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Moth

Moths are pollinating agents those are not attracted towards scent of flowers and the process by which they pollinate is known as phalaenophily.

Failure of fruit formation in rose may be due to several reasons. Some of the likely reasons are:
a. Rose plants may not produce viable pollen.
b. Rose plants may not have functional egg.
c. Rose plants may have abortive ovules.
d. Being hybrids, the meiotic process may be abnormal resulting in non-viable gametes.
e. There may be self-incompatibility.
f. There may be internal barriers to pollen tube growth and/or fertilisation.

Failure of fruit formation in rose may be due to several reasons. Some of the likely reasons are:

 a. Rose plants may not produce viable pollen.

 b. Rose plants may not have functional egg.

 c. Rose plants may have abortive ovules.

 d. Being hybrids, the meiotic process may be abnormal resulting in non-viable gametes.

 e. There may be self-incompatibility. f. There may be internal barriers for pollen tube growth and/or fertilisation.

Rose plants produce large, attractive bisexual flowers, but they seldom produce fruits. The reasons for failure of fruit formation in rose are as follows (i) Rose plants may not produce viable pollens, hence, no fertilisation can take place.

The correct answer is: (a) Shrinks

(c) Touching

(c) 30 to 300 MHz

(b) Low input capacitance

Correct option (B) low input impedance and high output impedance

Explanation:

Ideal current buffer has Z_i = 0

Z₀ = ∞

Correct option (B) voltage-current feedback  

Explanation:

Output sample is voltage and is added at the input or current 

∴ It is voltage – shunt negative feedback i.e, voltage-current negative feedback

f = 5KHz

Cut off frequency (LPF) = 18/2πR₂C = 5KHz

⇒ R₂ = 1/(2π x 5 x 10³ x 10 x 10^-9) = 3.18kΩ

S = (n/2)(a + (n-1)*d) 

where , 

S = Sum of terms, 

n = Number of terms, 

a = First term, 

d = Common difference

Given

Speed of train = 63 kmph

Time = 20 min

Formula

Distance = Speed × Time

Calculation

20 min = 20/60 = 1/3 hr

∴ Distance = 63/3 = 21 km = 21000 meter

x(t) is band limited to [−500Hz, 500Hz] 

y (t) is band limited to [1000Hz, 1000Hz]

z(t) = x (t) .y(t)

Multiplication in time domain results convolution in frequency domain.

The range of convolution in frequency domain is [−1500Hz, 1500Hz] 

So maximum frequency present in z(t) is 1500Hz Nyquist rate is 3000Hz or 3 kHz 

Given:

Speed of man = 8 km/hr.

Distance = 6 km

Time of rest = 4 minute

Formula used:

Speed = Distance/Time

Calculations:

⇒ 8 km distance covered by man = 1 hours

⇒ 8 km distance covered by man = 60 minutes

⇒ 1 km distance covered by man = 60/8 minute + 4 minute (rest )

⇒ 5km distance covered by man = 300/8 minute + 20 minute

⇒ Last 1 km distance = 60/8 minutes

⇒ Total time taken by him = (300/8) + (60/8) + 20

⇒ Total time taken by him = 65 minutes

∴ It will take 65 minutes to cover a distance of 6 km.

Correct option (D) not periodic

Explanation:

Assume x [n] to be periodic, (with period N)

⇒ x[n] = x [n + N]

⇒ sin(π²n) = sin(π²(n + N))

Every frigonometric function repeate after 2π interval.

⇒ 2πk = π²N ⇒ N = (2k/π)

Since ‘k’ is any integer, there is no possible value of ‘k’ for which ‘N’ can be an integer, thus non-periodic.

