Explore topic-wise InterviewSolutions in .

This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.

1.

Name the valve between left atrium and left ventricle and give its significance .

Answer» Bicuspid valve or Mitral valve. It prevents back flow or maintains unidirectional flow of blood.
Discussion
2.

Show that a homogeneous equations of degree two in x and y , i.e., `ax^(2) + 2 hxy + by^(2) = 0` represents a pair of lines passing through the origin if `h^(2) - 2ab ge 0`.

Answer» Let us consider a homogeneous equation of degree two in x and y .
i.e., ` ax^(2) + 2 hxy + by^(2) = 0` ….(1)
where, either a or b or h is non - zero .
We consider two cases :
Case 1 : If b = 0 , then equation becomes
` ax^(2) + 2 hxy = 0`
` x (ax + 2hy) = 0`
which is a joint equation of lines x = 0 and ax + 2hy = 0 thus , the lines pass through the origin.
Case 2 : If ` b ne 0`.
Multiplying both sides of quation (1) by b , we get
` abx^(2) + 2hbxy + b^(2) y^(2) = 0`
`b^(2)y^(2) + 2hbxy = - abx^(2)`
`b^(2)y^(2) + 2 hbxy + h^(2)x^(2) = - abx^(2) + h^(2) x^(2)`
` (by +hx)^(2) = (h^(2)-ab) x^(2)`
`(by + hx)^(2) = [(sqrt(h^(2)-ab))x]^(2)`
`(by+hx)^(2)-[(sqrt(h^(2)-ab))x]^(2) = 0`
`[(by+hx)+(sqrt(h^(2)-ab))x][(by+hx)]-(sqrt(h^(2)-ab))x)`
= 0
which is a joint equation of two lines
`(by+hx)+(sqrt(h^(2)-ab)) x = 0`
and ` (by+hx)-(sqrt(h^(2)-ab)) x = 0`
i.e., `(h+sqrt(h^(2)-ab)) x + by = 0 and (h - sqrt(h^(2)-ab)) x +by = 0 `
These lines passes through the origin when `h^(2) - ab ge 0` .
Hence, we can say that the equation `ax^(2) + 2hxy + by^(2) = 0` represents a pair of lines passing through the origin.
Discussion
3.

Find the principal value of `sec^(-1)(2/sqrt3)`A. `pi/3, (11 pi)/6`B. `pi/6, (11 pi)/6`C. `pi/6, (11pi)/4`D. `pi/6, (11pi)/4`

Answer» Correct Answer - B
Given, ` sec x = 2/sqrt3 `
` :. " " sec x = sec (pi/6)`
` sec x = sec (2pi - pi/6)`
` = sec ((11 pi)/6)`
such that ` 0 lt pi/6 lt 2 pi and 0 lt (11 pi)/6 lt 2 pi `.
` :. ` Principal solutions are ` x = pi/6 and x = (11 pi)/6`
Hence, the correct answer from the given alternatives is (b) .
Discussion
4.

Find the vector equation of the plane passing through the point `A(1, 0, 1), B(1,-1,1) and C (4,-3,2)`

Answer» Let `bara, barb, barc` be the position vectors of points A, B, C respectively.
`:. " " bara=hati+hatk, barb=hati-hatj+hatk, barc`
` = 4 hati-3hatj+2hatk.`
` :. bar(AB) = barb - bara = (hati-hatj+hatk) - (hati+hatk)`
` = - hatj`
` bar(AC) = barc-bara = (4hati-3hatj+2hatk) - (hati+hatk)`
` = 3 hati-3hatj+hatk`
` :. bar(AB) xx bar(AC) = |(hati,hatj,hatk),(0,-1,-0),(3,-3,1)|`
`= hati (-1+0) - hatj(0) + hatk(0+3)`
` = - hati + 3 hat k.`
Therefore , vector equation of the required plane is , `barr*(bar(AB) xx bar(AC)) = bara(bar(AB) xx bar(AC))`
` rArr barr * (-hati+3 hatk)=(hati+hatk) *(-hati+ 3 hatk)`
`rArr barr * (-hati+3 hatk) = 1 (-1) + 1 (3)`
` rArr barr*(-hati+3hatk) = - 1 + 3 =2`
` rArr barr * (-hati+ 3 hatk) = 2`
This is the required vector equation of the plane.
Discussion
5.

