1. In a \(\Delta\)ABC, the bisectors of angle ABC and angle ACB intersect each other at point O. If the angle BOC is 125\(^\circ\), then the angle BAC is equal to :
2. Simplify the given expression.
\((1 - 2x)^2\) - \((1 + 2x)^2\)
3. Find the HCF of 78, 84 , 90 and 112.
4. The height and the radius of the base of a right circular cone are in the ratio 12 : 5. If its volume is 314 \(cm^3\), then what is the slant height of the cone ? (Use \(\pi\) = 3.14)
5. Study the given bar graph carefully to answer the question that follows. Marks obtained by four students in Mid - I and Mid - II.
Marks obtain by Hemanth in Mid - I are what percentage of the total marks obtained by all the students in Mid - I ?
6. A right square pyramid having lateral surface area is 624 \(cm^2\).If length of the diagonal of the square is 24 \(\sqrt2\), then the volume of the pyramid is :
7. Find the least number which is exactly divisible by 20, 28, 34, 60 and 75.
8. A boy goes from home to school at a speed of 30 km/h and returns back at a speed of 70 km/h. What is his average speed for the journey ?
9. An item with a marked price of Rs. z was sold for Rs. 6,622, after a discount of 12 % was offered. what was the value of z?
10. The table below shows the number of laptops sold by the 4 sellers and the ratio of Brand 1 laptops sold to Brand 2 laptops sold.
The number of Brands 1 laptops sold by A seller is how many more than the number of Brand 2 laptops sold by B seller ?
11. The pie chart below show the spendings of a state on various sports during a particular year:
If the total amount spent on sports during the year was Rs. 75,00,000 then how much (in) was spent on cricket and hockey together?
12. If cos A = \(\frac12\), 0 \(\leq\) A \(\leq\) 90\(^\circ\), then what is the value of sin (180 -A) ?
13. In an election between two candidates, 20% of the voters on the voters list did not cast their votes and 80 voters cast their ballot papers blank. the winner secured 45 % of all the voters in the list and he got 280 votes more than his rival. The numbers of voters on the list was :
14. The value of \(\dfrac{1\frac12\div3\frac14+\frac12\div\frac{13}{14}+\frac15}{\frac15\times3\frac12- \frac13\div1\frac34\times3\frac12}\) is :
15. The total surface area of a solid hemisphere is 4158 \(cm^2\). Find its volume \(in\:cm^3\).
16. If interest be compounded half - yearly, then find the compound interest on Rs. 8,000 at 20% p.a. for 1 year.
17. If sin A = \(\frac23\), then find the value of (7 - tan A) (3 + cos A).
18. What is the HCF of (\(x^6 + 1\)) and (\(x^4 -1\))?
19. If 2 men or 4 women can build a wall in 34 days, in how many days can 6 men and 5 women build the same wall ?
20. The salary of Arpit fell by 5% after 1 year and further fell by 8% after the second year due to bad performance. Initially, his Salary was Rs. 80,000. What is his current salary (in Rs.)
21. Study the given table and answer the question that follows.
The table shows the number of students studying in 6 different classes of 6 different schools.
Which class has the minimum number of student from all schools together ?
22. The given pie - chart represents the survey report on favourite games of a group of young people.
If a total of 4980 people were surveyed, then what is the central angle produced by the sector indicating football ?
23. A shopkeeper increases the cost price of an item by 50% and offers a discount of 40% on this marked price. What is his loss percentage?
24. Mahesh agreed to sell rice with 24% loss, as the rice got rotten. However, he cheated customers and gave only 19 gm of rice in place of 50 gm of rice. what is the percentage of his profit or loss ?
25. The mean proportional between 0.03 and 0.0003 is :
26. Find the fourth proportional to 0.48, 0.84 and 32.
27. Which is the largest number that divides each of 1036, 1813 and 3885 without leaving any remainder ?
28. Rupu's income is 20% more than Madhu's income. Madhu's income is less than Rupu's income by :
29. If a + b + c = 5 and ab +bc + ca = 7, then the value of \(a^3\) + \(b^3\) + \(c^3\) - 3abc is :
30. If sin \(\beta\) = \(\frac13\), (\(\sec\beta\ - tan\:\beta)^2\) is equal to :
31. A and B complete a work in 24 and 30 day, respectively, working 10 hours per day. The work is to be done in two shifts. the morning shift is for 6 hours and the evening shift is for 4 hours. On the first day, A work in the morning and B works in the evening, and they interchange their shifts every day. On which day did the work get completed ?
