Explore topic-wise InterviewSolutions in Current Affairs.

This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.

1.

Match the following Column I- with Column-II

Answer»


SOLUTION :
`|K-15|=5, 3,1`
Discussion
2.

Find which of the operations given above has identity. a"*"b=(ab)/4

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SOLUTION :N/A
Discussion
3.

Equation of the plane passing through the point of intersection of lines (x-1)/(3)=(y-2)/(1)=(z-3)/(2)&(x-3)/(1)=(y-1)/(2)=(z-2)/(3) andperpendicular to the line (x+5)/(2)=(y-3)/(3)=(z+1)/(1) is

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`2x+3y+z+7=0`
`2x-3y-z+22=0`
`2x+3y+z-22=0`
`2x+3y+z+13=0`

ANSWER :C
Discussion
4.

The number of unit vectors perpendicular to the plane of vectors veca=2hati-6hatj-3hatk and vecb=4hati+3hatj-hatk is/are

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1
2
0
None of these

ANSWER :B
Discussion
5.

If the parabola y^2 = ax passes through (3,2) then the focus is

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`(4/3, 0)`
`(0,4/3)`
`(1/3, 0)`
`(0,1/3)`

ANSWER :C
Discussion
6.

If x+y le 800, 2x+y le 1000, 0 le x le 400, 0 le y le 700 then the minimum value of f=4x+2y is

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1000
1600
400
8000

Answer :B
Discussion
7.

The valueof sum_(n=0)^(m) log ((a^(2n-1))/(b^(m-1)))(a !=0 , 1 , b != 0 , 1 ) is

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`m LOG. (a^(2M))/(B^(m-1))`
`(m+1)log. a/(b^(m-1))`
`m/2 log -(a^(2m))/(b^(2m-2))`
`m/2 log.(a^(2m))/(b^(m+1))`

ANSWER :B
Discussion
8.

If p, q and r are in A.P. then which of the following are true?-

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X, y, Z are in H.P
`(1)/(x), (1)/(y), (1)/(z)` are in A.P.
x, y, z are in G.P.
`(1)/(x), (1)/(y), (1)/(z)` are in G.P.

Answer :A, B, C
Discussion
9.

Find X and Y,if X+Y=[{:(5,2),(0,9):}]andX-Y=[{:(3,6),(0,-1):}].

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ANSWER :`X=[{:(4,4),(0,4):}],Y=[{:(1,-2),(0,5):}]`
Discussion
10.

What happen in (i)|a|ge c?

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SOLUTION :In(i), if `|a| GT C`. then there is no LOCUS. But if`|a|=c,` then the locus REDUCES to a straight line.
Discussion
11.

Let DeltaABC be given triangle IF |barBA+tbarBC |ge |barAC| for any t in R then DeltaABC is

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Equilateral
Right angled
Isosceles
None of these

Answer :B
Discussion
12.

Find the pole of 3x + 4y -0 45 = 0with respect to x^(2) + y^(2) - 6x 8y + 5 = 0

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ANSWER :` (6,8) `
Discussion
13.

Two cards are drawn from a pack of 52 cards, find the probability that they are of different denomination.

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SOLUTION :Each denomination contains 4 CARDS. As the TWO cards drawn are of different denomination, their PROBABILITY `=52/52xx48/51`
Discussion
14.

P is a point on the ellipse (x^(2))/(a^(2)) +(y^(2))/( b^(2)) =1 with foci atS, S^(-1). Normal at P cuts the x-axis at G and (SP)/( S^(1)P)=(2)/(3)then (SG)/( S^(1)G)

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A) `(4)/(9) `
B) ` ( 3)/(2) `
C) ` ( 2A)/( 3b) `
D) ` ( 2)/(3) `

ANSWER :D
Discussion
15.

The product of lengths of the perpendiculars from the point of the hyperbola x^(2)-y^(2)=8 to its asymptotes is

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`(a^(2)+B^(2))/(a^(2)b^(2))`
`(a^(2)-b^(2))/(a^(2)b^(2))`
`(a^(2)b^(2))/(a^(2)+b^(2))`
`(a^(2)+b^(2))/(a^(2)-b^(2))`

ANSWER :C
Discussion
16.