The measure of acute angle between the lines whose direction ratios are `3, 2, 6 and `-2, -1, 2` isA. `cos^(-1)(1/7)`B. `cos^(-1)(8/15)`C. `cos^(-1)(1/3)`D. `cos^(-1)(8/21)`

Answer» Correct Answer - D
Here , ` a_(1) = 3, b_(1) = 2, c_(1) = 6 and a_(2) = - 2, b_(2) = 1, c_(2) = 2`.
We have,
`cos theta = |(a_(1)a_(2)+b_(1)b_(2)+c_(1)c_(2))/(sqrt(a_(1)^(2)+b_(1)^(2)+c+_(1)^(2.))sqrt(a_(2)^(2)+b_(2)^(2)+c_(2)^(2)))|`
`:. cos theta = |(3(-2)+2(1)+6(2))/(sqrt(3^(2)+2^(2)+6^(2.))sqrt((-2)^(2)+1^(2)+2^(2)))|`
` = |(-6+2+12)/(sqrt(49)*sqrt9)|`
` = |8/(7 xx 3)| = |8/21|`
` :. " " theta = cos^(-1) (8/21)` .
Hence , the correct answer from the given alternatives is (d) .
Discussion
6.

Find the vector equation of the line which passes through the point with position vector `4hati - hatj + 2 hat k` and is in the direction of ` - 2hati + hatj + hat k`.

Answer» The vector equation of a line passing through a point with position vector `bar a` and parallel to ` bar b` is given by ` bar r = bar a + lambda bar b`
Here, ` bar a = 4hati - hatj + 2hatk and bar b = - 2 hat I + hat j + hat k`.
Hence , the required vector equation is
`barr = (4hati- hatj+2hatk)+ lambda(-2hati+hatj+hatk)`
Discussion
7.

Write the negations of the following statements : (a) All students of this college live in the hostel . (b) 6 is an even number or 36 is a perfect square.

Answer» (a) Some students of this college do not live in the hostel .
(b) 6 is not an even number and 36 is not a perfect square.
Discussion
8.

Find the distance of the point `(1, 2-1)` from the plane `x -2y + 4z - 10 = 0`.

Answer» The distance of the point `(x_(1), y_(1), z_(1))` from the plane ` ax + by + cz + d = 0` is given by
` |(ax_(1) + by_(1) + cz_+(1) + d)/(sqrt(a^(2) + b^(2) + c^(2)))|`
Here, ` (x_(1) , y_(1) , z_(1)) = (1, 2, -1) and a= 1, b = - 2, c = 4, d = - 10 .`
` :. ` The required distance = `|(1 xx1 + 2 xx (-2) + 4 (-1) - 10)/(sqrt(1^(2) + (-2)^(2) + 4^(2)))|`
` = |(1 - 4 - 3 - 10)/sqrt(1 + 4 + 16)|`
` = |(-17)/21|`
` = 17/sqrt21 ` units.
Discussion
9.

If a line makes angles `alpha, beta, gamma` with the coordinate axes, prove that `cos2alpha + cos 2beta + cos2gamma + 1 = 0`.

Answer» `alpha , beta and gamma ` are the angles made by the line with the coordinate axes .
` :. ` We have ,
`cos^(2) alpha + cos^(2) beta + cos^(2) gamma = 1 ` ….(1)
Now, L.H.S. = ` cos 2 alpha + cos 2 beta + cos 2 gamma + 1 `
` = (2 cos^(2) alpha - 1) + (2 cos^(2) beta -1) + (2 cos^(2) gamma - 1) + 1`
` = 2 ( cos^(2) alpha + cos^(2) beta + cos^(2) gamma) - 3 + 1`
` = 2 * (1) - 2` [from (1)]
` = 2-2`
= 0= R.H.S.
` :. cos 2 alpha + cos 2 beta + cos 2 gamma + 1 = 0`.
Discussion
10.

What is primary treatment of sewage?

Answer» It is a physical process and involves removal of large pieces of floating debris, oily substances etc., through filteration and sedimentation.
Discussion
11.

Give two examples of microbial pesticides with their hosts

Answer» Pathogen`" "`Host range
(a) Bacteria: Bacillus thuringiensis `rarr` Caterpillars, larve of sedes, black files, some adult beetles, wax mohs etc.
(b) Fungi: Beauveria bassiana `rarr` Aphids, mealy bugs mites, white files etc.
Discussion
12.

