βHe often _____ the numbers. False claims are not going to help. Honesty _____ trustβ, said the manager. Choose the option with the correct order of words to fill the blanks.
a.
exaggerates; engenders
Correct Answer
b.
excels; encourages
c.
aggravates; alleviates
d.
diminishes; eliminates
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Q2mcq
In the sequence of tiles shown below, the missing tile indicated by the question mark should be
a.
b.
Correct Answer
c.
d.
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Q3mcq
A school has 100 students distributed among 1 st to 10 th standards. Based on this, which one of the following statements is always correct?
a.
There are at least 10 students who belong to the same standard.
Correct Answer
b.
There is at least one student in each standard.
c.
There are at most 10 students in 10 th standard.
d.
The total number of students from 1 st to 5 th standards is at least 50.
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Q4mcq
How many 3-digit numbers can be formed using three distinct single digit prime numbers?
a.
64
b.
24
Correct Answer
c.
12
d.
4
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Q5mcq
In a group of students, 10 students like Mathematics, 12 students like English, 4 students like both Mathematics and English, and 6 students like neither Mathematics nor English. The number of students in the group is ____
a.
18
b.
20
c.
24
Correct Answer
d.
32
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Q6mcq
Charity: P:: Retaliation: Q Choose the appropriate pair of words P and Q that fit the analogy.
a.
P = Parsimonious; Q = Vengeful
b.
P = Altruistic; Q = Amicable
c.
P = Resentful; Q = Spiteful
d.
P = Magnanimous; Q = Vindictive
Correct Answer
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Q7mcq
A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct?
a.
Only (i) can correspond to the unfolded cube in Panel I.
Correct Answer
b.
Only (ii) can correspond to the unfolded cube in Panel I.
c.
Both (i) and (ii) can correspond to the unfolded cube in Panel I.
d.
Neither (i) nor (ii) can correspond to the unfolded cube in Panel I.
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Q8mcq
Consider the cube shown below with its 8 corners labelled a, b, c, d, e, f, g, and h. The figure is representative. All corners are to be colored such that any two corners that are connected by an edge must be of different colors. The minimum number of colors required to achieve this is ________
a.
8
b.
4
c.
3
d.
2
Correct Answer
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Q9mcq
Four hills H1, H2, H3, and H4 are present in an area. The following observations are made about them: i. Neither H2 nor H3 is the easternmost hill. ii. Neither H2 nor H3 is the westernmost hill. iii. Neither the easternmost hill nor the westernmost hill is the southernmost iv. Two hills are located to the west of H2. v. The southernmost hill has at least two hills to its east.
hill. The southernmost hill is ________.
a.
H1
b.
H2
c.
H3
Correct Answer
d.
H4
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Q10mcq
As shown in the figure, circle $C$ 1 with center $O$ 1 and radius $r$ 1 touches the square $VWXY$ at points $P$ and $Q$ while circle $C$ 2 with center $O$ 2 and radius $r$ 2 touches the square $VWXY$ at points $R$ and $S.$ The two circles touch each other at $T.$
Μ Μ Μ Μ Μ = 4 cm, $r$ = _____ cm. Given $r$ = 1 cm and Μ Μ Μ Μ $VY$ = $VW$
2 1
a.
4 - $3\sqrt{2}$
b.
1 + $2\sqrt{2}$
c.
7 - $4\sqrt{2}$
Correct Answer
d.
5 + $3\sqrt{2}$
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expert in one of the performing arts, namely, dance, theatre, guitar and percussion, not necessarily in that order. The dancer is taller than the theatre expert. Aman is taller than Chiranjeevi. The percussionist is taller than Beena but shorter than Aman. Beena is shorter than the dancer. The guitarist is not the tallest. Dhiman is shorter than both, guitarist and Chiranjeevi. What is the expertise of Aman?
a.
Dance
b.
Theatre
c.
Guitar
d.
Percussion
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Let $βABC$ be an isosceles triangle with the base $AB$ of length 8 units. Let $CD$ be a perpendicular of length 4 units drawn from the vertex $C$ onto the base $AB$ and $AC$ = $BC.$ Then, which of the following is the set of values of the angles (in degrees) $CAB, ABC, BCA$ respectively?
a.
