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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. |
Prove that (cos x + cos y)2 + (sin x – sin y)= 4cos2((x + y)/2) |
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Answer» LHS = cos2x + cos2y + 2cosx cosy + sin2x + sin2y – 2sinxsin y = 1 + 1 + 2 (cosxcosy – sinxsiny) = 2[1 + cos (x + y)] = 4cos2((x + y)/2) |
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| 2. |
Greater trochanter occurs inA. HumerusB. RadiusC. UlnaD. Femur |
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Answer» Correct Answer - B Greater trochanter occurs in radius |
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| 3. |
For fourth class building the doors and windows shall be of _________ wood or country wood.(a) Sal(b) Neem(c) Teak(d) Mango |
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Answer» Correct choice is (d) Mango Easiest explanation: Technically mango is a hardwood with dense grains, so it has the strength to bear the weight necessary for chairs and heavy tables, but it’s still soft enough that it’s relatively easy to work with, requiring no special tools on behalf of the manufacturers. Mango furniture can stand the wear and tear of time as well as your grandmother’s oak kitchen table, but, unlike traditional hardwood furniture, it’s more affordable and, as we’ll get into, completely sustainable. |
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| 4. |
Extermities of long bones possess cartilageA. CalcifiedB. FibrousC. ElasticD. Hyaline |
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Answer» Correct Answer - D Extremities of long bones possess cartilage hyaline. |
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| 5. |
Let R: Z → Z be a relation defined by R = {(a, b) : a, b, ∈ Z, a – b ∈ z}. Show that (i) ∀ a ∈ Z, (a, a) ∈ R. (ii) (a, b) ∈ R ⇒ (b,a) ∈ R (iii) (a, b) ∈ R, (b, c) ∈ R ⇒ (a, c) ∈ R |
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Answer» ∀ a ∈ Z, (a, a) ∈ R since a – a = 0 ∈ Z (a, b) ∈ R ⇒ a – b ∈ Z ⇒ ∴ b – a ∈ Z ⇒ (b, a) ∈ R (a, b) ∈ R, (b, c) ∈ R ⇒ a – b ∈ Z, b – C ∈ Z ∴ a – b + b – c ∈ Z ⇒ (a, c) ∈ Z |
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| 6. |
Out of a group of 200 students (who know at least one language), 100 students know English, 80 students know Kannada, 70 students know Hindi. If 40 students know all the three languages, find the number of students who know exactly two languages. |
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Answer» writing n(E) = 100, n(K)= 80, n(H) = 70 . n(E ∪ K ∪ H) = 200, n (E ∩ K N ∩ H) = 40 We know that n(E ∪ K ∪ H) = n(E) + n (K) + n(H) –n (E ∩ K) – n (K ∩ H) -n (H ∩ E) + n (E ∩ K ∩ H) ∴ n (E ∩ K) + n (K ∩ H) + n (H ∩ E) = 90 |
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| 7. |
A: Why haven’t you told me about your problems before? B: Well, ________ all this week. A) I was trying to tell you all about them B) I’ve been trying to tell you all about them C) I’m trying to tell you all about them D) I tried to tell you all about them |
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Answer» Correct option is B) I’ve been trying to tell you all about them |
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| 8. |
He told me that I have done well |
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Answer» He said to me, "You have done well.” |
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| 9. |
6. What does the third level refer to? तीसरा तल किस ओर संकेत करता है? |
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Answer» Ans. The writer wanted to go Galesburg. Both for that he needed old-style bills to pay for the tickets on the third level. So he went to the coin dealer's.There he exchanged his three hundred dollars with old-style currency. He got less than two hundred in exchange. --> The third level refers to the subway of the Grand Central Station that takes passengers to Galesburg, Illinois.