32. If sin A = \(\frac{\sqrt3}2\), 0 \(\leq\) A \(\leq\) 90\(^\circ\), then find the value of 2 (cosec A + cot A).
33. Three numbers are in the ratio of 5 : 7 : 9 and their LCM is 34, 650. The H CF is :
34. In a circle of radius 42 cm, an arc subtends an angle of 60\(^\circ\) at the centre. Find the lenth of the arc.(take \(\pi = \frac {22}{7}\))
35. A cylinder has some water in it at a height of 16 cm. If a sphere of radius 9 cm is put into it, then find the rise in the height of the water if the radius of the cylinder is 12 cm.
36. Which of the following dance forms originated in Southeastern India ?
37. The term 'inning' is related to which of the following sports ?
38. Which of the following industries was NOT in schedule A of Industrial Policy 1956 ?
39. Which chemical element of group 18 of the periodic table is produced by the natural radioactive decay of uranium in soils and rocks ?
40. Ashtadhyayi, is a Sanskrit treatise on grammar, written in the 6th to 5th century BCE by ___________________.
41. Which of the following is NOT included in inventory investment when calculating national income?
42. The star - shaped temples were built during the reign of :
43. The provision of fundamental duties in the Indian Constitution is inspired by ________________.
44. How many types of the amendment are mentioned by the Indian Constitution as per Article 368 ?
45. In the game of Ice hockey, during normal play how many players are there in each team on the ice at any one time to compete ?
46. The 'Servants of India Society' was the brainchild of which of the following leaders?
47. Which of the following is NOT an example of a minor industrial region of India ?
48. Siachen in Himalayas is :
49. How many times has India won the ICC T20 Men's World Cup in cricket ?
50. The shape of a basketball court is a _______.
51. When was the Atmiya Sabha founded to attack the evils within Hinduism ?
52. The Eastern Ghats stretch from the ________ to the Nigiris in the south.
53. How many fundamental duties are listed in the Indian Constitution as of 2022 ?
54. The Himalayas have been divided on the basis of regions from west to east. The correct order of regions from west to east is :
55. Under which Article of the Indian Constitution shall the executive power of the Union be vested in the President ?
56. The ____________ birth rate indicates the number of live births occurring during the year per 1000 population estimated at midyear.
57. When was Khandesh merged into the Mughal empire by Akbar ?
58. Which of the following is the largest railway junction in India ?
59. In How many zones Indian Railways has been divided ?
60. Which is the fastest train in India ?
61. Which state has the longest route (in kilometers) of railway line in India ?
62. A station where the rail lines end, is called
63. The headquarters of South Railways is situated at
64. Which year is declared as ''Year of Rail Users'' by the Indian Railways ?
65. In which of the following cities, the first subway train was started ?
66. The first Shatabdi express was introduced between which of the following locations?
67. Which railway station has become the India's first station to run by all woman staff ?
68. In which type of rainfall, winds move out from a high - pressure area with wind direction clockwise in the northern hemisphere, and anti - clockwise in the southern hemisphere?
69. Which Article of the Constitution of India states that the Prime Minister is appointed by the President of India ?
70. The President of which of the following countries was invited as the Chief Guest for the Republic Day parade on 26 January 2020?
71. From the options, choose the one which is NOT a product of the decomposition reaction of lead nitrate.
72. In test match cricket, how many minimum overs can a team play in a day?
73. Which report is NOT associated with Fundamental Rights?
74. Who succeede Alivardi khan as Nawab of Bengal ?
75. Who among the following had written 'The Dark Room' that presents an Indian woman in stiff opposition to male domination?
76. The food component present in sugar is :
77. Cricket became an international game with the formation of the Imperial Cricket Conference (ICC) in the year _______.
78. Aluna Kabuini is associated with which of the following dances?
79. Which of the following can degrade detritus into simpler inorganic substances ?
80. The _________________ Five - Year Plan was the first plan to focus on gender issues, women empowerment and the growing inequalities amongst the states and inter - regional disparities.
81. Nauroz is celebrated by which of the following communities in India?
82. After how many days of absence from Parliament without permission will a Member of Parliament be disqualified ?
83. The Fundamental Rights in the Indian Constitution are inspired by the 'Bill of Rights' of which of the following countries?
84. 'Wings of Fire' is the autobiography of ____________.
85. Which of the following places experiences extreme cold in winter and pleasant weather in summer?
86. In a certain code language, 'GRAPE' is coded as 21-54-3-48-15 and 'MELON' is coded as 39-15-36-45-42. How will 'PEACH' be coded in the same language?
87. If A denotes ‘+’, B denotes ‘×’, C denotes ‘−’, and D denotes ‘÷’, then what will be the value of the following equation? 94 C 12 B 6 A 216 D 9 = ?
88. Select the correct mirror image of the given figure when the mirror is placed at line MN as shown.
89. Select the option figure which is embedded in the given figure as its part (rotation is NOT allowed).
90. In certain code language, 'EDUCATION' is written as 'FCVBBSJNO' and 'MICROSOFT' is written as 'NHDQPRPEU' .How will 'SEMICIRCLE' be written in that language ?
