Saved Bookmarks
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 the tangents and normals at the extremities of a focal chord of a parabola intersect at (x_(1),y_(1)) and (x_(2),y_(2)) respctively then |
|
Answer» `x_(1)=x_(2)` |
|
| 2. |
int dx/(sin x + sin 2x )= |
|
Answer» `1/2 log_(e) abs(1+ COS x ) + 1/6 log_(e) abs(1-cosx) -2/3 log_(e) abs(1+ 2cos x ) + c` |
|
| 3. |
The solution of (dy)/(dx) = (x-2y + 3)/(2x-y + 5) is |
|
Answer» `X^(2) - 4xy +y^(2) + 6x - 10 y = C` |
|
| 4. |
then |
|
Answer» F(x) attains itsminimum at x=0 |
|
| 5. |
If the line passing through P=(8,3) meets the circle S-=x^(2)+y^(2)-8x-10y+26=0 at A,B then PA.PB= |
|
Answer» 5 |
|
| 7. |
Find the derivative of the function given by f(x) = (1 + x) (1 + x^(2)) (1 + x^(4)) (1 + x^(8)) and hence find f'(1) |
|
Answer» |
|
| 8. |
Let a_(0)x^(n)+a_(1)x^(n-1)+…+a_(n-1)x+a_(n)=0 be the degree equation with a_(0),a_(1),…a_(n) integers. If p/q is a rational root of theis equation, then p is a divisor of a_(n) and q is a divisor of a_(0). If a_(0)=1, then every rational root of thsi equation must be an integer. At least one integral root of the equation x^(3)-13x^(2)+15x+189=0 exceeds another root by |
|
Answer» 1 |
|
| 9. |
Find the area of the region {(x, y) : y^(2) le 4x, 4x^(2) + 4y^(2) le 9} |
|
Answer» |
|
| 10. |
find the generalsolution : (dy)/(dx)= sin x |
| Answer» | |
| 11. |
For all real values of a _(0) , a _(1), a _(2), a _(3) satisfying a _(0)+ (a _(1))/(2) + (a _(2))/( 3) + ( a _(3))/(4) =0, the equationa _(0) + a _(1) x + a _(2) x ^(2) + a _(3) x ^(3) =0has a real root in the interval |
|
Answer» `[0,1] |
|
| 12. |
If f(x)={:{(3x^2+12"," x-1),(37-x ","2 lt x le 3):} then |
|
Answer» f(X) INCREASING on [-1,2] So f(x) is CONTINUOUS on [-1,3] THUS options (b) and (c ) are correct . ALSO `(LHD at x =2) ={d/(dx)(37 -x)}_(atx=2)`=24 Clearly f(x) is not differentiableat x=2 So f(2) does not exist. Now `f(x)={(6x+12","-1 lt xlt 2 ),(-1","2 ltx lt 3):}` Cleary `f' (x)lt 0 for all x in [-1, 2] ` So f(x) in increasing on [-1,2] Thus option (a) is correct . |
|
| 13. |
The parabola x^2=4ay makes an intercept of length sqrt40 units on the line y=1+2x then a values of 4a is |
|
Answer» A2 |
|
| 14. |
Evalute the following integrals int (1)/(sqrt(1 + x - x^(2)) dx |
|
Answer» |
|
| 15. |
{:(" "Lt),(n rarr oo):} sum_(r=1)^(n)((r^(3))/(r^(4)+n^(4)))= |
|
Answer» LOG 2 |
|
| 16. |
The matrix A =((p,-q),(q,p)) is orthogonal if and only if |
|
Answer» <P>`p^(2)+q^(2)=1` |
|
| 17. |
From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs. |
|
Answer» |
|
| 18. |
if 1,log_(9)(3^(1 - x) + 2),log_(3)[4.3^(x) - 1] are in A.P. then x equals |
|
Answer» `log_(3)4` |
|
| 19. |
If a plane P passes through the points (1, 0, 0), (0, 1, 0) and makes an angle pi/4 with the plane x+y=3, then the direction ratios of a normal to that plane P is |
|
Answer» `1, SQRT(2), 1` |
|
| 20. |