If a, b and c are respectively the p^(th),q^(th)and r^(th) terms of an A.P., then |(a" "p" "1),(b" "q" "1),(c" "r" "1)|=

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1
`-1`
0
`PQR`

ANSWER :C
Discussion
17.

Iff, g : R to R such that f(x) = 3 x^(2) - 2, g (x) = sin (2x)the g of =

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`3 sin^(2) X - 2 `
` sin 2 (3X^(2) - 1)`
` sin (6 x ^(2) - 4)`
`3 sin ^(2) 2 x - 2 `

Answer :C
Discussion
18.

If alpha, beta are the roots of x^(2) - x + 1 = 0, then the quadratic equation whose roots are alpha^(2015) beta^(2015) is

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`x^(2) - x + 1 = 0`
`x^(2) + x + 1 = 0`
`x^(2) + x - 1 = 0`
`x^(2) - x - 1 = 0`

ANSWER :B
Discussion
19.

Show that, (vec(a)-vec(b))xx(vec(a)+vec(b))=2(vec(a)xx vec(b)).

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ANSWER :`=2(VEC(a)XX vec(B))`
Discussion
20.

Solve -4x gt 30 when (i) x in Z(ii) x in N

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Answer :{……..-10, -9, -8}
II. `PHI`
Discussion
21.

Dual of (p rarr q) rarrr is

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`(q rarr p ) ^^ r `
`p rarr ( q rarr r )`
`(p VEE ~ q ) vee r `
NONE of these

Answer :A
Discussion
22.

Find the co-ordinates for the points on the ellipse x^2+3y^2+37 at which the normal is parallel to the line 6x-5y=2.

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ANSWER :`(5,2) (-5,-2)`
Discussion
23.

If n is a not a multiple of 3, then the coefficient of x^(n) in the expansion of log(1+x+x^(2)) is

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N
`(1)/(n)`
`(2)/(n)`
`(-2)/(n)`

ANSWER :B
Discussion
24.

Find the ratio in which the area bounded by the curves y^(2)=12x and x^(2)=12y is divided by the line x = 3.

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ANSWER :`15: 49`
Discussion
25.

A 2.5 gm impure sample containing weak monoacidic base (Mol. wt. = 45) is dissolved in 100 ml water and titrated with 0.5 M HCI when of ((1)/(5))^(th) the base was neutralised the pH was found to be 9 and at equivalent point pH of solution is 4.5. Given: All data at 25^(@)C & log 2 = 0.3. Select correct statement( s).

Answer»

`K_(b)` of base is less than `10^(-6)`
CONCENTRATION of salt (C) at equivalent point is 0.25 M
VOLUME of HCl is USED at equivalent point is 100 ml
Weight percentage of base in GIVEN sample is 80%.

ANSWER :bc
Discussion
26.

IQ of a person is given by the formulaIQ = (MA)/(CA) xx 100where MA is mental age and CA is chronological age. If 80 le IQ le 140 for a group of 12 years old children, find the range of their mental age.

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ANSWER :`9.6 LE MA le 16.8`
Discussion
27.

(a) Statement I is true, Statement II is true , Statement II is a correct explanation for statement I. (b) Statement I is true, Statement II is true, Statement II is not a correct explanation for Statement I.(C) Statement I is true, Statement II is false.(D) Statement I is false , Statement II is true. Statement I through the point (pi,pi+1),pilt2, there cannot be more than one normal to the parabola y^2=4ax . Statement II The point (pi,pi+1) cannot lie inside the parabola y^2=4ax .

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ANSWER :B
Discussion
28.

If the line joining the point A (a) and B(beta) on the ellipse x^2/25+y^2/9=1 is a focal chord, then one possible value of cot""alpha/2.cot""beta/2 is

Answer»

-3
3
-9
9

Answer :C
Discussion
29.

