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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. |
If (2x+1)/((x-1)(x^(2)+2))=(A)/(x-1)+(Bx+c)/(x^(2)+2) then B= |
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Answer» 2 |
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| 2. |
The orbital diagram in which both the Pauli"s exclusion principle and Hund's rule are violated is :- |
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| 3. |
If A^(-1)=[{:(3,-1,1),(-15,6,-5),(5,-2,2):}] and B=[{:(1,2,-2),(-1,3,0),(0,-2,1):}] then find (AB)^(-1) |
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| 4. |
The sum of infinite terms of the series 5 - 7/3 + (9)/(3 ^(2)) - (11)/( 3 ^(3))+……..o is |
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| 5. |
Assertion : A matrix A is orthogonal if and only if A is non singular and A^(-1)=A^(T)Reason : By definition A is orthogonal if A A^(T)=A^(T)A=I |
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Answer» Assertion can be PROVED USING REASON |
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| 6. |
If 8![1/(3!)+5/(4!)]=""^(9)P_(r), then the value of r is equal to |
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Answer» 4 |
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| 7. |
If z_1, z_2 and z_3 be the vertices ofDelta ABC, taken in anti-clock wise direction and z_0 be the circumstance, then ((z_0 - z_1)/(z_0-z_2)) (sin2A)/(sin2B)+((z_0 - z_3)/(z_0 - z_2)) (sin 2 C)/(sin2 B) is equal to |
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Answer» 0 |
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| 8. |
If A,B,C,D are the length of tangents to the curves 1) y=4x^2 at (-1,4) 2) y=x^3+1 at (1,2)3) y=(x^3)/(2-x) at (1,1) 4) 2x^2+3xy-2y^2=8 at (2,3)then the ascending order of A,B,C,D is |
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Answer» A,B,C,D |
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| 10. |
Evaluate the following integrals (i)int_(0)^(pi/2)(2 sin x +3 cos x)/(sin x + cos x)dx |
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| 11. |
If P and Q be the points as referred to the question 1 then the tangents at P and Q to respective hyperbolas |
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Answer» are perpendicular |
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| 12. |
The eccentricity of the hyperbola with asymptotes 3x+4y=2 and 4x-3y=2 is |
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| 13. |
If sin x+siny=1/4,cos x+cosy=1/3 then tan((x+y)/2)= |
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Answer» `1//4` |
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| 14. |
The relation S on set {1,2,3,4,5} is S = {(1,1),(2,2),(3,3),(4,4),(5,5)} . The S is ......... |
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Answer» Only SYMMETRIC |
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| 15. |
Let R = {(a,a^3) | ais a prime number less than 10}.Find rng R^(-1). |
| Answer» SOLUTION :R = {(a,a^3)| a is a prime number less than 10. RNG `R^(-1)` = {2,3,5,7} = dom R | |
| 16. |
Find the coefficent of x^(6) in (1+3x+9x^(2))^(10) |
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| 17. |
Find the coordinates of the point where the line through (5,1,6) and 3hati+4hatj+hatk crosses the yz-plane. |
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| 18. |
The points A(1, 2, 7), B(2, 6, 3) and C(3, 10, -1) are |