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| 10. |
(ii) \( \frac{1}{2} \) of \( \frac{1}{3} \times \frac{3}{4} \) |
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Answer» Ans.1/2 of 3/12 = 3/24
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| 11. |
A can do 20% of a work in 4 days. B can do 33.33% work in 10 days. They worked together for 9 days. C complete the remaining work in 6 days. B and C together will complete 75% of the same work in:1. 15 days2. 12 days3. 10 days4. 9 days |
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Answer» Correct Answer - Option 3 : 10 days Given: Time taken by A to complete 20% work = 4 days Time taken by B to complete 33.33% of work = 10 days They worked together for 9 days C completed the remaining work in 6 days Formula used: Work = Time × Efficiency Calculation: Time taken by A to complete 100% work = 4 × 5 = 20 days Time taken by B to complete 100% work = 10 × 3 = 30 days L.C.M of 20 and 30 = 60 = Total work Efficiency of A = 60/20 = 3 units/day Efficiency of B = 60/30 = 2 units/day Worked done by A and B together in 9 days = (3 + 2) × 9 ⇒ 45 units Remaining work = (60 – 45) units ⇒ 15 units C can complete the remaining work in 6 days Efficiency of C = 15/6 = 2.5 units/day Total efficiency of B and C = (2 + 2.5) units/day ⇒ 4.5 units/day Now, 75% of total work = 75% of 60 units ⇒ 45 units Required time = 45/4.5 days ⇒ 10 days ∴ B and C can complete 75% work in 10 days |
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| 12. |
What happens to the magnetic field in the solenoid when the current increases?(a) Increases(b) Decreases(c) Remains constant(d) Becomes zero |
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Answer» Right choice is (a) Increases Explanation: The magnetic field of a solenoid is directly proportional to the current in it. Hence as the current increases, the magnetic field also increases. |
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| 13. |
For eccentricity in ellipse (e) which relation is correct?(a) e < 1(b) e = 1(c) e > 1(d) e = ∞ |
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Answer» Correct option is (a) e < 1 The best explanation: Eccentricity can be defined as a parameter associated with every conic section. It can be thought of a measure of how much the conic section deviates from being circular. When (e < 1 Ellipse), (e = 1 Parabola), (e > 1 Hyperbola), (e = ∞ straight line), (e = 0 Circle). |
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| 14. |
Which geometric principle is used to justify the construction below?(a) A line perpendicular to one of two parallel lines is perpendicular to the other(b) Two lines are perpendicular if they intersect to form congruent adjacent angles(c) When two lines are intersected by a transversal and alternate interior angles are congruent, the lines are parallel(d) When two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel |
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Answer» Right option is (d) When two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel The best explanation: ∠A, ∠F, ∠G, ∠D are exterior angles. ∠B, ∠E, ∠H, ∠C are interior angles. ∠B and ∠E, ∠H and ∠C are consecutive interior angles. ∠A and ∠G, ∠F and ∠D are alternate exterior angles. ∠E and ∠C, ∠H and ∠B are alternate interior angles. ∠A and ∠E, ∠C and ∠G ∠D and ∠H, ∠F and ∠B are corresponding angles. |
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| 15. |
A line is a geometric primitive that has no ____________(a) length(b) point(c) direction(d) thickness |
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Answer» Right option is (d) thickness Easiest explanation: A point has no length or width. It has no thickness. Point is a mark of position. A point specifies the exact location. Point is denoted by a dot (.) and is named by an alphabet. Line is composed of infinite points and so here it can be said that a line also does not have thickness. |
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| 16. |