45,45,90
b.
100,40,40
c.
90,45,45
d.
40,40,100
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In the given passage, fill in the blanks with most suitable set of given words: The future must no longer be___ by the past. While, the effects of the past are still with us, each day is a new___. Therefore, one should ___from solely believing in destiny and crave towards charting their own path of success with grit and labour. Positive_______ is imperative.
a.
Determined, beginning, refrain, anticipation
b.
Fascinated, one, include, physiology
c.
Explored, suffering, content, psychiatry
d.
Marred, life, hinder, labyrinth
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Indian society is experiencing a boom in pet culture, where people are becoming responsible caretakers of pets rather than merely providing food and shelter. They no longer like to identify themselves as βpet-ownersβ but rather as βpet-parentsβ. This means that there is an emotional transaction rather than a utilitarian one. Which of the following weaken(s) the argument presented in the given passage?
a.
Some social media influencers are using their pets only for popularity.
b.
Food, medicines and clothes for pets are becoming easily available.
c.
Pet owners are expecting some provision for tax rebate.
d.
In todayβs stressful times, pets provide emotional support.
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Three statements, S1, S2 and S3 are given, followed with 4 conclusions, C1, C2, C3 and C4. S1: Hostel authorities organised a special lunch on 01-02-26 during 12 noon to 3 pm, for those residents of the Hostel, who paid hostel mess fees on time. S2: Hostel authorities issued a notice that, since elections for Mess Council is held during 4-5 pm of 01-02-26, residents of the Hostel who are contesting the elections need to stay away from the hostel since morning till 5 pm. S3: Hostel residents who were eligible to have special lunch, had it on 01-02-26. C1: Residents who did not have special lunch on 01-02-26, either did not pay hostel mess fees on time or were contesting elections. C2: Residents having special lunch on 01-02-26, were either not contesting elections or had paid hostel mess fees on time. C3: Residents who are contesting elections need not care about paying mess fees. C4: Residents who have paid hostel mess fees on time could join special lunch only if they are not contesting elections. Which of the conclusion(s) is/are incorrect?
a.
Only one among C1, C2, C3 and C4 is incorrect.
b.
C1 and C2 are incorrect.
c.
C2 and C3 are incorrect.
d.
C3 and C4 are incorrect.
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Six statements, S1 to S6, are given. S1: All GATE candidates are engineers. S2: Some GATE candidates are CAT candidates. S3: All GRE candidates are GATE candidates. S4: All engineers are GRE candidates. S5: Some CAT candidates are GRE candidates. S6: Some CAT candidates are engineers. Based on S1-S6, following options provide a set of three statements, followed by a fourth statement. Identify the option(s) where the fourth statement can be necessarily inferred from the set of three statements.
a.
{S1, S2, S3} => S5
b.
{S4, S1, S2} => S5
c.
{S6, S1, S3} => S5
d.
{S4, S3, S1} => S6
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Four couples M-N, O-P, R-L, S-E meet to have a dinner together on an eight- seater rectangular dining table with four seats each on opposite sides. The men are named as M, O, R, S. Two of the men, O, R, sit on the two corners of one side of the table and M sits beside R. Further, none of the couples occupy seats opposite to each other. However, a person sits adjacent to the seat opposite to his/her spouse. Based on the information, which of the following conclusions can be drawn?
a.
R sits opposite to N and S sits opposite to P.
b.
R sits opposite to P and O sits opposite to N.
c.
S sits opposite to N and O sits opposite to L.
d.
M sits opposite to L and O sits opposite to E.
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Me and my spouse have a big family, comprising 8 females and 6 males. We have two sons and two daughters, of whom the eldest is unmarried. Out of my two grandsons and three granddaughters, only one grandson is a single child. His mother is my younger daughter. Which of my children necessarily has two daughters?
a.
None of my sons
b.
One of my sons
c.
One of my daughters
d.
