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.

If A is a 3 × 3 matrix, A≠0 and 3A=kA then write the value of k.

Answer» If A is a 3 × 3 matrix, A≠0 and 3A=kA then write the value of k.
2.

f Z1, Z2 ∈ C, Z1^2 + Z2^2 ∈ R, Z1 (Z1^2-3z2^2) = 2 and Z2 (3z1^2-Z2^2) = 1 then what is the value of Z1^2 + Z2^2?

Answer» f Z1, Z2 ∈ C, Z1^2 + Z2^2 ∈ R, Z1 (Z1^2-3z2^2) = 2 and Z2 (3z1^2-Z2^2) = 1 then what is the value of Z1^2 + Z2^2?
3.

If one end of a focal chord of the parabola, y2=16x is at (1,4), then the length of this focal chord is:

Answer»

If one end of a focal chord of the parabola, y2=16x is at (1,4), then the length of this focal chord is:

4.

Express the following in the form a +bi, where a and b are real numbers.

Answer» Express the following in the form a +bi, where a and b are real numbers.
5.

In a triangle ABC, side a is equal to -

Answer» In a triangle ABC, side a is equal to -

6.

A curve is such that the mid point of the portion of the tangent intercepted between the point where the tangent is drawn and the point where the tangent meets the y−axis lies on the line y=x. If the curve passes through (1,0), then the curve is

Answer»

A curve is such that the mid point of the portion of the tangent intercepted between the point where the tangent is drawn and the point where the tangent meets the y−axis lies on the line y=x. If the curve passes through (1,0), then the curve is

7.

If A and B are two events such that A ≠ Φ, B = Φ, then(a) PAB=PA∩BPB (b) PAB=PA PB(c) PAB=PBA=1 (d) PAB=PAPB

Answer» If A and B are two events such that A ≠ Φ, B = Φ, then



(a) PAB=PA∩BPB (b) PAB=PA PB

(c) PAB=PBA=1 (d) PAB=PAPB
8.

3 The equation of one of the tangents to the curve y=cos(x+y),-2

Answer» 3 The equation of one of the tangents to the curve y=cos(x+y),-2
9.

Prove the following trigonometric identities.If a cos θ + b sin θ = m and a sin θ − b cos θ = n, prove that a2 + b2 = m2 + n2

Answer» Prove the following trigonometric identities.



If a cos θ + b sin θ = m and a sin θ − b cos θ = n, prove that a2 + b2 = m2 + n2
10.

Using elementary transformations, find the inverse of matrix⎡⎢⎣13−2−30−5250⎤⎥⎦, if it exists.

Answer»

Using elementary transformations, find the inverse of matrix⎡⎢⎣13−2−30−5250⎤⎥⎦, if it exists.



11.

SECTION-A1. Find the values of m and in for which the following system of linear equations has infinitely manysolutions:3x + 4y = 12(m + n) x + 2 (m-n) y = 5m-1

Answer» SECTION-A1. Find the values of m and in for which the following system of linear equations has infinitely manysolutions:3x + 4y = 12(m + n) x + 2 (m-n) y = 5m-1
12.

If 2sin−1x0+tan−1x0=5π√−x20+2x0+15, then the possible value(s) of dydx to the curve y=2xy+x at x=x0 is (are)

Answer»

If 2sin−1x0+tan−1x0=5π√−x20+2x0+15, then the possible value(s) of dydx to the curve y=2xy+x at x=x0 is (are)

13.

Find the equation of the line on which the length of the perpendicular segment from the origin to the line is 4 and the inclination of the perpendicular segment with the positive direction of x-axis is 30°.

Answer» Find the equation of the line on which the length of the perpendicular segment from the origin to the line is 4 and the inclination of the perpendicular segment with the positive direction of x-axis is 30°.
14.

If √2sinA=sinB−sin3B and √2cosA=cosB+cos3B, then the possible value(s) of sin(A−B) is/are

Answer»

If √2sinA=sinB−sin3B and √2cosA=cosB+cos3B, then the possible value(s) of sin(A−B) is/are

15.

The equation x2+y2+z2=0 represents

Answer»

The equation x2+y2+z2=0 represents


16.

Let S be the set of all points where the function f(x)=|x−π|(e|x|−1)sin|x| is not differentiable, then S is

Answer»

Let S be the set of all points where the function f(x)=|x−π|(e|x|−1)sin|x| is not differentiable, then S is

17.

The value of cos−1(−12) is

Answer»

The value of cos−1(−12) is

18.