Find the H.C.F of 6, 20 and 24.1. 22. 43. 54. 6 |
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Answer» Correct Answer - Option 1 : 2 Concept: Find the prime factors of 6,20 and 24 Explanation: Factors of 6 = 2 × 3 Factors of 20 = 2 × 2 × 5 Factors of 24 = 2 × 2 × 2 × 3 Hence, H.C.F. of 6,20 and 24 is 2. |
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| 17. |
If vector(a, b,c) are unit vectors and mutually perpendicular then |vector(a - b)|2 + |vector(b - c)|2 is equal to(A) 4 (B) 9 (C) 8 (D) 6 |
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Answer» correct option: (B) 9 |
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| 18. |
Modulus of the vector(2 i - 7 j - 3 k) is(A) √12(B) √50(C) √62(D) 2√5 |
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Answer» correct option: (C) √62 |
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| 19. |
lim(n →∞) (1 + √2 + √3 + ......+√n)/n3/2 is equal to (A) 1/2(B) 1/3(C) 2/3(D) 3/2 |
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Answer» correct option: (C) 2/3 |
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| 20. |
∫e|θ| dθ ,x ∈ [-1, 1] is equal to (A) (e – 1) (B) 2 (e –1) (C) 3 (e –1) (D) –2(e –1) |
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Answer» correct option: (B) 2 (e –1) |
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| 21. |
Find the coefficient of `a^(2)b^(3)c^(4)d` in the expansion of `(a-b-c+d)^(10)`. |
| Answer» Correct Answer - `-12600` | |
| 22. |
Find the coeffcient of `x^(17)` in `(2x^(2) -x-3)^(9)` |
| Answer» Correct Answer - 2304 | |
| 23. |
Find the square root of 16384.1. 1182. 1283. 1224. 1325. None of these. |
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Answer» Correct Answer - Option 2 : 128 Concept used:- Trick to find square root of a number. Method and Calculation:- • Find the unit digit of square root by looking at unit digit of given number. For ✓16384, unit digit must be 8 or 2 • Find other two digits by looking at number formed by first 3 digit. 144 < 163 < 169 (144 and 169 are squares of 12 and 13, so remaining part of square root will be 12. • Find the square root from the narrowed down options. ✓16384 = 122 or 128. To find this, we multiply 12 × 13, which is equal to 156 and is less than 163. Hence the bigger of two will be the square root Clearly, ✓16384 = 128 |
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| 24. |
In what ratio does `(4,1)` divide the line segment joining the point `(1,-2)` and `(5,2)`. |
| Answer» Correct Answer - `3 : 1` internally | |
| 25. |
consider a family of circles passing through two fixed points `S(3,7)` and `B(6,5)`. If the common chords of the circle `x^(2)+y^(2)-4x-6y-3=0` and the members of the family of circles pass through a fixed point (a,b), thenA. `a+3b=25`B. `3b-a=21`C. `3a+b=25`D. `3a-b=21` |
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Answer» Correct Answer - A::B Family of circle `S+lamdaL=0` `S_(1)-=(x-3)(x-6)+(y-7)(y-5)+lamda(2x+3-27)=0` `x^(2)+y^(2)+x(2lamda-9)+y(3lamda-12)+(53-27lamda)=0` common chord of family of circle and given circle is `S_(1)-S_(2)` `=0(S_(22)` given circle) `(-5x-6y+56)+lamda(2x+3y-27)=0` Which represents family of lines passing through the point `(2,(23)/(3))impliesa=2,b=(23)/(3)` |
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| 26. |
Find the ration in which the line joining the points `A(1,2)` and`B(-3,4)` is divided by the line. `x+y-5=0` |
| Answer» Correct Answer - `1 : 2` internally | |
| 27. |
If `z_(1),z_(2),z_(3)` are three points lying on the circle `|z|=2`, then minimum value of `|z_(1)+z_(2)|^(2)+|z_(2)+z_(3)|^(2)+|z_(3)+z_(1)|^(2)=`A. 6B. 12C. 15D. 24 |
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Answer» Correct Answer - B `|z|=|z_(2)|=|z_(3)|=2` `because |z_(1)+z_(2)+z_(3)|^(2)ge0implies(z_(1)+z_(2)+z_(3))(barz_(1)+barz_(2)+barz_3)ge0` `impliessum|z_(1)|^(2)+sum(z_(1)barz_(2)+barz_(1)z_(2))ge0implies2sum|z_(1)|^(2)+sum(z_(1)barz_(2)+barz_(1)z_(2))gesum|z_(1)|^(2)` `implies|z_(1)+z_(2)|^(2)+|z_(2)+z_(3)|^(2)+|z_(3)+z_(1)|^(2)ge12 {because |z_(1)|=|z_(2)|=|z_(3)|=2}` |