Elder daughter
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Three players named Arun, Babita and Chandu play a game by tossing an unbiased coin in turn whose rules are as follows: Initially each player has 100 candies. If the tossing of this coin results in a βheadβ then the player who tosses receives 10 candies from each of the other two players, whereas, if the toss results in a βtailβ then the player who tosses has to give away 20 candies to each of the other two players. A player with the highest number of candies at the end will be the winner. The game is started by Arun, followed by Babita and finally stopped after Chanduβs turn. Given that Arun is the only winner, which of the following hold(s) true?
a.
Arun has 90 candies more than Chandu
b.
Both Babita and Chandu have the same number of candies
c.
Arun has 90 candies more than Babita
d.
Babita and Chandu together have 120 candies
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Choose the correct sequence of sentences so that they form a coherent paragraph: P. However, in the context of texts dealing with science or engineering, this
condition may not be applicable. Q. One can infer, that there is something called discipline fidelity and within
this aspect, content, language, structure and scope of a text may vary. R. In the meaning-making process of a text, it is not always logic that is central. S. Most of the times, it is the expression of the experience that supersedes the
structure and argument. Which of the following options is/are correct and giving the most appropriate order and meaning to the sentence?
a.
RSPQ
b.
QRSP
c.
RSQP
d.
SPRQ
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Mental health is a global concern, especially among the youth. During the Covid- 19 pandemic, when schools and colleges were operating online, students were left with no option but to stay at home leading to negligible social interaction. Several studies indicate that even when offline classes have now resumed post Covid-19 pandemic, these students are finding it difficult to establish social connect leading to mental health issues. To deal with this situation, schools and colleges are trying hard to implement different strategies to combat their studentβs mental health depending on their unique culture, overall strength, and resources. Which of the following conclusions can be drawn from the above passage?
a.
India is a young nation.
b.
mental health.
c.
A combination of online and offline class is good for students.
d.
Social connect is important for mental health.
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On the basis of syntax and grammar, identify the incorrect sentence(s). I. Doctors have found high levels of cerebrospinal fluid in certain cases of
cerebral palsy around the world. They also suggested its abnormal impact
on speech and muscle movement. II. Doctors have found high levels of cerebrospinal fluid in certain cases of
cerebral palsy around the world which suggests the abnormal impact on
speech and muscle movement. III. Having found high levels of cerebrospinal fluid in certain cases of cerebral
palsy around the world, doctors are suggesting abnormal impact on speech
and muscle movement. IV. Having found high levels of cerebrospinal fluid in certain cases of cerebral
palsy around the world, doctors suggested its abnormal impact on speech
and muscle movement.
a.
I
b.
II
c.
III
d.
IV
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In a cricket match amongst 7 friends, named P1 β P7, P1 scored maximum individual runs of 25 and P7 scored minimum individual run of 0. No two friends had the same score. The median and average runs scored were 15 and 12.57, not necessarily in that order. Two players, P2 and P3, who scored more than median but less than maximum, scored less than 40 runs together. One player scored double the sum of non-zero scores of two players. What could be the possible value(s) of the second highest score?
a.
18
b.
20
c.
21
d.
22
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A police station has six personnel comprising an inspector (I) and five constables $(C$ 1, $C$ 2, $C$ 3, $C$ 4, $C$ 5). Normally, a βraid teamβ of two, three, or four members is formed depending upon the nature of the raid. As per rule, it is mandatory that the inspector is part of raid team. Number of distinct raid teams that can be formed is __________________. (Answer in integer)
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A man visits four relatives on a day. He purchases some sweets and gives a part of it to the first relative. Next, he purchases the same number of sweets he is left with after he visited his first relative. He repeats this process while visiting his other relatives. Finally, he gives all the sweets to his fourth relative. It is known that he gives equal number of sweets to all the relatives and is left with no sweets after the fourth relative. Assuming that he initially purchased more than 20 sweets, the minimum number of sweets he gave to each relative is _______________. (Answer in integer)
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$A$ is an $(n \times n)$ matrix. Consider the following two statements
Statement 1: Columns of matrix $A$ are linearly independent
Statement 2: Inverse of matrix $A$ exists Which one of the following statements is TRUE?
a.
