R.
Question 15 1.2 / -0
Study the given Venn diagram carefully and answer the following question.
Which region represents the persons who know both Telugu and Hindi but not English?
Solution
The number common to circle and triangle but not in rectangle is 3. So, 3 represents the persons who knows both Telugu and Hindi but not English.
Question 16 1.2 / -0
Which of the following statements is CORRECT?
Solution
A. Incorrect; For every rational number x, y and z,
x + (y
z) = x + yz
(x + y)
(x + z)
B. Correct; 0 can be written as, where
= 0, where a = 0 and b is any non-zero integer. So, zero is a rational number.
C. Incorrect; The rational number
lies to the right of the zero on the number line.
D. Incorrect; Addition and multiplication of rational numbers is commutative. But, subtraction and division is not.
Question 17 1.2 / -0
In the given figure, P is a point in the interior of
AOB. PM
OB and PN
OA. If
NOM = 60°, what is the measure of
NPM?
Solution
In the quadrilateral NOMP,
(Angle sum property)
60° + 90° +
+ 90° = 360°
= 360° - 240° = 120°
Question 18 1.2 / -0
Which of the following statements is CORRECT?
Solution
Statement in option C is correct, i.e. "A unique quadrilateral can be constructed if its three sides and two included angles are given".
Question 19 1.2 / -0
Directions For Questions
Directions:
...view full instructions
In which school is the number of players participating in Hockey and Basketball together the second highest?
Solution
Number of players participating in Hockey & Basketball together in School-1 = 68 + 42 = 110
Question 20 1.2 / -0
Directions For Questions
Directions:
...view full instructions
What is the total number of players participating in Tennis from all the five schools together?
Solution
Total number of players participating in Tennis from all the five schools together
Question 21 1.2 / -0
Find x:0.2 × 64 × 81.3 × 40.2 = (8)x
Solution
We have,
2
0.2 × 64 × 8
1.3 × 4
0.2 = (8)
x 2
0.2 × 2
6 × (2
3 )
1.3 × (2
2 )
0.2 = (2
3 )
x 2
(0.2 + 6 + 3.9 + 0.4) = 2
3x 10.5 = 3x
x = 3.5
Question 22 1.2 / -0
In the figure, ABCD is a square of sides 28 cm. Find the area of the shaded region if the radius of the circle is
cm.
Solution
Sides of square = 28 cm
Area of square = (28)
2 = 784 cm
2 Also, radius of circle, (r) =
cm
Area of circle =
=
= 1232 cm
2 Hence,
Area of shaded region
= Area of circle - Area of square
= (1232 - 784) cm
2 = 448 cm
2
Question 23 1.2 / -0
If r
2 +
= 7, then evaluate r +
.
Question 24 1.2 / -0
Find the value of
.
Solution
We have,
=
= [35.7 - (3 + 0.3) - (2 + 0.4)]
= [35.7 - 3.3 - 2.4]
= 35.7 - 5.7 = 30
Question 25 1.2 / -0
If the length and breadth of a rectangle are respectively increased and decreased by 20% and 10%, then what is the change in area of the rectangle?
Solution
Let the original length and breadth of the rectangle be l and b.
Area = I × b = lb
Now, after the given changes,
New length =
New breadth =
New area =
So, increase in area =
=
Question 26 1.2 / -0
Given below are the steps of construction of a quadrilateral ABCD, where AB = 3.5 cm and BC = 6.5 cm.
A = 75°,
B = 105° and
C = 120°. Which of the following steps is INCORRECT?
Step 1: Draw AB = 3.5 cm.
Step 2: Draw
XAB = 75° at A and
ABY = 105° at B.
Step 3: With B as centre and radius BC = 6.5 cm, draw an arc to intersect BY at C.
Step 4: At C, draw
ADC = 120° such that CZ meets AX at D.
Solution
Only step 4 is incorrect. The correct step is:
At C, draw
BCZ = 120° such that CZ meets AX at D.
Question 27 1.2 / -0
Which of the following is the top view of the given figure?
Solution
The top view of the given figure is:
Question 28 1.2 / -0
The given table shows the cost price of various items purchased from a showroom.
Items Cost (in Rs.) Shirt 1250 Trouser 1550 2 T-shirts 2200
What will these items cost, if the GST is 12%?
Solution
Cost of all the items = Rs. (1250 + 1550 + 2200)
= Rs. 5000
GST = 12%
So, total cost of all the items = Rs. (5000 + 12% of 5000)
= Rs.