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Answer» collinear Now, `AB=PV" of "B - PV " of "A` `vec(AB)=(2hati+6hatj+3hatk)-(1hati+2hatj+7hatk)` `=hati+4hatj-4hatk` `implies |AB|=sqrt((1)^(2)+(4)^(2)+(-4)^(2))` `=sqrt(1+16+16)=sqrt(33)` `BC=PV" of "C-PV" of "B` `=(3hati+10hatj-1hatk)-(2hati+6hatj+3hatk)` `=hati+4hatj-4hatk` `implies |BC|=sqrt((1)^(2)+(4)^(2)+(-4)^(2))` `=sqrt(1+16+16)=sqrt(33)` `AC=PV" of "C-PV" of "A` `vec(AC)=(3hati+10hatj-1hatk)-(1hati+2hatj+7hatk)` `=2hati+8hatj-8hatk` `implies |AC|=sqrt(2^(2)+8^(2)+(-8)^(2))=sqrt(4+64+64)` `=sqrt(132)=2sqrt(33)=sqrt(33)+sqrt(33)` `THEREFORE |AC|=|AB|+|BC|` Hence, the given points A, B and C are collinear. |
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| 19. |
A boxcontains 20 screws of which 5 are defective. Two screws are drawn at random. Find the probability of the event that (i) neither of the 2 screws is defective. (ii) atleast one of them is defective. |
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Answer» `(II) (17)/(38)` |
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| 20. |
For what value of lamda the system of equations x+y+z=6, 4x+lamda y-lamda z=0, 3x+2y-4z=-5 deos not possess a solution? |
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Answer» Solution :Let `Delta=[[1,1,1],[4,LAMDA,-lamda],[3,2,-4]]` `[[0,0,1],[4-lamda,2lamda,-lamda],[1,6,-4]]` (`C_1=C_2-C_1` `C_2=C_2-C_3`) =`1[[4-lamda,2lamda],[1,6]]` =`24-6lamda-2lamda=24-8lamda` We have `24-8lamda=0` or, `lamda=3` `therefore` The system of EQUATION does not POSSES solution for `lamda=3`. |
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| 21. |
If the range of the function f(x)={x/4}+cospi(((1-2[x]))/2)="sin"((pi[x])/2)+sin((pi[x])/2) is [(alpha),4,(beta)/4)uu[(gamma)/4,(delta)/4]uu[(2gamma+1)/4,(delta)/2],(where {.} and [.] represent fractional part and greatest integer part functions respectively), then alpha^(2)+beta^(2)+gamma^(2)+delta^(2) is |
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| 22. |
Solve the following LPP graphically : Maximise Z = 2x + 3y, subject to: x + y le 4, x ge 0, y ge 0. |
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| 23. |
The rank of the matrix [{:(3,2,1,-4),(2,3,0,-1),(1,-6,3,-8):}] is |
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Answer» 1 |
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| 24. |
int (1)/(4 sqrt((x - 1)^(3)(x + 2)^(5))) dx = |
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Answer» `(4)/(3) ((X- 1)/(x + 2))^((1)/(4))` + C |
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| 25. |
By using properties of determinants, prove that |[y+k,y,y],[y,y+k,y],[y,y,y+k]|=k^2(3y+k) |
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Answer» SOLUTION :`|[y+K,y,y],[y,y+k,y],[y,y,y+k]|` `|[3y+k,y,y],[3y+y,y+k,y],[3y+y,y,y+k]|(byC_1rarrC_2+C_3)` `=(3y+k)|[1,y,y],[1,y+k,y],[1,y,y+k]|` `(3y+k)|[1,y,y],[0,k,0],[0,0,k]|`(by`R_2rarrR_2-R_1`and`R_3rarrR_3-R_1`) `=(3y+k)k^2=k^2(3y+k)` |
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| 26. |
(d)/(dx) (sin^(-1)x + cos^(-1) x)=……..(|x| lt 1) |
| Answer» Answer :A | |
| 27. |
Show that lim_(nrarr infty) sum_(k=0)^(n)(""^(n)Ck)/(n^k(k+3))=e-2 |
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| 28. |
Which term in the expansion of (2-3x)^(19) has algebrically the last coefficients ? |
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Answer» `10^(th)` Using `r le (n+1)/(1+|(a)/(bx)|)`, we get `RLE(19+1)/(1+|2/3|)rArr r le 12` Therefore, `T_(13)` and `T_(12)` have numerically the greatest conefficient. `T_(12)` is ALGEBRICALLY the least as it is followedby negative sign. |
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| 29. |
The value of cos ycos((1)/(2)pi-x)-cos((1)/(2)pi-y)cosx+sinycos((1)/(2)pi-x)+cosxsin((1)/(2)pi-y) is zero is |
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Answer» `x=0` |
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| 30. |
Simplify (1 + cos x + i sin x)^n, n epsilon N. |
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| 32. |