Statement 1 is true if and only if Statement 2 is true
b.
Statement 1 and Statement 2 can be individually true or false
c.
Statement 1 implies Statement 2 but not the other way round
d.
Statement 2 implies Statement 1 but not the other way round
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Madhuβs utility function is given by $U$ = $max(2C, 3F),$ where $C$ represents the amount of cloth and $F$ represents the amount of food. Her preferences DO NOT satisfy which one of the following axioms?
a.
Completeness
b.
Continuity
c.
Convexity
d.
Transitivity
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Two players use the following procedure to divide a perfectly homogeneous and continuously divisible cake. First, Player 1 divides the cake into two pieces and then Player 2 chooses one of the pieces. Player 1 gets the remaining piece. Each player cares only about the size of the piece s/he gets. How is the cake divided in a sub-game perfect equilibrium if both the players are rational?
a.
Player 1 gets the whole cake
b.
Player 2 gets the larger piece
c.
Each player gets half of the cake
d.
The outcome cannot be decided based on the given information
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Unanticipated inflation rate, percentage change of output from full employment level, and the Okunβs law yield (i) ________ and it represents (ii) ______ side of the economy. Which one of the following combinations of (i) and (ii) make the above sentence correct as per economic theory?
a.
(i) Expectation augmented Phillips curve; (ii) supply
b.
(i) Expectation augmented Phillips curve; (ii) demand
c.
(i) Phillips-Okunβs curve; (ii) supply
d.
(i) Phillips-Okunβs curve; (ii) demand
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Suppose, a random variable $X$ follows a Normal distribution with mean $ΞΌ,$ and variance $Ο$ 2. The variance of the distribution is unknown. For testing $ΞΌ$ = 10 against the alternative $ΞΌ$ > 10, the distribution of the test statistic is
a.
Standard Normal distribution
b.
Studentβs t distribution
c.
Normal distribution
d.
F distribution
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Goods that come under the purview of βtragedy of commonsβ are (i)_____ and (ii)_____. Which one of the following combinations of (i) and (ii) makes the above sentence correct as per the economic theory?
a.
(i) non-rivalrous; (ii) excludable
b.
(i) rivalrous; (ii) excludable
c.
(i) non-rivalrous; (ii) non-excludable
d.
(i) rivalrous; (ii) non-excludable
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Consider a two-variable $(x, y)$ linear regression model given in Equations (1) and (2) below. The error term, $u t$, of Equation (1) is serially correlated as given in Equation (2). The error term, $Ξ΅ t$, of Equation (2) is white noise. All other assumptions of the Classical Linear Regression Model (CLRM) hold. Then, which of the following options is/are FALSE?
$y t$ = $Ξ±$ + $Ξ²x t$ + $u t$ (1)
$u t$ = $Οu t-1$ + $Ξ΅ t$; 0 < $Ο$ < 1 (2)
a.
Ordinary Least Squares estimators of the parameters in Equation (1) are biased
b.
Ordinary Least Squares estimators of the parameters in Equation (1) are asymptotically normally distributed
c.
Ordinary Least Squares estimators of the parameters in Equation (1) are efficient
d.
Ordinary Least Squares estimators of the parameters in Equation (1) are consistent
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Suppose, a random variable $X$ follows a Poisson distribution with parameter $Ξ»$ = 25. The coefficient of variation of the distribution is __________ (rounded off to two decimal places)
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You and three of your friends go to a restaurant for dinner. All four of you agree to divide the total bill equally amongst yourselves. One of your friends orders a dish worth INR 400. The marginal cost for ordering the dish for each one of you in INR is _________ (in integer)
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The inverse demand function for the first book on βEconomics of Digital Public Infrastructure in Indiaβ is given by $p$ = 200 - $0.002Q;$ where, $p$ is the price of the book, and $Q$ is the number of books purchased. The publisherβs marginal cost is 60 + $0.0168Q.$ The authorβs royalty is 25% of the total revenue. The optimal price of the book from the authorβs perspective is _____________ (in integer)
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Two companies, Company 1 and Company 2, are playing a simultaneous-move game. They are selling competing devices, whose quantity demanded are given by $x$ 1 and $x$ 2, and their prices are $p$ 1 and $p$ 2, respectively. The demand equation for the device of Company 1 is $x$ 1 = 300(90 - $0.5p$ 1 + $0.25p$ 2), and that of Company 2 is $x$ 2 = 300(90 - $0.5p$ 2 + $0.25p$ 1). The cost of production of both devices is zero. Each company is interested in maximizing its own profit. Which one of the following price combinations constitutes the Nash equilibrium of the game?