In triangle ABC, E is the mid-point of side BC and D is on side AC. Let the length of side AC be unity and ∠BAC=60∘, ∠ABC=100∘, ∠ACB=20∘, ∠DEC=80∘. If the area of the triangle ABC plus twice the area of triangle CDE equals √mn, where m and n are coprime, then the value of (m+n) is greater than

Answer»

In triangle ABC, E is the mid-point of side BC and D is on side AC. Let the length of side AC be unity and ∠BAC=60∘, ∠ABC=100∘, ∠ACB=20∘, ∠DEC=80∘. If the area of the triangle ABC plus twice the area of triangle CDE equals √mn, where m and n are coprime, then the value of (m+n) is greater than

19.

Find k if x = 3 is a root of equation kx2 – 10x + 3 = 0

Answer»
Find k if x = 3 is a root of equation kx2 – 10x + 3 = 0
20.

86.Explain cross and dot product of vectors

Answer» 86.Explain cross and dot product of vectors
21.

3.(2-x)+1

Answer» 3.(2-x)+1
22.

Solution set of x(2x−1)(3x−9)(x−3)<0 is

Answer»

Solution set of x(2x−1)(3x−9)(x−3)<0 is

23.

Identify the word which is common to the following.

Answer»

Identify the word which is common to the following.

24.

Which of the following is logically equivalent to ∼(∼p⇒q)

Answer»

Which of the following is logically equivalent to ∼(∼p⇒q)

25.

A(1, 2, 3), B(0, 4, 1), C(-1, -1, -3) are the vertices of a triangle ABC. Find the point in which the bisector of the angle ∠BAC meets BC.

Answer»

A(1, 2, 3), B(0, 4, 1), C(-1, -1, -3) are the vertices of a triangle ABC.

Find the point in which the bisector of the angle ∠BAC meets BC.


    26.

    133.In the circuit shown in figure charge stored in 6 microfarad capacitor will be

    Answer» 133.In the circuit shown in figure charge stored in 6 microfarad capacitor will be
    27.

    Match the followingFunctionsDerivatives(a)xn1)1x(logae)(b)ex2)1x,x&gt;0(c)ax3)nxn−1,n is a constant(d)logex4)axlogea,a&gt;0(e)logax5)ex

    Answer»

    Match the following

    FunctionsDerivatives(a)xn1)1x(logae)(b)ex2)1x,x>0(c)ax3)nxn−1,n is a constant(d)logex4)axlogea,a>0(e)logax5)ex





    28.

    If a,b,c are different real numbers and x is a variable then a factor of the determinant ∣∣∣∣∣0x2−ax3−bx2+a0x2+cx4+bx−c0∣∣∣∣∣ is

    Answer»

    If a,b,c are different real numbers and x is a variable then a factor of the determinant

    ∣∣
    ∣
    ∣
    ∣
    0x2−ax3−bx2+a0x2+cx4+bx−c0∣∣
    ∣
    ∣
    ∣
    is


    29.

    Prove that cos4x+cos3x+cos2xsin4x+sin3x+sin2x=cot3x

    Answer» Prove that cos4x+cos3x+cos2xsin4x+sin3x+sin2x=cot3x
    30.

    18. Three vectors A, B and C are such that A = B+Cand their magnitudes are in ratio 10 : 8 6respectively, then angle between A and B is(1) 53^° (2) 370(3) 90^° (4) 45^°

    Answer» 18. Three vectors A, B and C are such that A = B+Cand their magnitudes are in ratio 10 : 8 6respectively, then angle between A and B is(1) 53^° (2) 370(3) 90^° (4) 45^°
    31.

    The locus of points of trisection of double ordinate of y2=4ax is

    Answer»

    The locus of points of trisection of double ordinate of y2=4ax is

    32.

    Solve the following system of equations in R. 1|x|−3≤12

    Answer»

    Solve the following system of equations in R.
    1|x|−3≤12

    33.

    If CF is perpendicular from the centre C of the ellipse x249+y225=1 on the tangent at any point P, and G is the point where th e normal at P meets the minor axis, then (CF⋅PG)2 is equal to___

    Answer»

    If CF is perpendicular from the centre C of the ellipse x249+y225=1 on the tangent at any point P, and G is the point where th e normal at P meets the minor axis, then (CF⋅PG)2 is equal to___

    34.

    A point P lies on the X-axis. Which of the following represents the coordinates of point P?

    Answer»

    A point P lies on the X-axis. Which of the following represents the coordinates of point P?



    35.