The number of ways in which we can choose two positive integers from 1 to 100 such that their product is a multiple of 3 is |
|
Answer» `""^(100)C_(2)-""^(33)C_(2)` |
|
| 21. |
A pair of fair dice is rolled 2 times. Find the mean of the number of doublets on the dice. Find also variance of the number of doublets on the dice. |
|
Answer» |
|
| 22. |
ABCD is a parallelogram with vec(AC) = hati - 2hatj + hatk and vec(BD) = -hati + 2hatj - 5hatk. Area of this parallelogram is equal to: |
|
Answer» `sqrt(5)//2` sq. UNITS |
|
| 23. |
If a variable takes values 0, 1, 2,…,n with frequencies q^(n), (n)/(1)q^(n-1)p, (n(n-1))/(1.2)q^(n-2)p^(2),…,p^(n) where p+q = 1, then the mean is |
| Answer» ANSWER :B | |
| 24. |
Prove that cot((pi)/8) - tan((pi)/8) = 2 |
| Answer» SOLUTION :`COT(pi/8)-TAN(pi/8)=1/(tan(pi/8))-tan(pi/8)/1=1-tan^2(pi/8)/tan(pi/8)=2/tan(2xxpi/8)=2/tan(pi/4)=2` | |
| 25. |
Let A and B be 2xx2 matrices with real entries . Let I be the 2xx2 indentity matrix. Denote by tr (A) the sum of diagonal entries of A . Statement -1 : AB -BA ne I Statement -2 : tr (A+B ) = tr (A) +tr (B) and tr (AB) =tr (BA) |
|
Answer» |
|
| 26. |
No. of distinct terms in (x + y - z)^16 is |
|
Answer» 154 |
|
| 27. |
1+(2)/(4) + (2.5)/(4.8)+(2.5.8)/(4.8.12)+(2.5.8.11)/(4.8.12.16)+…..= |
|
Answer» `4^(-2//3)` |
|
| 28. |
Rajesh agrees to play the game of tossing dice. If number 1 or 2 comes up he looses ₹ 2 and if number 3 or 4 or 5 comes up he gets ₹ 5 and he loose ₹ 10 if number 6 comes up. If random variable X denotes the amount get by Rajesh then find expectation. |
|
Answer» |
|
| 29. |
Statement-1 : z_(1)^(2) + z_(2)^(2) +z_(3)^(2) +z_(4)^(2) =0 " where " z_(1) ,z_(2),z_(3) and z_(4) are the fourth roots of unity and Statement -2 :(1)^(1/4) = (cos0^(@) +isin0^(@))^(1/4) |
|
Answer» Statement -1 is True, Statement -2 is True, Statement -2 is a correct EXPLANATION for statement -4 |
|
| 30. |
If the system of linear equations x+2ky+3z=0 3x+2ky-2z=0 2x+4y -3z=0has a non -zero solution (x,y,z) then |(yz)/(2x^(2))|=____ |
|
Answer» |
|
| 31. |
Number of integral values of 'x' satisfying |x+4|+|x-4|=8 is :- |
|
Answer» 8 |
|
| 32. |
Area of the triangle formed by the lines through point (6, 0) and at a perpendicular distance of 5 from point (1, 3) and liney = 16in square units is : |
|
Answer» 160 |
|
| 33. |
In a certain college , 40% of the men and 10% of the women are taller than 2 meters. Further more in the college 60% of the students are women. If a student selected at random is found to be taller than 2 meters,the probability that the selected student is awoman is |
|
Answer» `(3)/(11)` |
|
| 34. |
lim_(ntooo)1/n{sin^(5)(pi/(6n))+sin^(5)((2pi)/(6n))+sin^(5)((3pi)/(6n))+...+sin^(5)(pi/2)}= |
|
Answer» `8/(15pi)` |
|
| 35. |
3^(2(n-1)) + 7 is divisible by 8 for every natural n ge 2. |
|
