An actress described in a screenplay is an average-sized lady aged 45-50, big body frame, grey hair, large blue eyes, fair skin, smiling face. The candidate has black hair, big blue eyes, fair complexion, is in her thirties, and medium build. Will she be selected?
Rani gives numbers 1-6 to friends named Amabad (1), Domabad (2), Taimabad (3), Chomabad (4), Pemabad (5), Chamabad (6). 1 likes Chamabad, 3 and 4 like Pemabad, 6 and 1 like Taimabad, Pemabad, Domabad. Which number likes Pemabad and Taimabad but not Chamabad?
Eight students 1-8 are seated around a circle facing center. 5 is second to the right of 3, who is third to the right of 2. 8 is third to the right of 6, who is not an immediate neighbor of 1. Who is second to the right of 5?
In a code language, JAVA is written as JVAA. How is MAWAA written?
In a dance school, five students B, L, P, R, D stand in a row facing north. Who stood to the immediate left of R? Statement I: B is at one extreme, L between B and P. Statement II: Only one between P and D, D is not to the right of L.
Using both statements, the exact arrangement can be determined, giving the person to the immediate left of R.
In a code language, SUM is coded as NLVTTR and LATE is coded as FDUSZMK. How is ROAST coded?
Following the coding pattern where each letter is transformed, ROAST becomes USTRBZPNSQ.
Statement: Every institute in India should be linked with an incubation centre. Arguments: I. Students will be aware of start-ups and benefits to society. II. More start-ups will help build the economy.
Argument I directly relates to the statement about incubation centres and student awareness. Argument II is about the broader economy which is indirectly related.
Statement: Schools should encourage extra-curricular activities alongside academics. Arguments: I. Sports is a good career option. II. Activities enhance learning abilities. III. Activities help build skills.
All three arguments support the statement that extra-curricular activities are beneficial alongside academics.
The probability of having at least one girl and one boy in a family of four children (equal probability of male and female) is:
$P(\\text{at least one boy and one girl}) = 1 - P(\\text{all boys}) - P(\\text{all girls}) = 1 - (1/2)^4 - (1/2)^4 = 1 - 1/16 - 1/16 = 14/16 = 0.875$.
Find the distance between the points of intersection of the tangent to the hyperbola $xy = 1$ at $(2, 1/2)$ with the axes.
The tangent to $xy=1$ at $(2,1/2)$ is $x/2 + 2y = 2$ or $x + 4y = 4$. Intercepts: x-intercept = 4, y-intercept = 1. Distance = $\\sqrt{4^2 + 1^2} = \\sqrt{17}$.
If $\\alpha$ and $\\beta$ are roots of $px^2 + qx + r = 0$, then $(\\alpha^3 + \\beta^3) / (\\alpha^{-3} + \\beta^{-3})$ equals:
$(\\alpha^3+\\beta^3)/(\\alpha^{-3}+\\beta^{-3}) = (\\alpha^3+\\beta^3) / ((\\alpha^3+\\beta^3)/(\\alpha^3\\beta^3)) = \\alpha^3\\beta^3 = (r/p)^3 = r^3/p^3$.
If $1 \\leq x \\leq 3$ and $-8 \\leq y \\leq 16$, and the minimum value of $(x+y)/y$ is $a/b$, then:
$(x+y)/y = x/y + 1$. Minimum occurs at smallest $x$ and negative $y$ with largest magnitude: $x=1, y=-8$, giving $(1-8)/(-8) = 7/8$. So $a=7, b=8$. Checking options: $a+b=15$, $a^2+b^2=113$, $a-b=-1$, $a^2-b^2=49-64=-15$. The correct option is $a^2-b^2=-15$.
If the roots of $2x^3 - 3x^2 - 11x + 6 = 0$ are in arithmetic progression, find the greatest positive integer root.
If real numbers x, y, z satisfy $(x+y)^2 + (y+z)^2 + (z+x)^2 = 2(xy+yz+zx)$, find the value of $3x + 5y + 7z$.
Login identities use four distinct letters from the alphabet followed by a fixed number of digits. To generate 999 crore identities, how many digits should be in a login identity?
In 2014, what percentage (to nearest value) of persons of voting age were male?
Male voting age population = 61, total voting age = 115. Percentage = $61/115 \\times 100 = 53.04\\%$.
In 2009, how many females of voting age voted?
Female voting age population = 59 million, percentage voted = 69%. Number = $59 \\times 0.69 = 40.71$ million.
Over three elections (2009, 2014, 2019), what is the ratio of total votes cast by females to those by African-Americans?
Total female votes = (59×0.69)+(62×0.68)+(65×0.70) = 40.71+42.16+45.5 = 128.37. Total African-American votes = (15×0.56)+(18×0.54)+(20×0.52) = 8.4+9.72+10.4 = 28.52. Ratio ≈ 128.3:28.5.
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