Given circuit is a Ripple (Asynchrnous) counter. In Ripple counter, o/p frequency of each flip-flop is half of the input frequency if their all the states are used otherwise o/p frequency of the counter is 

=  input frequency/modulus of the counter

So, the frequency at Q₃ = input frequency/16

= ((1 x 10⁶)/16)H_z = 62.5kHz 

Correct option (A) X

Explanation:

Given Boolean Expression is (x + y)(x + bar y)+ bar(xy  + x)

As per the transposition theorem

(A + BC) = (A + B)(A + C)

So, (x + y)(x + bar y) = x + y bar y = x + 0

(x + y)(x + bar y) + bar (xy + x) = x + bar(xy).x

= x + (bar x + y).x = x + bar xx + y.x = x + 0 + y.x

Apply absorption theorem = x(1 + y) = x.1 = x

Let the original time taken by Surbhi to reach point B from point A = t hours

Then, original time taken by Pragati to reach point B from point A = (t – 1.5) hours

Also, let original speed of Pragati = v km/hr

So, the distance between point A and B = v × (t – 1.5) = (v – 6) × (t – 1) = 45t      ---- (1)

\Rightarrow v/(v – 6) = (t – 1)/(t – 1.5)

\Rightarrow v/6 = (t – 1)/0.5      {applying a/b = c/d \Rightarrow a/(a – b) = c/(c – d)}

\Rightarrow v = 12(t – 1)      ---- (2)

From eq. (1) and eq. (2)

\Rightarrow 12(t – 1)(t – 1.5) = 45t

\Rightarrow 4(t² – 2.5t +1.5) = 15t

\Rightarrow 4t² – 10t + 6 = 15t

\Rightarrow 4t² – 25t + 6 = 0

\Rightarrow 4t² – 24t - t + 6 = 0

\Rightarrow 4t(t – 6) – (t – 6) = 0

\Rightarrow (4t – 1)(t – 6) = 0

\Rightarrow t = ¼ or t = 6

Since t > 1, so t = ¼ not possible, thus t = 6

Let the age of Rajesh, Jayant and Basu be 5x, 7x and 3x respectively

The age of Jayant 1 year later will be twice the age of Basu 4 years later

⇒ 7x + 1 = 2 (3x + 4)

⇒ 7x + 1 = 6x + 8

⇒ x = 7

Sum of age of all three persons = 5x + 7x + 3x = 15 × 7 = 105

∴ Sum of age of all three persons 5 years back

⇒ 105 – 3 × 5 = 105 – 15 = 90

∴ Sum of age of all three persons 5 years back is 90

Given:

126 + 10√5

Formula used:

(a + b)² = a² + b² + 2ab

Calculation:
126 + 10√5

10√5 = 2 × 1 × 5√5

Let a = 1 , b = 5√5

⇒ (a + b)² = a² + b² + 2ab

⇒ (1 + 5√5)² = 1 + 125 + 2 × 1 × 5√5

⇒ (1 + 5√5)² = 126 + 10√5

⇒ √(126 + 10√5) = √(1 + 5√5)²

⇒ √(126 + 10√5) = 1 + 5√5

∴ The square root of (126 + 10√5) is (1 + 5√5).

Calculation 

Let the number added be x 

⇒ (53/44) + x = (169/88)

⇒ x = (169/88) - (53/44) = (63/88)

∴ The required answer is 63/88

Given:

Numbers are 12384, 12358, 12368,12376

Concept Used:

A number is divisible by 6 if its last digit is an even number or zero and the sum of the digits is a multiple of 3.

Calculation:

All the four given number's last digits are even that is 4, 8, 8, 6 respectively 

Now, sum of digits 

Option 1) 12384 

⇒ 1 + 2 + 3 + 8 + 4 = 18

⇒ 18 is a multiple of 3 

⇒ 12384 is divisible by 6

Option 2) 12358 

⇒ 1 + 2 + 3 + 5 + 8 = 19

⇒ 19 is not a multiple of 3

⇒ 12358 is not divisible by 6

Option 3) 12368 

⇒ 1 + 2 + 3 + 6 + 8 = 20  

⇒ 20 is not a multiple of 3

⇒ 12368 is not divisible by 6

Option 4) 12376

⇒ 1 + 2 + 3 + 7 + 6 = 19

⇒ 19 is not a multiple of 3

⇒ 12376 is not divisible by 6

∴ 12384 is divisible by 6

Given:

Prime pairs between 100 and 200

Concept Used:

A twin prime is the prime number that is either two less or two more than the another prime number.

Calculation:

Prime numbers between 100 and 200 are :

101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199

The prime pairs whose difference is 2 are : (101, 103), (107, 109), (137, 139), (149, 151), (179, 181), (191, 193), (197, 199)

⇒ There are 7 such pairs.