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| 28. |
For the straight lines `2x - y + 1 = 0` and `x - 2y - 2 = 0` find the equation of the (i) bisector of the obtuse angle between them , (ii) bisector of the acute angle between them , |
| Answer» Correct Answer - `x + y + 3 = 0, 3x - 2y = 1` | |
| 29. |
The area ofa triangle is 5. Two of its vertices are `(2, 1)`and `(3, -2)`. The thirdvertex lies on `y=x+3`. Find thethird vertex. |
| Answer» Correct Answer - `(7/2,13/2)` or `(-3/2,3/2)` | |
| 30. |
the length of the perpendicular from the origin to a line is `7` and a line makes an angle of `150^@` with the positive direction of `y`-axis . then the equation of the line is: |
| Answer» Correct Answer - `sqrt(3)x - y + 14 = 0` | |
| 31. |
Find the coordinates of the centre of the circle inscribed in a triangle whose angular points are `(-36, 7), (20, 7) and (0, - 8)`. |
| Answer» Correct Answer - `(28)` , `(-1,0)` | |
| 32. |
If three vectors `(sec^(2)A) hati+hatj+hatk`, `hati+(sec^(2)B)hatj+hatk,hati+hatj+sec^(2)hatk` are complnar, then the value of `cosec^(2)A + cosec^(2)B+ cosec^(2)C` is -A. 1B. 2C. 3D. None of these |
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Answer» Correct Answer - B `|{:(sec^(2)A,1,1),(1,sec^(2)B,1),(1,1,sec^(2)C):}|` `tan^(2)Atan^(2)Btan^(2)C+tan^(2)Atan^(2)B+tan^(2)Ctan^(2)B+tan^(2)Ctan^(2)A=0` `cot^(2)A+cot^(2)B+cot^(2)C+1=0` `"cosec"^(2)A+"cosec"^(2)B+"cosec"^(2)C=2` |
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| 33. |
Find all points on x - y + 2 = 0 that lie at a unit distance from the line `12x - 5y + 9 = 0` |
| Answer» Correct Answer - `(2,4)` or `(-12//7,2//7)` | |
| 34. |
There are 12 points in a plane of which 5 are collinear. Except these five points no three are collinear, thenA. The number of quadrilaterals one can form using these points is 420B. the number of Deltas one can form using these points is 210C. the number of lines one can form using these points is 57D. the number of lines one can form using these points is 56 |
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Answer» Correct Answer - A::B::C (A) .^(12)C_(4)-(` .^(5)C_(4)+^(5)C_(3).^(7)C_(1))=495-(5+70)=420` (B). .^(12)C_(3)-(` .^(5)C_(3))=220-10=210` (C). .^(12)C_(2)-(` .^(5)C_(2))+1=66-10+1=57` |
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| 35. |
The solution of `x^(3)(dy)/(dx)+4x^(2)tan y=e^(x)sec y` satisfying y(1) = 0, isA. `tan y = e^(x)(x-2)lnx`B. `siny=e^(x)(x-1)x^(-4)`C. `tany=e^(x)(x-1)x^(-3)`D. `siny=e^(x)(x-1)x^(-3)` |
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Answer» Correct Answer - B `x^(3)(dy)/(dx)+4x^(2)tany=e^(x)secyimpliesx^(3)cosy(dy)/(dx)+4x^(2)siny =e^(x)` `implies x^(3).(dt)/(dx)+4x^(2).t=e^(x), " "("where " t=siny)` `impliesx^(4)(dt)/(dx)+4x^(3)t=xe^(x)implies(d)/(dx)(x^(4).t)=xe^(x)impliesx^(4)t=(x-1)e^(x)+c` `impliesx^(4)siny=(x-1)e^(x)+c` `becausey(1)=0impliesc=0impliessiny=(e^(x)(x-1))/(x^(4))` |
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| 36. |
For a function `f:AtoB` such that `n(A)=a,n(B)=b(a,b in N)` then which of the following statements must be CORRECT?A. if function is one - one, onto then `agtb`B. if function is one - one into, then `agtb`C. iif function si many - one, onto then `agtb`D. if function is many - one into, then `altb` |
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Answer» Correct Answer - B::C (A). If function is one-one & onto then `a=b` since every element of seb should have exactly one preimage in A. (B). For one-one, into function every element of set B should have either one pre-image or no preimage in set A `implies` no of elementsin set `Bge` no. of elements in A `becauseBgea` (C) for many one onto function every element of set B should have one or more tha one pre-images in A. `impliesn(B)len(A)impliesblea` or `ageb` (D). for many- one into function `a in N` & `b in N`. |
