# Recent questions tagged cat2010

1
Let $\text{S}$ be the set of rational numbers with the following properties: $\frac{1}{2}\in S$ If $x\in S$ then both $\frac{1}{x+1}\in S$ and $\frac{x}{x+1}\in S$ Which of the following is true? $S$ contains all rational numbers in the interval $0 < x < 1$. ... $S$ contains all rational numbers in the interval $-1 < x < 0$. $S$ contains all rational numbers in the interval $1 < x <\infty$.
1 vote
2
If $\text{r, s and t}$ are consecutive odd integers with $\text{r < s < t}$, which of the following must be true? $\text{rs = t}$ $\text{r + t = 2t – s}$ $\text{r + s = t – 2}$ $\text{r + t = 2s}$
1 vote
3
$\text{P, Q and R}$ are three consecutive odd numbers in ascending order. If the value of three times $P$ is three less than two times $R$, find the value of $R$. $5$ $7$ $9$ $11$
1 vote
4
Consider the following statements : When two straight lines intersect, then : adjacent angles are complementary adjacent angles are supplementary opposite angles are equal opposite angles are supplementary Of these statements: (I) and (III) are correct (II) and (III) are correct (I) and (IV) are correct (II) and (IV) are correct
1 vote
5
Let $S$ denote the infinite sum $2+5x+9x^{2}+14x^{3}+20x^{4}+\ldots$ where $\mid x \mid < 1$ and the coefficient of $x^{n-1}$ is $\dfrac{1}{2}n\left ( n+3 \right ), \left ( n=1,2,\ldots \right ).$ Then $S$ equals $\frac{2-x}{(1-x)^{3}}$ $\frac{2-x}{(1+x)^{3}}$ $\frac{2+x}{(1-x)^{3}}$ $\frac{2+x}{(1+x)^{3}}$
6
A pole has to be erected on the boundary of a circular park of diameter $13$ meters in such a way that the difference of its distances from two diametrically opposite fixed gates $A$ and $B$ on the boundary is $7$ meters. The distance of the pole from one of the gates is: $8$ metres $8.25$ metres $5$ metres None these
7
From a square piece of card-board measuring $2a$ on each side of a box with no top is to be formed by cutting out from each corner a square with sides $b$ and bending up the flaps. The value of $b$ for which the box has the greatest volume is $b= \frac{a}{5}$ $b= \frac{a}{4}$ $b= \frac{2a}{3}$ $b= \frac{a}{2}$
1 vote
8
The sum of the areas of two circles which touch each other externally is $153\pi$. If the sum of their radii is $15$, find the ratio of the larger to the smaller radius $4$ $2$ $3$ None of these
1 vote
9
Consider the following statements: If $a^{x}=b,b^{y}=c,c^{z}=a,$ then $xyz=1$ If $p=a^{x},q=a^{y},\left ( p^{y}q^{y} \right )^{z}=a^{2},$ then $xyz=1$ If $x^{a}=y^{b}=z^{c}$ and $ab+bc+ca=0$ then $xyz=1$ Of these statements: I and II are correct II and III are correct Only I is correct All I, II and III are correct
1 vote
10
If $a, b$ and $c$ are three real numbers, then which of the following is not true? $\mid a+b \mid\leq \mid a \mid+\mid b \mid$ $\mid a – b \mid \leq \mid a \mid + \mid b\mid$ $\mid a-b \mid \leq \mid a \mid -\mid b \mid$ $\mid a-c \mid \leq \mid a-b \mid+\mid b-c \mid$
11
Let $f$ be an injective map with domain $\left \{ x, y, z \right \}$ and the range $\left \{ 1, 2, 3 \right \}$ such that exactly one of the following statements is correct and the remaining are false. $f\left \{x \right \}=1,f\left ( y \right )\neq 1,f\left ( z \right )\neq 2.$ The value of $f^{-1}\left ( 1 \right )$ is $x$ $y$ $z$ None of the above
1 vote
12
If $a=b^{2}=c^{3}=d^{4}$ then the value of $log_{a}$ $(abcd)$ would be $log_{a}1+log_{a}2+log_{a}3+log_{a}4$ $log_{a}24$ $1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}$ $1+\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}$
13
$ABCD$ is a rectangle. The points $P$ and $Q$ lie on $AD$ and $AB$ respectively. If the triangle $PAQ, QBC$ and $PCD$ all have the same areas and $BQ = 2$, then $AQ =$ $1+\sqrt{5}$ $1-\sqrt{5}$ $\sqrt{7}$ $2\sqrt{7}$
1 vote
14
For which value of $k$ does the following pair of equations yield a unique solution for $x$ such that the solution is positive? $x^{2}-y^{2}=0$ $(x-k)^{2}+y^{2}=1$ $2$ $0$ $\sqrt{2}$ $\sqrt{-2}$
15
In an examination, the average marks obtained by students who passed was $x$ %, while the average of those who failed was $y$ %. The average marks of all students taking the exam was $z$ %. Find in terms of $x, y$ and $z$ ... $\left ( y-z \right )\left ( z-y \right )$ $\left ( y-z \right )\left ( x-z \right )$
1 vote
16
If three positive real numbers $a, b$ and $c(c>a)$ are in Harmonic Progression, then $log\left ( a+c \right )+log\left ( a-2b+c \right )$ is equal to: $2\:log\left ( c-b \right )$ $2\:log\left ( a-c\right )$ $2\:log\left ( c-a\right )$ $log\:a+log\:b+log\:c$
17
The colour black is an example of A surface colour An achromatic colour An organic colour A diffuse colour
18
For constructing the working class consumer price index number of a particular town, the following weights corresponding to different group of items were assigned : Food - $55$, Fuel - $15$, Clothing - $10$, Rent - $8$ and Miscellaneous - $12$. It is known that the rise in food prices is double ... $317.14,158.57,94.64,189.28$ $311.14,159.57,90.64,198.28$ $321.14,162.57,84.46,175.38$
1 vote
19
Geetanjali Express, which is $250$ metre long when moving from Howrah to Tatanagar crosses Subarnarekha bridge in $30$ seconds. What is the speed of Geetanjali Express? Statement I: Bombay Mail, which runs at $60$ km/hour crosses the Subranarekha bridge in $30$ seconds. Statements II: Bombay Mail when running at $90$ km/hour crosses a lamp post in $10$ seconds.