91. In a certain code language, 'YATCH' is coded as 67 and 'DINE' is coded as 40. How will 'Mango' be coded in that language ?
92. Choose one of the following correct combinations of mathematical signs which can be filled to balance the following equation.
93. Given below are two statements and two conclusions. Take the statements to be true even if they are at variance with commonly known facts, and decide whether the conclusion(s) follow (s) the given statements.
Statements:
Some dates are hazelnuts.
All hazelnuts are walnuts.
Conclusions:
I. Some dates are walnuts.
II. Some walnuts are hazelnuts.
94. Select the correct mirror image of the given figure when the mirror is placed at line MN as shown.
95. Which number will replace the question mark (?) in the following series?
96. Three different position of the same dice are shown. Find the number on the face opposite the face showing '6'.
97. Select the set in which the numbers are related in the same way as are the numbers of the following set.
(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is NOT allowed)
(2, 5, 341)
(1, 7, 510)
98. Pooja drives 4 km towards east from point A. She takes a right turn and drives 2 km. Then she takes a left turn and drives 3km. Again, she takes a left turn and drives 2 km to reach point B. How far and towards which direction should she drive now in order to reach point A again ?
99. Which letter - cluster will replace the question mark (?) to complete the given series?
ZFKQ, BCMN, ?, FWQH, HTSE
100. Select the set in which the numbers are related in the same way as are the numbers of the following sets.(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is NOT allowed.)
101. Six friends are sitting in a circle facing the centre. Sumit sits second to the right of Amit. Karan is an immediate neighbour of Param. Tony sits third to the right of Amit. Dharam is an immediate neighbour of Amit and Sumit. Karan sits second to the right of Sumit.
Who sits fourth to the right of Param?
102. Select the correct option that indicates the arrangement of the given words in the order in which they appear in an English dictionary.
- Desperate
- Desolate
- Destruction
- Desire
- Descend
- Destination
103. Which of the following numbers will replace the question mark (?) in the given series?
104. Select the option that represents the letters which, when sequentially placed from left to right in the blanks below, will complete the letter series.
_L_ _ K S_ T U _ S L _ _ K
105. Select the correct mirror image of the given pattern when the mirror is placed at 'MN' as shown below.
106. Six student are sitting around a circular table facing the centre. A is an immediate neighbour of both E and D. E sits third to the right of C. D sits third to the left of F. E is an immediate neighbour of F.B sits second to the left of E. Who is the immediate neighbour of both A and C ?
107. If '+' means '-', '-' means '\(\times\)', '\(\times\)' means '\(\div\)' and '\(\div\)' means '+', what will come in place of '?' in the following equation ?
42 \(\times\) 6 - 7 \(\div\) 13 + 28 = ?
108. Select the option that represents the correct order of the given words as they would appear in an English dictionary?
109. Select the option that is related to the fifth number in the same way as the first number is related to the second number and the third number is related to the fourth number.
32 : 10 : : 24 : 12 : : 98 : ?
110. P is to the north of Q. T is to the east of Q and S is to the east of P. S is to the north-east of T and south-west of R. What is the position of R with respect to Q? (All positions are arranged in GRID pattern)
111. In a certain code language, ‘COLD’ is coded as ‘6428’ and ‘TIDE’ is coded as ‘9673’. What is the code for ‘D’ in the given code language ?
112. Three of the following letter - clusters are alike in some manner and one is different. Select the one that is different.
113. Which of the following terms will replace the question mark (?) in the given series ?
HKOE, KNOE, ?, QTOE, TWOE
114. If the given sheet is folded to form a cube, which of the given figures is/are possible ?
(The numbers are shown to indicate the sides only.)
115. Which two sings should be interchanged to make the given equation correct?
729\(\times\) 9 - (56 - 6) \(\times\) 5 \(\div\) 2 + 152 \(\times\) 19 = 69
116. Which of the following numbers will replace the question mark (?) in the given series
32, 32 , 32, 34, ?, 106, 530
117. Given below are two statements and two conclusions. Take the statements to be true even if they are at variance with commonly known facts, and decide whether the conclusion(s) follow (s) the given statements.
Statements :
All irons are coppers.
All coppers are aluminiums.
Conclusions :
I. Some aluminiums are irons
II. Some aluminiums are coppers
118. Which figure from the given options would replace the question mark (?) if the following figure series were to be continued ?
119. In a certain code language, 'STORY' is coded as '97' and 'PULL' is coded as '61'. How will 'INCOME' be coded in that language ?
120. F is the brother of J. E is the sister of D.K is the sister of L. D is the son of L. J is the father of E. How is D related to F?