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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 veca. veci =veca. (veci+vecj)=veca.(veci+vecj+veck)," then "veca is equal to |
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Answer» `HATI` |
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| 2. |
If (e^x)/(1-x)=B_0 +B_1 x +B_2 x^2 + ....... + B_(n-1) x^(n-1) +B_(n)x^n+ .... then the value of (B_n-B_(n-1)) is |
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Answer» `1/((N-1)!)` |
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| 4. |
In the matrix A=[[2,5,19,-7],[35,-2,5/2,12],[sqrt3,1,-5,17]] Write: The order of this matrix |
| Answer» SOLUTION :Since A has 3 rows and 4 COLUMNS. The ORDER of A is `3xx4 (3by4)` | |
| 5. |
Differentiate w.r.t.x the function in Exercises 1 to 11. sin^(-1)(x sqrt(x)), 0 le x le 1. |
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| 6. |
Evaluate the following integrals: int_4^5 e^x dx |
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Answer» SOLUTION :`int_4^5 e^x DX = (e^x)_4^5` =`e^5-e^4 = e^4(e-1)` |
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| 7. |
If 1,omega,omega^2 are cube roots of unity, then, : Delta=|(1,omega^n,omega^(2n)),(omega,1,omega),(omega^n,omega^(2n),1)| is equal to : |
| Answer» Answer :D | |
| 8. |
A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag. |
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| 9. |
The sides of a rectangle , with maximum perimeter, inscribedin a semicircle of radius R are |
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Answer» `R/2,R/2` |
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| 10. |
The term independent of x in the expansion of (x^(2) - 1/(3x))^(9) is equal to |
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Answer» `28/81` |
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| 11. |
For points P -= (x_(1) ,y_(1)) and Q = (x_(2),y_(2)) of the coordinate plane , a new distance d (P,Q) is defined by d(P,Q) = |x_(1)-x_(2)|+|y_(1)-y_(2)| Let O -= (0,0) ,A -= (1,2) B -= (2,3) and C-= (4,3) are four fixed points on x-y plane Le T(x,y) such that T is equisdistant from point O and C with respect to new distance and if T lie in first quadrant , then T consists of the union of a line segment of finite length and an infinite ray whose labelled diagramis |
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| 12. |
Let f(x)=[x]+{x}^(3) then the area of the figure bounded by y=f^(-1)(x),y=0 between the ordinates x=2 and x=9/2 is alpha, then alpha-3/(2^(10//3))+1/2 is equal to ________(where [.] denotes the greatest integer function) |
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Answer» So, `int_(2)^(9//2)[x]dx+int_(2)^(9//2){x}^(1//3)=17/2+3/(2^(10//3))` |
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| 14. |
A particle covers distance S in time t is given by S=t^(3)-6t^(2)+6t+8. When the acceleration is 0, the velocity is ………… |
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Answer» 5 cm/sec |
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| 16. |
A+C=2B then (cosC-cosA)/(sinA-sinC)= |
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Answer» cotB |
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| 17. |
Every gram of wheat provides 0.1 gm of proteins and 0.25 gm of carbohydrates. Thecorresponding values of rice are 0.05 gm and 0,5 gm respectively. Wheat costs Rs 4 per kg and rice Rs 6. The minimum daily requirements of proteins and carbohydrates for an average child are 50 gm and 200 gm respectively. In what quantities should wheat and rice be mixed in the daily diet to provide minimum daily requirements of proteins and carbohydrates at minimum cost? |
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| 18. |
For points P -= (x_(1) ,y_(1)) and Q = (x_(2),y_(2)) of the coordinate plane , a new distance d (P,Q) is defined by d(P,Q) = |x_(1)-x_(2)|+|y_(1)-y_(2)| Let O -= (0,0) ,A -= (1,2) B -= (2,3) and C-= (4,3) are four fixed points on x-y plane Let R(x,y) such that R is equisdistant from tthe point O and A with respect to new distance and if0 le x lt 1 and 0 le y lt 2, then R lie on a line segment whose equation is |
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Answer» `x+y=3` |
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| 19. |