Let the vectorsveca"and"vecbbe such that |veca|=3"and"|vecb|=sqrt2/3,then vecaxxvecbis a unit vector, if the angle between veca"and"vecbis :a)pi/6b)pi/4c)pi/3d)pi/2

Answer»

`pi/6`
`pi/4`
`pi/3`
`pi/2`

ANSWER :B
Discussion
30.

Each of the following graphs in the standard (x,y) coordinate plane has the same scale on both axes. One graph is the graph of ax + by le c, where 0 < a < b < c. Which one is it?

Answer»




ANSWER :D
Discussion
31.

(a) Statement I is true, Statement II is true , Statement II is a correct explanation for statement I. (b) Statement I is true, Statement II is true, Statement II is not a correct explanation for Statement I.(C) Statement I is true, Statement II is false.(D) Statement I is false , Statement II is true. Statement I If there exist points on the circle x^2+y^2=pi^2 from which two perpendicular tangents can be drawn to the parabola y^2=2ax, then pige1/2. Statement II Perpendicular tangents to the parabolameet at the directrix.

Answer»


ANSWER :A
Discussion
32.

In which of the following reactions 3^(@) alcohol will be obtained as a product.

Answer»


`PhMgBr(excess)+CH_(3)-overset(O)overset(||)(C)-CL to UNDERSET(H^(+))to`
`CH_(3)MGBR(excess)+CH_(3)-overset(O)overset(||)(C)-O-overset(O)overset(||)C-CH_(3)to underset(H^(+))to`
`CH_(3)MgBr(excess)+Cl-overset(O)overset(||)(C)-O-Et to underset(H^(+))to`

Solution :`Ph=MgBr+CH_(3)-overset(O)overset(||)C-Cl to CH_(3)-overset(O)overset(||)C-Phoverset(PhMgBr)(to)CH_(3)-underset(Ph)underset(|)overset(OH)overset(|)C-Ph`
`CH_(3)MgBr+CH_(3)-overset(O)overset(||)C-O-overset(O)overset(||)C-CH_(3)toCH_(3)-overset(O)overset(||)C-CH_(3)overset(CH_(3)MgBr)underset(H^(o+))toCH_(3)-underset(CH_(3))underset(|)overset(OH)overset(|)C-CH_(3)`
`CH_(3)MgBr+Cl-overset(O)overset(||)C-O-Et toCH_(3)-overset(O)overset(||)C-OEt overset(CH_(3)MgBr)underset(H^(o+))toCH_(3)-underset(CH_(3))underset(|)overset(OH)overset(|)C-CH_(3)""]`
Discussion
33.

If A is both diagonal and skew - symmetric then

Answer»

A is a SYMMETRIC MATRIX
A is a NULL matrix
A is a unit matrix
none of these matrix

Answer :B
Discussion
34.

Write the direction cosines of the normal to the plane x-y+1=0.

Answer»

SOLUTION :The equation of the PLANE through (1,2,3) WHOSE normal has DRS`lt3,5,7gtis(x-1)3+(y-2).5+(z-3).7=0rArr3x+5y+7z=34`
Discussion
35.

Determine the truth of falsity of theA sub phi "if and only if "A = phi propositions with reasons.

Answer»

SOLUTION :`A PHI` if and only if `A = phi` is TRUE
Discussion
36.

The value of (1)/(10) (int_(0)^(100pi+V) | sin x| dx) + cos V is (0 le V le pi)

Answer»


ANSWER :`20.10`
Discussion
37.

An unbounded solution of a linearprogramming problem is a solution whoseobjectivefunctionis

Answer»

ZERO
a large positive real NUMBER
a large NEGATIVE real number
INFINITE

Answer :D
Discussion
38.

intsqrt(1+2x-x^2)dx

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SOLUTION :`intsqrt(1+2x-x^2)DX=intsqrt((SQRT2)^2-(x-1)^2)dx`
=`(x-1)/2sqrt((sqrt2)^2-(x-1)^2)+(sqrt2)^2/2 sin^-1((x-1)/sqrt2)+C`
`[becauseintsqrt(x^2-a^2)dx
=`x/2sqrt(x^2-a^2)+a^2/2sin^-1(x/a)+C]`
=`(x-1)/2sqrt(1+2x-x^2)sin^-1((x-1)/sqrt2)+C`
Discussion
39.