= Rs. (5000 + 600) = Rs. 5600
Question 29 1.2 / -0
The given pie chart shows the marks scored by a student in an examination in 5 different subjects.
If the total marks obtained by the students were 1080, then find the marks obtained by them in Mathematics and Hindi together.
Solution
Total marks obtained = 1080
Marks obtained in Mathematics =
= 270
Marks obtained in Hindi =
= 210
So,
Marks obtained in Mathematics and Hindi together
= 270 + 210 = 480
Question 30 1.2 / -0
The given bar graph represents sales of two wheelers and four wheelers in a city from 2008 to 2011.
Difference between the number of vehicles (two wheelers and four wheelers) sold from 2008 to 2011 is:
Solution
Total number of two wheelers sold = (5.7 + 6.3 + 9.1 + 10) × 500 = 31.1 × 500 = 15,550
Question 31 1.2 / -0
Find the values of A and B respectively.
Solution
We have,
So, A = 5 and B = 6
Question 32 1.2 / -0
Six more than four times a number is four less than five times the number. Find the number.
Solution
Let the number be x.
According to the question,
4x + 6 = 5x - 4
x = 10
∴ Required number = 10
Question 33 1.2 / -0
In the given figure, MS is the internal bisector of
S. Find the value of x + y - z.
Solution
y =
QPR +
PQR [Exterior angle property]
= 35° + 70° = 105°
Now,
z = y +
MSR [Exterior angle property]
z = 105° + 25° = 130°
Now, MS is the bisector of
S.
∴
NSM =
RSM = 25°
Also, x = z +
NSM [Exterior angle property]
x = 130° + 25° = 155°
∴ x + y – z = 155° + 105° – 130° = 130°
Question 34 1.2 / -0
If
, then find the value of x
4 +
.
Question 35 1.2 / -0
Find the total area of the shaded region in the given figure.
Solution
AB = 1 m = 100 cm
Shaded area = Area of
ADE + Area of
BCF
=
× AD × GE +
× BC × FH
=
× 50 × GE +
× 50 × FH
= 25 × GE + 25 × FH
= 25 × [GE + FH]
=25 × [GH - EF]
= 25 × (100 - 50) cm
2 = (25 × 50) cm
2 = 1250 cm
2
Question 36 1.2 / -0
The value of a machine increases every year at the rate of 10% on its value at the beginning of that year. If the present value of the machine is Rs. 729, then its worth 3 years ago was ______.
Solution
Let the value of machine 3 years ago be Rs. x.
∴ Value of machine 2 years ago = Rs. (x + 10% of x)
= Rs.
Value of machine 1 year ago = Rs.
= Rs.
Value of machine at present = Rs.
= Rs. 729 (Given)
x =
= 547.70
Hence, value of machine 3 years ago = Rs. 547.70
Question 37 1.2 / -0
A trader lists his articles 20% above C.P. and allows a discount of 10% on cash payment. What is his gain percent?
Solution
Let the C.P. be Rs. x.
Now, marked price = Rs. (x + 20% of x)
= Rs.
Discount = 10% of Rs.
∴ S.P. = Rs.
Gain = S.P. - C.P. = Rs.
∴ Gain % =
= 8%
Question 38 1.2 / -0
A car worth Rs. 1,50,000 is sold by Rajat to Vihan at 5% profit. Vihan sells the car back to Rajat at 2% loss.
Solution
Money spent by Rajat = Rs. 1,50,000
Money received by Rajat is 105% of 1,50,000
=
= Rs. 1,57,500
C.P. to Rajat = 98% of 1,57,500 =
= Rs. 1,54,350
∴ Rajat gains Rs. (1,57,500 - 1,54,350) = Rs. 3,150
Question 39 1.2 / -0
The length of a rectangular plot is 10 metres more than its breadth. If the cost of fencing the plot at Rs. 13.25 per metre is Rs. 5,300, then find the length of the plot.
Solution
Let the breadth of the plot be 'x' m.
So, the length of the plot = (x + 10) m
∴ Perimeter of the plot = 2(l + b) = 2[(x + 10) + x]
= 2 [2x + 10] m
According to question, 13.25 × 2(2x + 10) = 5,300
13.25 × 4(x + 5) = 5,300
x + 5 =
x + 5 = 100
x = 95
So, length of the plot = 95 + 10 = 105 m
Question 40 1.2 / -0
The greatest possible length which can be used to exactly measure the lengths 7 m, 3 m 85 cm, and 12 m 95 cm is _____.