For points P -= (x_(1) ,y_(1)) and Q = (x_(2),y_(2)) of the coordinate plane , a new distance d (P,Q) is defined by d(P,Q) = |x_(1)-x_(2)|+|y_(1)-y_(2)| Let O -= (0,0) ,A -= (1,2) B -= (2,3) and C-= (4,3) are four fixed points on x-y plane Let S(x,y) such that S is equisdistant from points O and B with respect to new and if x ge 2 and 0 le y lt 3 then locusof S is |
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Answer» a line SEGMENT of INFINITE length |
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| 20. |
If the equation of the parabola whose axis is parallel to x-axis and passing through (2,-1),(6,1),(3,-2)is ay^(2)+bx+cy+d=0 then the ascending order of a,b,c,d is |
| Answer» Answer :D | |
| 21. |
lim_(ntooo)([6^(2)+12^(2)+18^(2)+....+(6n)^(2)]^(2))/([5+10+15+...+5n][2^(3)+4^(3)+6^(3)+...+8n^(3)]) |
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Answer» `4/5` |
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| 23. |
Find the vector equation of line passing through point (1,2,-4) and perpendicular to two lines (x-8)/3 = (y+19)/-16 = (z-10)/7 and (x-15)/3 = (y-25)/8 =(z-5)/-5 |
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Answer» `(x-1)/(2)=(y-2)/(3)=(z+4)/(8)` |
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| 24. |
Find the area of the region bounded by x^(2)=4y,y=2,y=4 and the y-axis in the first quadrant. |
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| 25. |
Construct truth tables for the following and indicate which of these are tautologies ~p^(p^q)arrow q |
Answer» SOLUTION :
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| 26. |
Using differential find the approximatevalue of tan 46^(@) , Ifit is being given that 1^(@) = 0.01745 radian. |
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| 27. |
If 2x+y le 8, y le 4, x le 3, x ge 0, y ge 0, then the maximum value of f=2x+y is |
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Answer» 4 |
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| 28. |
A manufacturer producestwo models A and Bof a product each pieceof model A requires 9 labourhours for fabricating and 1 labour hours for fabricating and 3 labour hour for for finishing for fabnricating and finishing the maximum labour hours available are 180 and 30 respectively the company makes a profit of Rs 8000on eachpieceof model A and Rs 12000oneach pieceof model Bformulate a LPPso as to maxmizehis profitper week and solvethe problem graphically |
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| 29. |
The total revenue in Rupees received from the sale of x units of a product is given by R(x)=3x^(2)+36x+5. The marginal revenue, when x = 15 is ……… |
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Answer» 116 |
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| 30. |
Given the parabola C : y = x^(2). If the circle at y axis withradius 1 touches parabola C at two distinct points, then find the coordinate of the center of the circle K and the area of the figure surrounded by C and K. |
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| 31. |
Two similar boxes B_(i) (i-=1,2) contain(i+1) red and (5-i-1) black balls. One box is chosen at random and two balls are drawn randomly. What is the probability that both the balls are of different colours? |
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Answer» `(1)/(2)` |
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| 33. |
Which one of the following is not correct for the features of exponential function given by f(x) = b^(x) where b gt 1 ? |
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Answer» For every LARGE NEGATIVE values of X, the function is very close to 0. |
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| 34. |
If(3x)/((x - a ) (x - b)) = (2 )/(x-a)+ (1)/(x - b),thena :bis equalto |
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Answer» ` 1: 2 ` ` rArr (3x )/((x - a )(x - b)) = (2(x - b)+(x-a))/((x-a)(x-b)) ` ` rArr3x= 3x - 2b - a` ` rArr - 2 b - a =0 ` ` rArr- 2 b =a ` ` rArr(a)/(b) =( -2)/(1)` `thereforea : b =- 2 :1 ` |
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| 35. |
Prove that |{:(a^2,bc,ac+c^2),(a^2+ab,b^2,ac),(ab,b^2+bc,c^2):}|=4a^2b^2c^2 |
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| 36. |
