Explore topic-wise InterviewSolutions in Current Affairs.

A² - 10A + 25

= A² - 5A - 5A + 25

= A(A - 5) - 5(A - 5)

= (A - 5) ( A - 5)

She should hold the umbrella a little inclined towards the west from the vertical.

The drops which are falling a little ahead of the current position of the woman, will fall on her, because she moves in that direction.

relative velocity of the rain drops wrt cyclist
   = velocity of woman - velocity of rain

the magnitude of relative velocity the rain drops  wrt  woman
     = √(12² + 35²) = 37 m/s

direction of relative velocity of the rain drops =
       = tan^-1 (12/35)  =  18.92  deg. from the vertical.

So the cyclist should hold the umbrella at 18.92 deg to the vertical in the forward direction.

The Banqiao Reservoir Dam (along with 63 other dams) in the Henan province of China failed in 1975, killing an estimated 171 000 people (although some reports suggest the number could be as high as 230 000). When the dam failed, it destroyed the homes millions of people and is considered the largest dam failure in history.

In August 1975, the region experienced an extreme flood, resulting in quantities of water falling that had not been considered during the construction of the dam. More than a year's worth of rain fell in only 24 hours, and the dam failed on August 8. Early on August 8, the dam was breached and 700 million cubic meters of floodwater was released, flooding communities and homes downstream. After this burst, a chain reaction began and the other 61 reservoirs located in the area collapsed—releasing another six billion cubic meters of floodwater. The water covered an area equal to 10,000 square kilometers. The failure to plan and account for extreme floodwaters resulted in the immediate death of 26,000 as a result of the water itself. 145 000 more people died as a result of epidemics and famine following the flood.

(b) Feed water 

(c) Induced draught 

If in an ionic crystal of type A+B− an equal number of cations and anions are missing from their lattice sites so that electrical neutrality, as well as stoichiometry, is maintained, then, this defect is called a Schottky Defect. The presence of holes causes the density of the crystal to decrease. It is a vacancy defect (due to missing ions) and also a stoichiometric defect, as the ratio of the number of cations and anions remains the same. The energy needed to form a Schottky defect is very less but the production of lattice defects of Schottky is an endothermic process. Hence the lattice energy increases. The defect increases the electrical conductivity of the solid due to a migration of the ions into the holes.

Correct option is (c) Nitrogen 

(a) 2405 kg/h 

Output = 35 MW

Heat input = \(\cfrac{35}{0.8}\) MW

Mass of fuel = \(\cfrac{35\times10^6}{0.8\times26\times10^6}\) = 1.682 kg/sec

Mass of sulphur = 0.036 × 1.682 = 0.06057 kg/sec

Moles of sulphur = \(\cfrac{0.06057}{32}\) = 0.001893

Moles of CaCO₃ = 3 × 0.001893 = 0.005679 kmoles/sec = 20.44 kmoles/hr 

Mass = 20.44 × 100 = 2044 kg/hr

Mass of CaCO₃ = \(\cfrac{2044}{0.85}\) = 2405 kg/hr

Correct option is (a) 40% 

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

p = probability of getting a heart = \(\frac{13}{52} = \frac14\)

q = 1 - p 

\(= 1 - \frac14 = \frac34\) 

n = 6

∵ P(x = r) = \(^n C_r p^rq^{n -r}\)

∴ P(x = r) = \(^6 C_r p^rq^{6 -r}\)

Required probability = \(P(x\ge 3)\) 

= P(x = 3) + P(x = 4) + P(x = 5) + P(x = 6)

\(=\, ^6 C_3 \left(\frac14\right)^3 \left(\frac34\right)^3 +\, ^6C_4\left(\frac14\right)^4 \left(\frac34\right)^2 + \,^6C_5\left(\frac14\right)^5\left(\frac34\right)+\,^6C_6\left(\frac14\right)^6\)

\(= \frac{6.5.4}{3.2.1}\times \frac{27}{4^6}+ \frac{6.5}{2.1}\times \frac9{4^6}+ 6\times \frac{3}{4^6}+ \frac1{4^6}\)

\(= \frac1{4^6}(540 + 135 + 18 + 1)\)

\(= \frac{694}{4096} \)

\(= \frac{347}{2048}\)

\(\lim\limits_{x\to 0}\frac{12^x - 3^x - 4^x + 1}{x\, sinx} \)     \(\left(\frac 00-case\right)\)

\(= \lim\limits_{x\to0} \frac{12^x log 12 - 3^x log3 -4^xlog4 }{x\, cos x + sinx}\)    \(\left(\frac 00-case\right)\) 

(By using D.L.H. Rule)

\(= \lim\limits_{x\to0} \frac{12^x (log 12)^2 - 3^x (log3)^2 -4^x(log)^2}{-x\, sin x + 2cosx}\)  (By using D.L.H. Rule)

\(= \frac{(log12)^2 - (log3)^2-(log4)^2}{2}\)