∴ The number of twin prime pairs between 100 and 200 are 7.

Given:

X, Y, and Z together can complete the work = 15 days

X and Y can complete the work = 30 days

Formula used:

W = E × T

(Where W = The work, E = The efficiency, and T = Time)

Calculation:

Let us assume Z alone can complete the work in X days

⇒ The efficiency of X, Y, and Z = \({1\over 15}\)

⇒ The efficiency of X and Y = \({1\over 30}\)

⇒ The efficiency of Z = \({1\over X}\)

⇒ \({{1\over 30}\ +\ {1\over X}}\ =\ {1\over 15}\)

⇒ By solving the value of X

⇒ X = 30 days

∴ The required result will be 30 days.

Given 

Quotient = 125 

Divisor = 28 

Formula Used 

Dividend = divisor × quotient + remainder 

Calculation 

Dividend = 28 × 125 + 13 = 3513 

∴ The required answer is 3513 

GIVEN:

The number “x” is divided by 16, the remainder is 14.

CONCEPT:

Dividend = (Divisor × Quotient) + Remainder

CALCULATION:

According to question –

⇒ x = 16k + 14

If we square the same number, then, the remainder will be –

Remainder of (16k + 14)²/16

⇒ Remainder of 256k² + 196 + 2 × 16k × 14

⇒ Remainder of 16(16k² + 28k) + 196

First part is divisible by 16 so the remainder the will be 196/16

⇒ Remainder of 196/16

196 = 16 × 12 + 4

∴ Remainder is 4

Let the required wages be Rs. x.

More men, More wages (Direct Proportion) 

Less days, Less wages (Direct Proportion) 

Men 6: 9 : :2100:x 

Days 15:12 

Therefore (6 x 15 x)=(9 x 12 x 2100) 

x=(9 x 12 x 2100)/(6 x 15)=2520 

Hence the required wages are Rs. 2520.

Given:

4 men + 8 boys, build a wall in 5 days

2 men + 6 boys, build a wall in 8 days.

Formula Used:

(m1 × d1 × t1 × e1/w1 × c1) = (m2 × d2 × t2 × e2/w2 × c2)

m = number of men required to complete the work

d = number of days required to complete the work

t = time used for work in a single day

e = efficiency of man

w = amount of work

c = consumption of a man 

Calculation:

Using the above formula,

⇒ (4m + 8b) × 5 days = (2m + 6b) × 8 days

⇒ 20m + 40b = 16m + 48b

⇒ 20m – 16m = 48b – 40b

⇒ 4m = 8b

⇒ m : b = 2 : 1

The efficiency of a Man and a Boy is 2, and 1 respectively.

Now the same wall built by 2 men and 4 boys

Let the number of days required be x days

⇒ (4m + 8b) × 5 days = (2m + 4b) × x

⇒ {4(2) + 8(1)} × 5 = {2(2) + 4(1)} × x

⇒ (8 + 8) × 5 = (4 + 4) × x

⇒ x = (16 × 5)/8

⇒ x = 10

∴ The number of days taken by 2 men and 4 boys to build the same wall is 10 days.

Let the required length be x metres

More men, More length built (Direct Proportion)

Less days, Less length built (Direct Proportion)

Men 20: 35 Days 6: 3 : : 56 : x 

Therefore (20 x 6 x x)=(35 x 3 x 56)

x=(35 x 3 x 56)/120=49 

Hence, the required length is 49 m.

Given:

To build a house in 50 days 138 people are needed

Calculation:

⇒ Total work is done = 50× 138 unit

⇒ Work is done by 207 men in 20 days = 207× 20

The fraction of work done by 207 men = (207× 20)/(50× 138)

∴ 3/5  

Correct option is C) at 

Correct option is A) went 

Correct option is A) at 

d.All of the above

Correct option is B) on 

b.Peak load period

Correct option is B) on 

Correct option is C) of 

Correct option is C) on

Correct option is A) on 

Correct option is A) because 

Correct option is C) when 

Correct option is A) had had

Correct option is B) until 

Correct option is C) bed

Correct option is D) had