a.
$p$ 1 = 90, $p$ 2 = 90
b.
$p$ 1 = 120, $p$ 2 = 120
c.
$p$ 1 = 45, $p$ 2 = 45
d.
$p$ 1 = 105, $p$ 2 = 75
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Match Column I with Column II
Column II Column I P 1 Working capital loan e-Nam Q PM Micro Food Processing 2 A seed capital of INR 40,000, and
Scheme 50% branding/marketing grant R Adivashi Mahila Sashaktikaran 3 Loan up to INR 2 lakhs at 4%
Yojna interest S Swayam Shakti Sahakar Yojna 4 Innovative agricultural
technologies and price discovery
mechanism
a.
b.
c.
d.
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Suppose that $X$ 1, $X$ 2, $X$ 3 and $X$ 4 are independent random variables with common distribution $N(4,$ 12). Observations $x$ 1 = 6, $x$ 2 = 3, $x$ 3 = 1, and $x$ 4 = 10 correspond to $X$ 1, $X$ 2, $X$ 3 and $X$ 4, respectively. What is the sample mean and its sampling distribution?
a.
4 and $N(4,$ 3)
b.
5 and $N(4,$ 3)
c.
4 and $N(5,$ 12)
d.
5 and $N(4,$ 12)
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Consider a Solow growth model with the production function $Y t$ = $K tΞ± N t1-Ξ±$; 0 < $Ξ±$ < 1; where, $Y t$ is aggregate output at time $t; K t$ is aggregate capital stock at time $t; N t$ is the number of workers at time $t.$ There is population growth but no technology growth. Let 0 < $s$ < 1 be the savings rate, 0 < $n$ < 1 be the population growth rate, and 0 < $Ξ΄$ < 1 be the rate of depreciation of capital stock. What is the growth rate of aggregate output at steady state?
a.
$n$
b.
$s$ + $n$
c.
$n+Ξ΄$
d.
0
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Consider the following IS-LM model where, $C$ 0 is autonomous consumption, $c$ is marginal propensity to consumption, $T$ 0 is the autonomous tax, $t$ is the tax rate on income $Y, b$ is the interest sensitivity of investment to real interest rate $r, M S$ is exogenously determined nominal money supply, $P$ is the aggregate price level, $l$ 1 is the income sensitivity of money demand to income, $l$ 2 is the interest sensitivity of money demand Consumption function: $C$ = $C$ 0 + $cY d$; 0 < $c$ < 1 Disposable Income: $Y d$ = $Y$ - $T$ Tax function: $T$ = $T$ 0 + $tY;$ 0 < $t$ < 1 Investment function: $I$ = $I$ 0 - $br; b$ > 0
$M S$ LM equation: = $l Y$ - $l r; l$ > 0, $l$ > 0
$P$ 1 2 1 2 Closed economy without government: $Y$ = $C$ + $I$
$βY$ Which one of the following options gives the investment multiplier ()?
$βI$ 0
a.
1 1 - $c(1$ - $t)$
b.
1
$l$ 1 [1 - $c(1$ - $t)]$ + () $b$
$l$ 2
c.
1 $l$ 1 (1 - $c)$ + () $b$ $l$ 2
d.
$l$ 1 1 - $c(1$ - $t)$ + () $b$ $l$ 2
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The estimated energy demand is given in the Equation below, where, $yΜ t$ is the estimated value of the log of energy demand at time $t.$ The numbers in the parentheses are the values of the $t-statistic$ of the corresponding coefficients.