To find the equation of the hyperbola from the definition that hyperbola is the locus of a point which moves such that the difference of its distances from two fixed points is constant with the fixed point as foci |
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| 37. |
The perpendicular distance of the point (3,2,1) from the plane 3x+4y-2z - 10 = 0 is............... |
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Answer» `(3)/(sqrt(14))` |
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| 38. |
What is the slope of line l shown in the xy-plane above? |
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| 39. |
Read the following writeup carefully: In argand plane |z| represent the distance of a point z from the origin. In general |z_1-z_2| represent the distance between two points z_1 and z_2. Also for a general moving point z in argand plane, if arg(z) =theta, then z=|z|e^(itheta), where e^(itheta) = cos theta + isintheta. Now answer the following question [|z-z_1|-|z-z_2|]=t, where t is real parameter always represents |
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Answer» ellipse |
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| 40. |
There are 2m persons sitting in a row. Two of them are selected at random. If the probability the selected are not together is 15/17, then m is equal to _____ |
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| 41. |
Read the following writeup carefully: In argand plane |z| represent the distance of a point z from the origin. In general |z_1-z_2| represent the distance between two points z_1 and z_2. Also for a general moving point z in argand plane, if arg(z) =theta, then z=|z|e^(itheta), where e^(itheta) = cos theta + isintheta. Now answer the following question The equation |z-z_1|+|z-z_2|=10 if z_1 =3 + 4i and z_2 =-3 -4i represents |
| Answer» Answer :D | |
| 42. |
The region of the argand plane defined by |z-i| + |z +i| le 4 is |
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Answer» interior of an ellipse |
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| 43. |
If f(x)=lim_(nrarroo)((x^(2)+ax+1)+x^(2n)(2x^(2)+x+b))/(1+x^(2n)) and lim_(xrarrpm1)f(x) exists, then The value of b is |
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Answer» `-1` `={{:(x^(2)+ax+1",",|x|lt1),(2x^(2)+x+b",",|x|gt1),((-a+b+3)/(2)",",x=-1),((a+b+5)/(2)",",x=1):}` `underset(xrarr-1)(lim)f(x)" EXISTS if"` `underset(xrarr -1)(lim)f(x)=underset(xrarr-1^(+))(lim)f(x)` `rArr""underset(xrarr-1^(-))(lim)(2x^(2)+x+b)=underset(xrarr-1^(+))(lim)(x^(2)+ax+1)` `rArr""2-1+b=1-a+1` `rArr""a+b=1"(i)"` `underset(xrarr1)(lim)f(x)" exists if"` `underset(xrarr1^(-))(lim)f(x)=underset(xrarr1^(+))(lim)f(x)` `rArr""underset(xrarr1^(-))(lim)(x^(2)+ax+1)=underset(xrarr1^(+))(lim)(2x^(2)+x+b)` `rArr 1+a+1=2+1+b` `rArr a-b=1"(ii)"` `"Solving EQS. (i) and (ii), we get a = 1 and b=0."` |
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| 44. |
A polygon has 54 diagonals. Number of sides of this polygon is |
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Answer» 12 |
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| 45. |
For eachnaturalnumberthestatement P(n)= n(n +1) (2n +1)isdivisibleby |
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Answer» 6 |
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| 46. |
Differentiate e^(tan^(-1) x^2) |
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Answer» Solution :LET y = `e^(tan^(-1)x^2) IMPLIES dy/dx = e^(tan^(-1)x^2) CDOT d/dx(tan^(-1)x^2) e^(tan^(-1)x^2)1/(1+x^4) d/dx(x^2)` |
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| 47. |
If V is the volume of the parallelepiped having three coterminous edges, as vec(a),vec(b)andvec(c), then the volume of the parallelepiped having three coterminous edges as alpha=(vec(a).vec(a))vec(a)+(vec(a).vec(b))vec(b)+(vec(a).vec(c))vec(c) beta=(vec(a).vec(b))vec(a)+(vec(b).vec(b))vec(b)+(vec(b).vec(c))vec(c) gamma=(vec(a).vec(c))vec(a)+(vec(b).vec(c))vec(b)+(vec(c).vec(c))vec(c) is |
| Answer» Answer :A | |
| 48. |
Let f :R to R is not identically zero, differentiable function and satisfy the equals f(xy)= f(x) f(y) and f (x+z) = f(x) + f (z), then f (5)= |
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Answer» 3 |
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| 49. |
Integrate the following functions : (5+logx)/((6+logx)^(2)) |
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