If alpha,beta,gamma are the rootsof x^3-2x^2+3x-4=0 find the value of sum1/(betagamma)

Answer»


ANSWER :`1/2`
Discussion
40.

A(x)=|{:(x+1,2x+1,3x+1),(2x+1,3x+1,x+1),(3x+1,x+1,2x+1):}|" then "int_(0)^(1)A(x)dx=

Answer»

`-15`
`-15//2`
`-30`
`-5`

ANSWER :B
Discussion
41.

A plane passes through the point (3, 5, 7). If the direction ratios of its normal are equal to the intercepts made by the plane x + 3y + 2z = 9 with the coordinate axes, then the equation of that plane is

Answer»

`x + y + Z =5`
`6X + 2y + 3Z = 105`
`12x + 4Y + 6z = 49`
`6x + 2y + 3z = 49`

Answer :D
Discussion
42.

If |z| = sqrt2 then the point given by "3 + 4z" lies ona circle whose radius is

Answer»

`2 sqrt2`
`3 sqrt2`
`4 sqrt2`
`5 sqrt2`

Answer :C
Discussion
43.

(Transportaion problem) : There are two factories located one at place P and the other at place Q. From these locations, a certain commodity is to be delivered to each of the three depots situated at A,B and C. The weekly requirements of the depots are respectively 5,5 and 4 units of the commodity while the production capacity of the factories at P and Q are respectively 8 and 6 units. The cost oftransportaion per unit is given below: How many units should be transported from each factory to each depot in order that the transportation cost its minimum. What will be the minimum transportation cost?

Answer»


ANSWER :RS. 1550
Discussion
44.

If (-1,-1) is the focus and x + y + 4=0 is the directrix of a parabola, then its vertex is

Answer»

A.`(-(3)/(2), -(3)/(2))`
B.`(-(5)/(2), -(5)/(2))`
C.`(-(1)/(4), -(1)/(4))`
D.`((1)/(4), (1)/(4))`

Answer :A
Discussion
45.

Consider f,g and h be three real valued functions defined on R. Let f(x)={:{(-1","xlt0),(0","x=0","g(x)(1-x^(2))andh(x) "be such that"),(1","xgto):}h''(x)=6x-4. Also, h(x) has local minimum value 5 at x=1 Range of function sin^(-1)sqrt((fog(x))) is

Answer»

`(0,pi//2)`
`{0,pi//2}`
`{-[pi//2,0,pi//2}`
`{pi//2}`

ANSWER :B
Discussion
46.

The perpendicular distance of the plane y-2x + 5 = z from the point (0,0,0) is .....

Answer»

`5(SQRT(6))`
`(5sqrt(6))/(6)`
`(sqrt(6))/(5)`
`2sqrt(6)`

ANSWER :B
Discussion
47.

If a tangent to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1(a gt b gt 0) having slope 1/3 is anormal to the circle x^(2)+y^(2)+2x+2y+1=0, then the maximum value of ab is

Answer»

`2/3`
9
`4/9`
`1/3`

ANSWER :A
Discussion
48.

Prove that :int_(0)^(pi) (x dx)/( 1+cos alpha. sin x)=(pialpha)/(sin alpha) , 0 lt alpha lt pi

Answer»
Discussion
49.

Define optimal solution in linear programming problem .

Answer»


Answer :Any POINT in the FEASIBLE REGION that GIVES the optimal value (maximum or minimum) of the OBJECTIVE function `z=ax+by` is called an optimal solution.
Discussion
50.

Consider f,g and h be three real valued functions defined on R. Let f(x)={:{(-1","xlt0),(0","x=0","g(x)(1-x^(2))andh(x) "be such that"),(1","xgto):}h''(x)=6x-4. Also, h(x) has local minimum value 5 at x=1 The area bounded by y=h(x),y=g(f(x))between x=0 and x=2 equals

Answer»

`23//2`
`20//3`
`32//3`
`40//3`

ANSWER :C
Discussion