$yΜ t$ = 1.24 + 0.56 ln(GDP $t$) - 0.03 ln(energyprice $t$)
(10.73) (7.28) (5.28) Which one of the following statements is CORRECT?
a.
Demand for energy is price inelastic
b.
Demand for energy is price elastic
c.
Demand for energy is unit elastic
d.
Sufficient information has not been provided to calculate price elasticity
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Nominal exchange rate is defined as the amount of domestic currency that can fetch one unit of foreign currency. Suppose that there is a fall in nominal exchange rate. Which of the following statements is/are TRUE?
a.
Appreciation of domestic currency with respect to foreign currency
b.
Depreciation of domestic currency with respect to foreign currency
c.
Fall in the price of foreign currency in terms of domestic currency
d.
Rise in the price of foreign currency in terms of domestic currency
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In the town of Belapur, 5000 used cars are available for sale. The cars vary in quality and only the car owners know the true worth of their car. All used cars look the same to potential buyers. If a car is of quality $x,$ then the original owner is ready to sell it for any price greater than or equal to $x.$ For a buyer, the expected worth of a car is equal to half of the number of cars selling in the market. As the buyer does not know the exact quality of the car, he is willing to pay a price that is equal to 1000 more than the expected worth of the car. At the equilibrium, the number of cars that remain unsold in the market is ________ (in integer)
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Suppose that Ritwick owns two plants, Plant $X$ and Plant $Y.$ Both plants produce the same industrial good. The marginal cost to produce at Plant $X$ is 4 + $2Q X$; where, $Q X$ is the quantity produced in Plant $X,$ and the marginal cost to produce at Plant $Y$ is 40 + $Q Y$; where, $Q Y$ is the total quantity produced in Plant $Y.$ If Ritwick plans to produce 15 units of this good, the amount of the good produced in Plant $Y$ is _________ (in integer)
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Consider the function $G(x, y, z)$ = 0. This function allows us to implicitly define each of three variables as a function of the other two variables. Assume that all partial derivatives of the function $G(x, y, z)$ exist everywhere. Then, the value of $βz βx βy$ ($\times \times$) is _________ (in integer) $βx βy βz$
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The market for torch is perfectly competitive. The market demand function for torch is given by $X d$ = min(400 - $p,$ 0), $p \ge$ 0, where $p$ is the price of a torch. The market
$p$ 80 supply for the same good is $X s$ = max (0, (-)), $p \ge$ 0. If a specific tax of 40 is
7 7 imposed on the purchase of each unit of torch, the corresponding decrease in the consumer surplus is _______ (rounded off to one decimal place)
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An individual lives for two periods, Period 1 and Period 2. In Period 1, her income is 210, and in Period 2, her income is 0. She saves in Period 1 and earns a real interest rate of 10% on these savings in Period 2. She does not save anything in Period 2. She consumes equal amounts in both the time periods. Her consumption in the current period is ________ (in integer)
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$M$ The money demand function is = 800 + $0.3Y$ - $2000i;$ where, $M$ is nominal $P$ money supply, $P$ is the aggregate price level, $Y$ is the real GDP, and $i$ is the nominal interest rate. Suppose that $Y$ = 2000, and $i$ = 0.20. The velocity of money is ________ (in integer)
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Consider the estimated regression Equation below, where, $yΜ t$ is the estimated value of the log (to the base $e)$ of real GDP at time $t.$ The numbers in the parentheses are the value of the $t-statistic$ of the corresponding coefficients.
$yΜ t$ = 6.20 + 0.05 $t$
(10.25) (4.62) The growth rate of real GDP (in %) is _________________ (rounded off to the nearest integer)
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Table 1 and Table 2 represent a 3-player game. The payoff (a, b, c), in each cell, represents Player 1, Player 2, and Player 3βs payoffs respectively. Player 1 (P1) decides to play either A, B, or C. Player 2 (P2) decides to play either X, Y, or Z. Player 3 (P3) decides between Table 1 and Table 2. The number of Nash equilibrium in pure strategy in this game is _______ (in integer)
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