Shanu Singhal: Tutoring for Knowledge Excellence

Answer

Total students = 152 

Passed in prelims = 63

Passed in both prelims and mains = 32

Let draw a venn diagram for it. 

From venn diagram it is clear that 31 students passed prelims only. 

Answer

Red balls = 4

White balls = 6

Green balls = 8

Black balls = 10

Total balls = 4+6+8+10=28

One ball is drawn at random. 

Probability that the ball is black = number of black balls/ total balls 

                                                  = 10/28 = 5/14

Answer

Total oranges = 12

rotten oranges = 1/3 * 12 = 4

So 4 oranges are rotten. 

Now 4 oranges are taken out and we have to find the probability that all are orange is rotten.

First we take out one orange and probability of its being rotten = 4/12

Second we take out another orange and probability of its being rotten = 3/11

Third we take out another orange and probability of its being rotten = 2/10

Fourth we take out another orange and probability of its being rotten = 1/9

So overall probability = 4/12*3/11*2/10*1/9 = 1/495

Answer

Given set of numbers = {1,2,3,4,....,100}

Total numbers = 100

Numbers that are square = {1,4,9,16,25,36,49,64,81,100} 

So, there are 10 numbers that are square. 

Numbers that are cube = {1,8,27,64} 

So, there are 4 numbers that are cube. But in these 4 numbers, 2 numbers (1 and 64) are square also. So we will count them once. 

So total required numbers = 10+4-2=12

Probability = 12/100 = 3/25

Answer

Since we have given that product of zeros is equal to 1/7. 

Let consider a general polynomial -- ax2+bx+c=0

the product of zeros of this polynomial = c/a

Now let consider all options one by one. 

option 1 -- a = 1, b = 8, c = 7

c/a = 7/1 = 7

option 2 -- a = 1, b = 7, c = 8

c/a = 8/1 = 8

option 3 -- a = 7, b = 8, c = 1

c/a = 1/7

option 4 -- a = 7, b = 1, c = 8

c/a = 8/7

Hence option (3) is correct answer. 

Answer

Equation of a polynomial whose zeroes are p and q is following -- 

x2 - (p+q)x + pq = 0

Since we have given that sum of zeroes (p+q) = -3/2

product of zeroes (pq) = -1

x2 - (-3/2)x + (-1) = 0

x2 + (3/2)x + (-1) = 0 

2x2 + 3x - 2 = 0 

Hence option (2) is correct. 

Answer

Given polynomial is -- x2 + 2x - 35 = 0

one zero = 5

Let other zero = p

Consider a general polynomial ax2+bx+c = 0.

Sum of zeroes of this polynomial = -b/a

Comparing to given polynomial --- a = 1, b = 2, c = -35

5 + p = -2/1

5 + p = -2

p = - 2 - 5

p = -7

Hence other zero is -7.

Answer

Hence for maximum i, freezing point would be lowest. 

Hence answer is option (A) Aluminium sulphate. 

Answer

In a unit cell, an atom present at corner contributes 1/8 th part of whole atom. 

Number of corners in a unit cell = 8

So number of A = 1/8 * 8 = 1

In a unit cell, an atom present at side edge contributes 1/4 th part of whole atom. 

Number of edges in a unit cell = 12

So number of B = 1/4 * 12 = 3

So formula -- AB3

Answer

Since there are two bone pairs and two lone pairs. So hybridization is sp3. 

So according to hybridization, bond angle should be 109 degree 28 minutes. But there are two lone pairs which reflect each other and bond angle becomes 105 degree.