IIT JEE & NEET Question Bank with Solution

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Q.1. Least pore size seen in

A) Clayey soil

B) Sandy soil

C) Loamy soil

D) Gravelly soil

Q.2. Which one is a transported soil

A)Alluvial

B) Colluvial

C) Black soil

D) Both (A) and (B)

Q.3. The Environment Protection Act of Government of India was passed in

A) 1976

B) 1986

C) 1966

D) 1996

Q.4. E. P. Odum is a leading

A) Mycologist

B) Ecologist

C) Physiologist

D) Bryologist

Q.5. There is no life on moon because there is no

A) Water

B) Oxygen

C) Nitrogen

D) Carbon

Q.6. The swimming fishes comprise

A) Nektons

B) Benthos

C) Planktons

D) Neustons

Q.7. Taj Mahal is threatened due to the effect of

A) Chlorine

B) Sulphur dioxide

C) Oxygen

D) Hydrogen

Q.8. Safe limit of water fluoride level is

A) $0.1 cross times 0.4 space mg divided by litre$

B) $0.5 cross times 0.8 space mg divided by litre$

C) $0.9 cross times 1.2 space mg divided by litre$

D) $1.3 cross times 1.6 space mg divided by litre$

Q.9. Which plant is found in mangrove zone?

A) Rhizophora

B) Acacia

C) Pinus

D) Tectona grandis

Q.10. Which part of body is first to be affected by nuclear radiation ?

A) Bone marrow

B) Liver

C) Lungs

D) Brain

Q.1. If a line lies in the octant OXYZ and It makes equal angles with the axes, then [ MP PET 1988 ]

A) $I equals m equals n equals fraction numerator 1 over denominator square root of 3 end fraction$

B) $I equals m equals n equals plus-or-minus fraction numerator 1 over denominator square root of 3 end fraction$

C) $I equals m equals n equals negative fraction numerator 1 over denominator square root of 3 end fraction$

D) $I equals m equals n equals plus-or-minus fraction numerator 1 over denominator square root of 2 end fraction$

Q.2. If the co-ordinates of the points P, Q, R, S be (1, 2, 3), (4, 5, 7), (-4, 3, -6) and (2, 0, 2) respectively, then

A) $P Q space parallel to space R S$

B) $P Q space perpendicular R S$

C) $P Q equals R S$

D) None of these

Explanation-

Find angle between the lines PQ and RS, we get that neither $P Q space parallel to space R S$ nor $P Q space perpendicular R S$ . Also, $P Q not equal to R S.$

Q.3. The co-ordinates of a point in the xy plane which is equidistant from the three points A, B and C whose position vectors are i, j and k, is

A) (1, 1, 0)

B) (0, 0, 0)

C) (0, 1, 0)

D) (1, -1, 0)

Explanation-

A point has the same distance from points A, B and Cin xy plane because point is on the origin whose coordinate is (0, 0, 0).

Q.4. The equation of a line passing through the point (- 3, 2, - 4) and equally to the axes, are

A) $x minus 3 equals y plus 2 equals z minus 4$

B) $x plus 3 equals y minus 2 equals z plus 4$

C) $fraction numerator x plus 3 over denominator 1 end fraction equals fraction numerator y minus 2 over denominator 2 end fraction equals fraction numerator z plus 4 over denominator 3 end fraction$

D) None of these

Explanation-

Required equation of line is

$fraction numerator open parentheses x plus 3 close parentheses over denominator 1 end fraction equals fraction numerator y minus 2 over denominator 1 end fraction equals fraction numerator z plus 4 over denominator 1 end fraction.$

Q.5. A plane making intercepts of lengths 1, 2, 3 on the rectangular coordinate axes is represented by the equation [ MP PET 2007 ]

A) $x plus y divided by 2 plus z divided by 3 equals 1$

B) $x plus 2 y plus 3 z equals 1$

C) $x minus 1 equals y minus 2 equals z minus 3$

D) None of these

Explanation-

Formula $x over a plus y over b plus z over c equals 1 rightwards double arrow x over 1 plus y over 2 plus z over 3 equals 1.$

Q.6. The direction cosines of three lines passing through the origin are $l subscript 1 comma space m subscript 1 space comma n subscript 1 space semicolon space l subscript 2 comma space m subscript 2 comma space n subscript 2 space a n d space l subscript 3 comma space m subscript 3 comma space n subscript 3$ . The lines will be coplanar, if

A) $negative open vertical bar table row cell l subscript 1 end cell cell n subscript 1 end cell cell m subscript 1 end cell row cell l subscript 2 end cell cell n subscript 2 end cell cell m subscript 2 end cell row cell l subscript 3 end cell cell n subscript 2 end cell cell m subscript 2 end cell end table close vertical bar equals 0$

B) $space open vertical bar table row cell l subscript 1 end cell cell m subscript 2 end cell cell n subscript 3 end cell row cell l subscript 2 end cell cell m subscript 3 end cell cell n subscript 1 end cell row cell l subscript 3 end cell cell m subscript 1 end cell cell n subscript 2 end cell end table close vertical bar equals 0 space$

C) $l subscript 1 space l subscript 2 space l subscript 3 space end subscript plus m subscript 1 space m subscript 2 space m subscript 3 space plus n subscript 1 space n subscript 2 space n subscript 3 space equals 0$