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| 37. |
The energies of electrons emitted in β− decays have a continuous spectrum because: A. the original neutron has a continuous spectrum B. a neutrino can carry off energy C. the emitted electron is free D. energy is not conserved E. the daughter nucleus may have any energy |
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Answer» B. a neutrino can carry off energy |
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| 38. |
For \( a \leq 0 \), the roots of the equation \( x^{2}-2 a|x-a|-3 a^{2}=0 \) |
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Answer» \(x^2 - 2a |x - a| - 3a^2 = 0\) Case I: \(x < a \) then \(|x - a| = -(x - a)\) \(\therefore x^2 - 2a|x - a| -3a^2 = 0\) ⇒ \(x^2 + 2a(x - a) - 3a^2 = 0\) ⇒ \(x^2 + 2ax - 5a^2 = 0\) ⇒ \(x = \frac {-2a \pm \sqrt{4a^2 + 20a^2}}{2}\) \(= \frac {-2a \pm 2\sqrt 6 a}2\) \(= ( - 1 \pm \sqrt 6)a\) \((\because a \le 0)\) (\(\therefore\) only possibility \(( - 1 \pm \sqrt 6)a\)) Case II: \(x > a\) then \(|x - a| = x - a\) \(\therefore x^2 - 2a|x -a| - 3a^2 = 0\) ⇒ \( x^2 - 2a(x -a)- 3a^2 = 0\) ⇒ \(x^2 - 2ax + 2a^2 - 3a^2 = 0\) ⇒ \(x^2 - 2ax - a^2 = 0\) ⇒ \(x = \frac {2a \pm \sqrt{4a^2 + 4a^2}}{2} \) \(= \frac {2a \pm 2\sqrt 2a}2\) \(= a\pm \sqrt 2 a\) \(= (1\pm \sqrt 2)a\) only possibility is \(( 1- \sqrt2)a\) as \(x > a\) & \(a \le0\). Hence, possible roots are \(( - 1 \pm \sqrt 6)a\) & \(( 1- \sqrt2)a\). |
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| 39. |
Let `vec(OA) = hat(i)+2hat(j)+2hat(k)`. In the plane of `vec(OA)` and `hat(i)`, rotate `vec(OA)` through `90^(@)` about the origin O such that the new position of `vec(OA)` makes an acute angle with the positive x-axis. The new position of `vec(OA)` isA. `(1)/(sqrt(2))(4hat(i)-hat(j)-hat(k))`B. `(1)/(sqrt(2))(-4hat(i)+hat(j)+hat(k))`C. `sqrt(2)(2hat(i)-2hat(k))`D. `sqrt(2)(6hat(i)-3hat(k))` |
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Answer» Correct Answer - A Given `vec(OA)=hat(i)+2hat(j)+2hat(k)` Let new position of `vec(OA) " is " vec(r)=ahat(i)+bhat(j)+chat(k)` `because vec(OA),vec(r) " and " hat(i) " are coplaner" =|(1,2,2),(a,b,c),(1,0,0)| = 0 implies b = c` `because vec(r)_|_vec(OA) implies a+2b+2c=0impliesa=-4b{because b=c}` `therefore vec(r)=-4bhat(j)+bhat(j)+bhat(k)=-b(4hat(i)-hat(j)-hat(k))` Also `|vec(r)|=|vec(OA)|impliesb=pm(1)/(sqrt(2))impliesvec(r)=pm(1)/(sqrt(2))(4hat(i)-hat(j)-hat(k))` `because vec(r)` makes acute angle with positive x-axis `implies vec(r)=(1)/(sqrt(2))(4hat(i)-hat(j)-hat(k))` |
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| 40. |
if `3^(x)=5^(y)(75)^(z)` then `Z=`A. `(y)/(2+log-(5)3)`B. `(x^(2)y^(2))/(2x+y)`C. `(x)/(2log_(3)+5+1)`D. `(xy)/(2x+y)` |
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Answer» Correct Answer - A::C::D `3^9x)=5^(y)=(75)^(z)=k` `x=(lnk)/(ln3),y=(lnk)/(ln5)=(xln3)/(ln5)` `z=(lnk)/(ln75),z=(lnk)/(ln3+2ln5)=(xy)/(2x+y)` `=(x)/(2log_(3)5+1)=(y)/(2+log_(5)3)` |
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| 41. |
The becquerel is the correct unit to use in reporting the measurement of: A. the rate of decay of a radioactive source B. the ability of a beam of gamma ray photons to produce ions in a target C. the energy delivered by radiation to a target D. the biological effect of radiation E. none of the above |
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Answer» A. the rate of decay of a radioactive source |
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| 42. |
The gray is the correct unit to use in reporting the measurement of: A. the rate of decay of a radioactive source B. the ability of a beam of gamma ray photons to produce ions in a target C. the energy per unit mass of target delivered by radiation to a target D. the biological effect of radiation E. none of the above |
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Answer» C. the energy per unit mass of target delivered by radiation to a target |
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| 43. |