Deforestation.

Answer» The permanent removal, decrease or deterio- ration of forests and woodlands is called deforestation.
Discussion
13.

In a food chain, the herbivores are represented byA. producersB. primary consumersC. secondary consumsersD. decomposers

Answer» Correct Answer - B
Discussion
14.

………..is used for desalination of brackish water.A. Reverse osmosisB. Ion-exchangeC. AdsorptionD. Electrodialysis

Answer» Correct Answer - A
Discussion
15.

The phenotypic ratio of incomplete dominance isA. `1:1`B. `3:1`C. `1:2:1`D. `9:3:3:1`

Answer» Correct Answer - C
Discussion
16.

Nucleoside is a nucleotide without ........A. sugarB. nitrogen baseC. hydrogen. bondD. phosphate group

Answer» Correct Answer - D
Discussion
17.

The enzymes required for synthesis of ATP are located on ........A. oxysomesB. cristaeC. matrixD. ribosomes

Answer» Correct Answer - A
Discussion
18.

The reaction centre of P. S. II is ........A. Chl-a, 700B. Chl-a, 680C. Chl-a, 673D. Chl-a, 650

Answer» Correct Answer - B
Discussion
19.

Brown rust of wheat is caused by ...........A. virusesB. bacteriaC. fungiD. aphids

Answer» Correct Answer - C
Discussion
20.

Which of the following is white button mushroom ?A. Agaricus bisporusB. PleurotusfloridaC. Volvariella volvaceaD. Candida species

Answer» Correct Answer - A
Discussion
21.

What is leaching ?

Answer» Water soluble inorganic nutrients go down into the soil horizon and get precipitated as salts, this prosess is called leaching.
Discussion
22.

Give the microbial source of Vit. `B_(12)`

Answer» Pseudomonas denitrificans.
Discussion
23.

Enlist the basic steps involved in recombinant DNA technology.

Answer» (a) Isolation.
(b) Fragmentation
(c) Screening
(d) Cloning vector
(e) Introducing recombinant vector into competent host cell
(f) Culturing (g) Expression of desired genes.
Discussion
24.

Describe different steps involved in tissue culture technique.

Answer» (a) Explant Culture :
1. Proper explant is excised from the plant which may be cell, tissue ot a piece of plant organ.
2. Parenchyma tissue or Meristem is used as explants.
3. It is sterilized properly and placed on solid nutrient medium.
4. The cells from explant absorb ntutrients and start multiplying.
(b) Callus formation and its culture :
1. Explant forms uhorganised mass of cells or callus.
2. It has thin walled parenchyma cells.
3. Cells divided by mitosis.
4. Cells are identical.
(c) Organogenesis: Auxins, cytokinins induce organ formation. If auxins are more, roots are formed. If cytokinins are more, shoot system develops.
(d) Formation of cell or suspension culture :
1. Callus is transferred to liquid nutrient medium and agitated.
2. Agitation is carried out constantly at 100-250 rpm.
3. Agitation serves the purpose of aeration mixing of medium and prevents the aggregation of cells.
4. Suspension culture grows much faster than callus culture.
Discussion
25.

Find the variance and standard deviation of the random variable X whose probability distribution is given below : `{:(x,0,1,2,3),(P(X=x),1/8,3/8,3/8,1/8):}`

Answer» ` E(X) = sum p_(i) x_(i) `
` = 1/8 xx 0 + 3/8 xx 1 + 3/8 xx 2 + 1/8 xx 3`
` = 3/8 + 6/8 + 3/8 = 12/8 = 3/2`
` E(X^(2)) = sum p_(i)x_(i)^(2)`
` - 1/8 xx 0^(2) + 3/8 xx 1^(2) + 3/8 xx 2^(2) + 1/8 xx 3^(2) `
` = 0 + 3/8 + 12/8 + 9/8 = 24/8 = 3`
Var (X) = `E (X^(2)) - [E(X)]^(2)`
` = 3 - (3/2)^(2)`
` = 3 - 9/4 = (12 - 9)/4 = 3/4 `
Standard deviation, `sigma = sqrt("Var(X)") = sqrt(3/4)`
`sigma = sqrt3/2`
` :. " " Var (X) = 3/4 , sigma = sqrt3/2`
Discussion