D) None of these

Explanation-

(a) Here, three given lines are coplanar if they have common perpendicular

Let d. c. 's of common perpendicular be l, m, n

$rightwards double arrow l l subscript 1 plus m m subscript 1 plus n n subscript 1 equals 0 space space space space space l l subscript 2 plus m m subscript 2 plus n n subscript 2 equals 0 a n d space space l l subscript 3 plus m m subscript 3 plus n n subscript 3 equals 0$ $............ left parenthesis i right parenthesis ............. left parenthesis i i right parenthesis ................. left parenthesis i i i right parenthesis$

Solving (ii) and (iii), we get

$fraction numerator l over denominator m subscript 2 n subscript 3 minus n subscript 2 m subscript 3 end fraction equals fraction numerator m over denominator n subscript 2 l subscript 3 minus n subscript 3 l subscript 2 end fraction equals fraction numerator n over denominator l subscript 2 m subscript 3 minus l subscript 3 m subscript 2 end fraction equals k rightwards double arrow l equals k open parentheses m subscript 2 n subscript 3 minus n subscript 2 m subscript 3 close parentheses comma space m equals k open parentheses n subscript 2 l subscript 3 minus n subscript 3 l subscript 2 close parentheses comma space n equals k open parentheses l subscript 2 m subscript 2 minus l subscript 3 m subscript 2 close parentheses$

Substituting in (i), we get

$l subscript 1 open parentheses m subscript 2 n subscript 3 minus n subscript 2 m subscript 3 close parentheses plus m subscript 1 open parentheses n subscript 2 l subscript 2 minus n subscript 3 l subscript 2 close parentheses plus n subscript 1 open parentheses l subscript 2 m subscript 3 minus l subscript 3 m subscript 2 close parentheses equals 0 space rightwards double arrow open vertical bar table row cell l subscript 1 end cell cell m subscript 1 end cell cell n subscript 1 end cell row cell l subscript 2 end cell cell m subscript 2 end cell cell n subscript 2 end cell row cell l subscript 3 end cell cell m 3 end cell cell n subscript 3 end cell end table close vertical bar equals 0 rightwards double arrow negative open vertical bar table row cell l subscript 1 end cell cell n subscript 1 end cell cell m subscript 1 end cell row cell l subscript 2 end cell cell n subscript 2 end cell cell m subscript 2 end cell row cell l subscript 3 end cell cell n subscript 3 end cell cell m subscript 3 end cell end table close vertical bar equals 0.$

Q.7. A point moves in such a way that the sum of its distance from xy - plane and yz - plane remains equal to its distance from zx - plane. The locus of the point is

A) $x minus y plus z equals 2$

B) $x plus y minus z equals 0$

C) $x minus y plus z equals 0$

D) $x minus y minus z equals 2$

Explanation-

According to question, z + x = y or x - y+ z = 0.

Q.8. The line drawn from (4, -1,2) to the point (-3,2,3) meets a plane at right angles at the point (-10,5,4) then the equation of plane is [DSSE 1985]

A) 7x-3y-z+89=0

B) 7x+3y+z+89=0

C) 7x-3y+z+89=0

D) None of these

Explanation-

Required plane is $7 vertical line left parenthesis x plus 10 right parenthesis minus 3 left parenthesis y minus 5 right parenthesis minus left parenthesis z minus 4 right parenthesis equals 0 o r space 7 x minus 3 y minus z plus 89 equals 0$

Q.9. If a plane cuts off intercepts $O A equals a comma space O B equals b comma space O C equals c space$ from the co-ordinate axes, then the area of the triangle ABC =

A) $1 half square root of b squared c squared plus c squared a squared plus a squared b squared end root$

B) $1 half open parentheses b c plus c a plus a b close parentheses$ .

C) $1 half a b c$

D) $1 half square root of open parentheses b minus c close parentheses squared plus open parentheses c minus a close parentheses squared plus open parentheses a minus b close parentheses squared end root$

Explanation-

(a) Length of sides are $square root of a squared plus b squared end root space comma square root of b squared plus c squared end root space comma square root of c squared plus a squared end root$ respectively

Now use $increment equals 1 divided by 2 square root of s open parentheses s minus a close parentheses open parentheses s minus b close parentheses open parentheses s minus c close parentheses end root space.$

Trick : Put $a equals 2 comma space b equals 2 comma space c equals 2 comma$ then sides will be $2 square root of 2 comma space 2 square root of 2 space a n d space 2 square root of 2$ i.e.

equilateral triangle. So area of this triangle will be $increment equals fraction numerator square root of 3 over denominator 4 end fraction cross times open parentheses 2 square root of 2 close parentheses squared equals square root of 3 space s q. space u n i t s$

Now, option (a) $rightwards double arrow increment equals 1 divided by square root of 16 plus 16 plus 16 end root$

$equals 1 divided by 2 cross times 4 square root of 3 equals 2 square root of 3.$

Q.10. Distance of the point (2, 3, 4) from the plane $3 x minus 6 y plus 2 z plus 11 equals 0 space i s$ [ MP PET 1990, 96, 2001, 03, 13; Odisha JEE 2010 ]

A) 1

B) 2

C) 3

D) 0

Explanation-

Required distance $equals open vertical bar fraction numerator 6 minus 18 plus 8 plus 11 over denominator 7 end fraction close vertical bar equals 1.$

IIT JEE & NEET Question Bank with Solution

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Tuesday, August 24, 2021

Ecology and Environment : Biology

Co-ordinate Geometry : Mathematics MCQ