20
A line graph on a graph sheet shows the revenue for each year from $1990$ through $1998$ by points and joints the successive points by straight line segments. The point for revenue of $1990$ is labeled $A$, that for $1991$ as $B$, and that for $1992$ as $C$. What is the ratio of ... , and the angle between $CB$ and $x$-axis is $80$ degrees. Statement II: The scale of $y$-axis is $1$ cm = $1000$.
21
In a factory making radioactive substances, it was considered that the three cubes of uranium together are hazardous. So the company authorities decided to have the stack of uranium interspersed with lead cubes. But there is a new worker in a company who does not know the rule. So he ... he wanted. What is the number of hazardous combinations of uranium in a stack of $5$? $3$ $7$ $8$ $10$
22
According to the passage, lighting engineers need not Plot photometric curves Utilizes photometric data Understand Photometric techniques Have mathematical expertise
23
Paint is an example of a substance containing Inorganic material Body colours Surface colours Metallic colours
24
Which of the following conclusion can be drawn from the passage? Precise measurement is a sufficient condition to ensure validity of conclusions resulting from an experiment. Experimental data might support multiple theoretical explanations same time, hence validity ... s knowledge of the theory underpinning the experiment is sufficient to ensure the validity of conclusions drawn from experiments.
25
As per Mayo’s perspective, which of the following best defines the phrase “scientific explanation”? One which is most detailed in its explanation of natural phenomena. One which survives examination better than other explanations. One which has been thoroughly tested by scientific experts. One which refutes other explanations convincingly,
26
The author’s use of Snell’s law of refraction to illustrate Mayo’s perspective can best said to be Contrived Premediated Superfluous Illustrative
27
Biotic disturbances in the context means Attacks from other living things, animals, etc. The disturbances caused by the natives on seeing the strange foreigners. The political disturbances causing the closedown of the parks. Disturbances caused by the wild animals on seeing the tourists.
28
By using the expression “environmentally destructive tourism” the author means The preservation of the wild beasts. Destruction of the wildlife and sancturies. Destroying the attractive sources of wild animals and birds. The maintenance of the flora and fauna of the country
29
To implement the most scientific ways of tourism, we should Get industries and talented persons trained in the field. From a commission and a plan out how to implement the suggestions. Send a group of scientists abroad to learn more about tourism. Speed as much finance as possible to better the suggestions made.
30
Justice Minister Bola lge, confronted with the general incivility of local police, placed a ______ on the cads. Said the Hon. Bola lge, “I pray that god will make big holes in their pokets”. malediction sanction proscription plea
31
During the heated discussion, the leader of the group ________ refuted all the claims brought by his opponents. Later everybody acknowledged that he survived by most _______ luck. ingeniously, incredible ingeniously, incredulous ingenuously, incredible ingenuously, incredulous
32
Choose the option that point out sentence(s) with grammatical error(s). I love the man dancing on the table. I love the man's dancing on the table. In $1986$ Elie Wiesel was named the Nobel Peace Prize recipient, an honour established by Alfred Nobel. Neither of teh ... 's wife will have to excuse themselves from the reception to speak to the caterer III and V I and IV II and V III and IV
33
Infer ... $A-G;B-E;C-H;D-F$ $A-F;B-H;C-E;D-G$ $A-H;B-G;C-F;D-E$ $A-E;B-F;C-G;D-H$
34
Catch ... $A-H;B-F;C-E;D-G$ $A-F;B-G;C-E;D-H$ $A-G;B-F;C-E;D-H$ $A-G;B-H;C-F;D-E$
35
The _____ of the country should take a greater interest in promoting the indigenous works that are rooted in the deep traditions of scholarship across the world. LITERATI LITERATE LITERATURE LITERAL
36
Trace to Sparing of Replete with wonder at I and III I, II and III II, III and IV None of the above
37
________ of different categories of problems often leads to design of improper solutions that fail to address the complexities of the problem. CONFABULATION CONFLATION CONFLICT CONFESSION
Which of the following statements is wrong ? Depreciation expense is the lowest for food industry Power and fuel expenses are $5$th largest item in the expenditure of diverifies industries. Electricity industry earns more of other income as a percentage of total income compared to other industries. Raw material cost is the largest item of expense in all industry sectors