    Let S be the set of all integer solutions (x,y,z) of the system of equationsx−2y+5z=0−2x+4y+z=0−7x+14y+9z=0,such that 15≤x2+y2+z2≤150. Then, the number of elements in the set S is equal to

    Answer» Let S be the set of all integer solutions (x,y,z) of the system of equations

    x−2y+5z=0

    −2x+4y+z=0

    −7x+14y+9z=0,

    such that 15≤x2+y2+z2≤150. Then, the number of elements in the set S is equal to
    36.

    If →A and →B are two unit vectors such that 3→A+4→B and 5→A−3→B areperpendicular, then the angle between →A and →B is

    Answer» If →A and →B are two unit vectors such that 3→A+4→B and 5→A−3→B areperpendicular, then the angle between →A and →B is
    37.

    Minimize and miximize Z = x + 2y subject to constraints are x + 2y ≥ 100, 2x - y ≤ 0, 2x + y ≤ 200 and x, y ≥ 0.

    Answer»

    Minimize and miximize Z = x + 2y subject to constraints are x + 2y ≥ 100, 2x - y ≤ 0, 2x + y ≤ 200 and x, y ≥ 0.

    38.

    Find the mean deviation about the median for the data. xi 5 7 9 10 12 15 fi 8 6 2 2 2 6

    Answer»

    Find the mean deviation about the median for the data.
























    xi



    5



    7



    9



    10



    12



    15



    fi



    8



    6



    2



    2



    2



    6


    39.

    A tank with a small circular hole contains oil on top of water. It is immersed in a large tank of the same oil. Water flows through the hole. What is the velocity of flow initially?

    Answer»

    A tank with a small circular hole contains oil on top of water. It is immersed in a large tank of the same oil. Water flows through the hole. What is the velocity of flow initially?


    40.

    45 If sinx + siny =1/2 and cosx +cosy = 1, then tan(x+y) =

    Answer» 45 If sinx + siny =1/2 and cosx +cosy = 1, then tan(x+y) =
    41.

    Which one the following relations on A = {1, 2, 3} is a function?f = {(1, 3), (2, 3), (3, 2)}, g = {(1, 2), (1, 3), (3, 1)} [NCERT EXEMPLAR]

    Answer» Which one the following relations on A = {1, 2, 3} is a function?

    f = {(1, 3), (2, 3), (3, 2)}, g = {(1, 2), (1, 3), (3, 1)} [NCERT EXEMPLAR]
    42.

    If 1∫0cot−1(1−x+x2)dx=λ1∫0tan−1xdx, then λ is equal to

    Answer» If 1∫0cot−1(1−x+x2)dx=λ1∫0tan−1xdx, then λ is equal to
    43.

    9. x + y = tan-lyугу, + уг +1=0

    Answer» 9. x + y = tan-lyугу, + уг +1=0
    44.

    Fill in the blank with the appropriate verb form. The example ________ my point completely.

    Answer»

    Fill in the blank with the appropriate verb form.

    The example ________ my point completely.


    45.

    If exy2+ycosx2=5, then absolute value of y′(0)=

    Answer» If exy2+ycosx2=5, then absolute value of y′(0)=
    46.

    If ∫dx(x−4)√x+5=13ln∣∣∣∣√f(x)+1−α√f(x)+1+β∣∣∣∣+C, then which of the following is/are CORRECT?(where α,β are fixed constants and C is integration constant.)

    Answer»

    If ∫dx(x−4)√x+5=13ln∣∣
    ∣
    ∣
    √f(x)+1−α√f(x)+1+β∣∣
    ∣
    ∣
    +C,
    then which of the following is/are CORRECT?

    (where α,β are fixed constants and C is integration constant.)

    47.

    Integrate the following functions. ∫1cos2x(1−tanx)2dx.

    Answer»

    Integrate the following functions.
    ∫1cos2x(1−tanx)2dx.

    48.

    If,for some prove thatis a constant independent of aand b.

    Answer»

    If,
    for some

    prove that



    is a constant independent of a
    and
    b.

    49.

    If θ lies in the first quadrant and cos θ=817, then the value of cos(30∘+θ)+cos(45∘−θ)+cos(120∘−θ) is

    Answer»

    If θ lies in the first quadrant and cos θ=817, then the value of cos(30∘+θ)+cos(45∘−θ)+cos(120∘−θ) is



    50.

    If B × A = {(x, a), (x, b), (x, c), (y, a), (y, b), (y, c), (z, a), (z, b), (z, c)} Find set A and set B.

    Answer»

    If B × A = {(x, a), (x, b), (x, c), (y, a), (y, b), (y, c), (z, a), (z, b), (z, c)} Find set A and set B.