Kellogg is a new cereal formedof a mixtureof bran and ricethat constains at least 88 gramsof protein and at least 36milligrams ofironknlowing that bran contains 80 grams of protein and 40 milligrams of iron per kilogram and that rice contains 100 gramsof proteinand 30 milligrams of iron per kilogramif bran costs Rs 5 per kilogramand rice costs Rs 4 per kilogram |
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| 33. |
A conic section is defined by the equations x=-1+sec t, y=3+3 tan t. the coordinates of the foci are |
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Answer» `(-1-sqrt(10),2) and (-1+sqrt(10),2)` |
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| 34. |
Integrating the following functions ((x-3) e^x)/(x-1)^3 |
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Answer» SOLUTION :`int ((x-3) e^x)/(x-1)^3 DX = int ((x-1)-2)/(x-1)^3 e^x dx` =`int (1/(x-1)^2- 2/(x-1)^3)e^x dx` `e^x/(x-1)^2+c, f(x) = 1/(x-1)^2` `f^.(x) = -2/(x-1)^2` |
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| 35. |
Prove that- omega, " and " - omega^(2) arethe roots ofz6(2) - z + 1= 0, where omega " and " omega^(2) are thecomplex cube roots of unity . |
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| 37. |
If f'(x)=x e^(x) and f(0)=1then find f(x). |
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| 38. |
Find the variance and standard deviation of the following data5,12 , 3 , 18 , 6 , 8 , 2, 10 . |
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| 39. |
The solution of (dy)/(dx) + (2x)/(1 + x^(2)) y = (1)/((1 + x^(2))^(2)), is |
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Answer» `y(1+X^(2)) = Tan^(-1)x-(pi)/(4)` |
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| 40. |
Prove the following: [[a+b+c,-c,-b],[-c,a+b+c,-a],[-b,-a,a+b+c]] =2(b+c)(c+a)(a+b) |
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Answer» SOLUTION :`[[a+b+c,-c,-b],[-c,a+b+c,-a],[-b,-a,a+b+c]]` `[[a+b,-c-b,-b],[a+b,b+c,-a],[-a-b,b+c,a+b+c]]` `(C_1=C_1+C_2, C_2=C_2+C_3)` =`(a+b)(b+c)[[1,-1,-b],[1,1,a],[-1,1,a+b+c]]` `(a+b)(b+c)[[0,-1,-b],[2,1,a],[0,1,a+b+c]]` `(C_1=C_1+C_2)` =`(a+b)(b+c)xx(-2)[[-1,-b],[1,a+b+c]]` =-2(a+b)(b+c)(-a-b-c+b) =2(a+b)(b+c)(c+a) |
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| 41. |
Find the area enclosed by xy=a^2,x=0,y=alpha,y=beta(beta gt alpha gt 0) |
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Answer» SOLUTION :AREA = `int_alpha^betaxdy=int_alpha^betaa^2/ydy` `=a^2[In y]_alpha^beta=a^2In(beta//alpha)` |
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| 42. |
Integrate the following functions x^2/(1-x^6) |
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Answer» SOLUTION :LET t = `x^3`. Then DT = `3x^2 dx` `gt x^2 dx = 1/3 dt` therefore` int x^2/(1-x^6) dx = int x^2/(1-(x^2)^3) dx` = `int 1/(1-t^2) 1/3 dt` =`1/3 xx 1/2 log |(1+t)/(1-t)|+C` =`1/6 log|(1+x^3)/(1-x^3)|+c` |
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| 43. |
Which of the following is not true for any two statements p and q? |
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Answer» `~[pvv(~Q)]-=(~p)^^q` |
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| 44. |
Integrate the following functions : x^(2)tan^(-1)x |
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| 48. |
From a collection of 20 consecutive natural numbers,four are selected such that they are not consecutive .The number of such selections is |
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Answer» `284xx17` |
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| 49. |
IF3x^2+ 8xy- ky^2+ 29x-3y+ 18is resolvableintotwolinearfactorsthen k= |
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Answer» 2 |
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