Answer» SOLUTION :Let `P_n = 3^(2(n-1)) + 7` When `n =2. 3^2 + 7 = 16` is divisible by 8. `THEREFORE P_2` is true. `P_k` be true. i.e, `3^(2(k-1)) + 7` is divisible y 8. Let `3^(2k-2) + 7` = 8m. M in Z . Now `3^(2(k+1-1) +7 = 3^2k + 7` `3^(2k-2).3^2 + 63-56` = `9(3(2k-2) + 7)-56` = `9 xx 8m - 56` = 8(9m-7) Which is divisible by 8. `therefore P_(k+1)` is true. `therefore P_n` is true for all values on `n le 2` |
|
| 36. |
Rajat observes that the angle of elevation of the first floor of a building at a point A on the ground is 30^(@). He moves sqrt(3) units towards the building to the point B and finds that the angle of elevation of the second floor of the building is 60^(@). If each floor has the same height, height of the 7th floor from the ground in units is |
|
Answer» 5 |
|
| 37. |
lim_(x rarr 0) ((tan x - x)/(x)) sin ((1)/(x)) is : |
|
Answer» a real number other than 0 and 1 |
|
| 38. |
Find the number of positive integers n such that 105 is a divisor of n^(2)+n+1 |
|
Answer» `IMPLIES` 5 does not divides `n^(2)+n+1` `implies` 105 is not a divisor of `n(n+1)+1`, |
|
| 39. |
Let S_(2) = 0 is the mirror image of S_(1) : x_(2) + y_(2) – 4x – 6y + 12 = 0 w.r.t the line L_(1) : 10^(4)x + (10^(4) + 10)y + (10^(4) + 20) = 0. Let L_(2) : 2^(11) x + (2^(11) + 2^(12))y + (2^(11) + 2^(13)) = 0 be a line then the equations of line passing through the point of intersection of the line L^(2) = 0 with radical axes of S_(1) = 0, S_(2) = 0 and making equal intercepts in magnitude with the coordinate axes is/are |
|
Answer» ) x – y – 3 = 0 |
|
| 40. |
The plane passes through the point (1,-1,-1) and its normal is perpendicular to both the lines (x-1)/(1) = (y+2)/(-2) = (z-4)/(3) and (x-2)/(2) + (y+1)/(-1) = (z+7)/(-1). The distance of the point (1,3,-7) from thise plane is .......... |
|
Answer» `(10)/(SQRT(74))` |
|
| 41. |
Integrate the following functions (1+logx)^2/x |
|
Answer» SOLUTION :Let t = 1+logx. Then DT = 1/x dx. ` THEREFORE INT (1+logx)^2/x dx = int t^2dt` = `t^3/3 +c = (1+logx)^3/3 +c` |
|
| 42. |
Differentiate the following w.r.t. x : cot(logx+e^(sqrtx)) |
|
Answer» |
|
| 43. |
Two numbers x and y are selected at random from the set {1, 2, 3,… 3n}. Find the probability that x^(2) - y^(2) is divisible by 3. |
|
Answer» |
|
| 45. |
Given the following table Computeri) E(4X+5) ii) E(X^(2)) iii) V(X)iv) V(2X+-3) |
|
Answer» |
|
| 46. |
If centre (1, 2), axes are parallel to co-ordinate axes, distance between the foci 8, e = (1)/sqrt(2)then equation of the ellipse is |
|
Answer» `(x-1)^(2)/(32)+(y-2)^(2)/(16)=1` |
|
| 47. |
The position vector of the point which divides the join of points 2bar(a)-3bar(b) and bar(a)+bar(b) in the ratio 3 : 1, is …………. |
|
Answer» `(3BAR(a)-2BAR(b))/(4)` |
|
| 48. |
Which of the following is equivalent to (x ^(2) + 3x + 7)/(x +4 ) ? |
|
Answer» `(3+7)/(4 )` |
|
| 49. |
If f(x)={{:(cos^(-1) (cotx),","x lt pi/2),(a(x[x]-1),"," x ge pi/2):} The value of a for f to be continuous at x=pi/2 is |
|
Answer» `PI/(2(pi-1))` |
|