Solution
Given lengths are 7 m, 3 m 85 cm and 12 m 95 cm, i.e. 700 cm, 385 cm, and 1295 cm.
Question 41 1.2 / -0
A P.T. teacher asks 20,736 students to stand in such a way that there are as many rows as there are students in each row. Find the number of rows.
Solution
Let the number of rows be x.
∴ Number of students in each row = x
Total number of students = 20,736
∴ x × x = 20,736
x
2 = 20,736
x = 144
∴ Number of rows = 144
Question 42 1.2 / -0
A can do a piece of work in 8 days, B can do it in 16 days, and C can do it in 80 days. In how many days can they complete the whole work working together?
Solution
A's 1 day work =
B's 1 day work =
C's 1 day work =
∴ (A + B + C)'s 1 day work =
=
∴ Required number of days = 5
Question 43 1.2 / -0
Pluto is 5913000000 km away from the Sun. Express this distance (in km) in the standard form.
Solution
Distance of Pluto from the Sun6 km9 km
Question 44 1.2 / -0
The ratio of a man's age to his son's age is 4 : 1. The product of their ages is 196. What will be the ratio of their ages after 5 years?
Solution
Let the age of the man and his son be 4x years and x years, respectively.
According to question,
(4x)(x) = 196
4x
2 = 196
x
2 = 49
x = 7
So, ratio of their ages after 5 years =
, i.e. 11 : 4
Question 45 1.2 / -0
Ashima has three cylindrical containers.
(i) P having radius 2r and height h
(ii) Q having radius 3r and height 2h
(iii) R having radius 3r and height
Arrange the volume of containers in decreasing order.
Solution
The volume cylinder = πr2 h, ∴ (Radius = r, height = h)2 x h = 4πr2 h2 × 2h = 18πr2 h2 × (h/3) = 3πr2 h
Question 46 1.2 / -0
Which of the following statements shows inverse proportions?
Solution
(A) Inverse Proportion:
Number of workers and time taken to complete the work is inverse proportion.
(B) Direct Proportion:
(C) Direct Proportion: More is the use of electricity, more is the electricity bill.
Question 47 1.2 / -0
Fill in the blanks:P __ is an equality, which is true for all values of the variables in the equality. An ___Q ___ is not an identity. __R __ are formed from variables and constants.
Solution
Identities and equations are equalities with two sides, where the equal sign separates the mathematical expressions of the LHS and RHS.
Question 48 1.2 / -0
Select the INCORRECT match.
Faces Edges Vertices A. Triangular Prism 5 9 6 B. Triangular Pyramid 4 6 4 C. Square Prism 6 12 8 D. Square Pyramid 5 5 6
Question 49 1.2 / -0
Match the following.
Column - I Column - Il (P) (x2 - 3x + 2) × (x2 + 2x + 1) (i) 3x3 - 4x2 - 12x + 8 (Q) (2x2 - 3x + 1) + (3xy - 4x2 - 2x + 5) (ii) x4 - x3 - 3x2 + x + 2 (R) (2x3 - 3x2 - 7x + 6) - (x2 - x3 + 5x - 2) (iii) 2x - 2y (S) (4x2 + 4y2 - 8xy) (iv) - 2x2 + 3xy - 5x + 6
Solution
(P) (x2 - 3x + 2) × (x2 + 2x + 1)4 + 2x3 + x2 - 3x3 - 6x2 - 3x + 2x2 + 4x + 24 - x3 - 3x2 + x + 22 - 3x + 1) + (3xy - 4x2 - 2x + 5)2 - 5x + 6 3 - 3x2 - 7x + 6) - (x2 - x3 + 5x - 2)3 - 3x2 - 7x + 6 - x2 + x3 - 5x + 23 - 4x2 - 12x + 82 + 4y2 - 8xy) ÷ (2x - 2y)2 ÷ (2x - 2y) = 2x - 2y
Question 50 1.2 / -0
Which of the following steps is INCORRECT while constructing a quadrilateral KITE, given that KI = 9 cm, IT = 6 cm, KE = 5 cm, diagonal KT = 14 cm and diagonal IE = 6 cm?
Solution
Steps 3 and step 4 are wrong. The correct steps are as follows:
Step 3 : Join KE and IE. With K and I as centres and 14 cm and 6 cm as radii, respectively, draw arcs to cut each other at T.
Step 4 : Join KT and TI. Join TE also.
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