A straight line through the point A `(-2,-3)` cuts the line `x+3y=9` and `x+y+1=0` at B and C respectively. If AB.AC`=20` then equation of the possible line isA. `x-y=1`B. `x-y+1=0`C. `3x-y+3=0`D. `3x-y=3` |
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Answer» Correct Answer - A::C Any point on line through A is `(-2+rcostheta,-3+rsintheta)` `because(-2+Abcostheta,-3+Absintheta)` liesd on `x+3y=9` `becauseAB=(20)/((costheta+3sintheta))` similarly `AC=(4)/((costheta+sintheta))` `because4=cos^(2)theta+4sinthetacostheta+3sin^(2)theta` `4+4tan^(2)theta=1+4tantheta+3tan^(2)theta` `tan^(2)theta-4tantheta+3=0` `tantheta=1` or `tantheta=3` `implies` required lines are `y+3=x+2` or `y+3=3(x+2)` |
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| 44. |
In `DeltaABC` if `a cos B =b cosA` then which of the following is always correct :A. `DeltaABC` is an equilateral traingleB. `DetlaABC` is an isosceles traingleC. `DeltaABC` is an isosceles right angle traingleD. None of these |
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Answer» Correct Answer - D `z^(2)+az+b=0` `& |z_(1)+z_(2)|=|z_(1)|+|z_(2)|` `implies" "z_(2)=kz_(1)(kgt0)` Now `z_(1)+z_(2)=-a" "z_(1)z_(2)=b` `impliesz_(1)(k+1)=-a" "implies" "kz_(1)^(2)=b` Given `a^(2)=lambda b` `implies (k+1)^(2)=lambda k` `implies lambda=((k+1)^(2))/(k)=k+(1)/(2)+2` Minimum value of `lambda` is 4 |
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| 45. |
To produce energy by fusion of two nuclei, the nuclei must: A. have at least several thousand electron volts of kinetic energy B. both be above iron in mass number C. have more neutrons than protons D. be unstableE. be magic number nuclei |
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Answer» A. have at least several thousand electron volts of kinetic energy |
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| 46. |
The sievert is the correct unit to use in reporting the measurement of: A. the rate of decay of a radioactive source B. the ability of a beam of gamma ray photons to produce ions in a target C. the energy delivered by radiation to a target D. the biological effect of radiation E. none of the above |
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Answer» D. the biological effect of radiation |
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| 47. |
The binding energy per nucleon: A. increases for all fusion events B. increases for some, but not all, fusion events C. remains the same for some fusion events D. decreases for all fusion events E. decreases for some, but not all, fusion events |
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Answer» A. increases for all fusion events |
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| 48. |
The least value of the expression `y=(1)/((3sin^(2)x + 3 sin x cos x + 7 cos ^(2)x))` is equal toA. `(2)/(15)`B. `(2)/(5)`C. `(2)/(3)`D. `-(2)/(5)` |
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Answer» `I_(n) = inte^(-x)s^(n)` `I_(n) = intn.(s)^(n-1).c.e^(-x)dx` `I_(n) = n(s)^(n-1).c.e^(-x)(-1)]_(0)^(oo)+int(n(n-1)s^(n-2).c^(2)-ns^(n))e^(-x)dx` `I_(n) = int(n(n-1).S^(n-2)-n(n-1)s^(n)-n.s^(n))e^(-x)dx` `I_(n) =n(n-1).I_(n-2)-n^(2).I_(n)` `I_(n) =(n(n-1))/(1+n^(2)).I_(n-2)` |
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| 49. |
If the nucleus of a lead atom were broken into two identical nuclei, the total mass of the resultant nuclei would be: A. the same as before B. greater than before C. less than before D. converted into radiation E. converted into kinetic energy |
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Answer» C. less than before |
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| 50. |
The void relation on a set A isA. ReflexiveB. Reflexive and symmetricC. Symmetric and TransitiveD. Reflexive and Transitive |
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Answer» Correct Answer - C The void relation on a set A are always symmetric and transitive relation. |
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