\(= \frac{(log 3 + log 4)^2-(log3)^2 - (log4)^2}{2}\)

\((\because log12 = log(3 \times 4) = log 3 + log 4)\)

\(= \frac{2log3 \,log4}{2}\)

\(= log3 \,log4\)

\(\therefore \lim\limits _{x\to 0} \frac{12^x - 3^x - 4^x+1} {x\, sinx}= log3\,log4 \)

(i) \((4 - i) (3 - 5i)\)

\(= 12 + 5i^2 -3i - 20i\)

\(= 7 - 23i\)       (\(\because i^2 = -1\))

(ii) \((4 + i)(3 - i)\)

\(= 12 - i^2 + 3i - 4i\)

\(= 13 - i\)

Given (a + b + c) = 9 and (ab + bc + ca) = 26
(a + b + c)² = 92
⇒ a² + b² + c² + 2(ab + bc + ca)  = 81
⇒ a² + b² + c² + 2(26)  = 81
⇒ a² + b² + c² + 52  = 81
⇒ a² + b² + c²   = 81 − 52 

= 29

(i)so -3-2=-5

(ii) so-3+2=-1

X³ - 3x² - 9x - 5

= x³ + x² - 4x² - 4x - 5x - 5

= x²( x + 1) - 4x ( x + 1) - 5(x + 1)

= (x + 1)(x² - 4x - 5)

= (x + 1)(x² -5x + x - 5)

= (x + 1)(x - 5) (x + 1)

Hence, (x +1), (x -5) and (x +1) are the factors of given polynomial .

We have,

\(0.041 = \frac{0.041}{1}\)

\(= \frac{0.041\times 1000}{1 \times 1000}\)   [Multiply both numerator and denominator by 1000]

\(= \frac{41}{1000}\)

The three different classifications of decimal expansion are terminating decimals, non-terminating repeating decimals and non-terminating non-repeating decimals.

10/3=3.333333333

\(\text{Total no. of parts } = \frac{\text{Length of the rope}}{\text{Length of one equal part}}\)

\(= \cfrac{24}{\frac6{11}} \)

\(=24\times \frac{11}6 \)

\(= 44\)

Hence, rope of length 24 m long is cut into 44 equal parts of length \(\frac6{11}\)m.

add answer pls

Average = \(\frac{a + b}2\)

\(= \cfrac{\left(\frac{-8}9\right)+ \left(\frac{-5}3\right)}{2} \)

\(= \frac{-8 - 15}{18}\)

\(= \frac{-23}{18}\)

A rational number is terminating if it can be expressed in the form:

p/(2ⁿ×5^m)

The prime factorization of 25 is 5×5

11/25=11/(2⁰×5²)

Answer: 11/25 is a terminating rational number.

Average = \(\frac{a+ b}2\)

\(= \cfrac{\frac37 + \frac46}{2}\)

\(= \frac{18 + 28}{84}\)

\(= \frac{46}{84}\)

\(= \frac{23}{42}\)

A rational number is terminating if it can be expressed in the form:

p/(2ⁿ×5^m)

The prime factorization of 25 is 5×5

11/25=11/(2⁰×5²)

Answer: 11/25 is a terminating rational number.

\(\frac{2\sqrt5}{2\sqrt3 - 3\sqrt5}\)

\(= \frac{(2\sqrt5)(2\sqrt3 + 3\sqrt5)}{12 - 45}\)

\(= \frac{4\sqrt{15}+ 30}{-33}\)

Correct option (a) T/12

(7+√3)(5+√2)

= 35 +7√2 + 5√3 + √6

c) gradation in physical properties

Correct option (b) 10

Correct option is C) remote control

Aquarium and farm house, are artificial or man made ecosystem.

Organic ecosystems- ocean, amazon rainforest, national parks, coral reefs

1/√10 x √10/√10 + √10
= √10/10 + √10
= (√10+10√10)/10
= 11√10/10
= 11 x 3.162/10
= 3.4782

\(\frac{1}{\sqrt{10}} + \sqrt{10}\)

= \(\frac{1}{\sqrt{10}} \times \frac{\sqrt{10}}{\sqrt{10}} + \sqrt{10}\)

= \(\frac{\sqrt{10}}{10} + \sqrt{10}\)

= \(\sqrt{10} + 10\sqrt{10}\over10\)

= \(11\sqrt{10} \over10\)

= \(11 \times 3.162\over10\)

= \(34.782\over10\)

= 3.4782

Correct option is B) sort out

Correct option is D) teaspoon

Hydra is the organism which can reproduce by both budding and regeneration. The most common form of reproduction is budding in which a genetically identical new organism grows attached to the body of parent and separates later on when they get matured. However, they reproduce by regeneration also where they get cut into fragments and each fragment grows into a new individual.

The Correct option is (C)

Correct option is E) liven

The teacher asked the students," Are you ready for the test?"

Correct option (A) Titan

Explanation: 

All except Titans are planets of the solar system.