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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. |
Find the condition for the line y=mx+c to be a tangent to the parabola x^(2)=4ay. |
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| 2. |
Through a given point O a straigt line is drwan to cut two given straight line in R and S. find the locus of a point P on this variable stright line which is such that 2OP = OR +OS |
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| 3. |
Let a, b, c, p, q be five different non-zero real numbers and x,y,z be three numbers satisfying the system of equations (x)/(a) + (y)/(a - p) + (z)/(a - q) = 1(x)/(b) + (y)/(b - p) + (z)/(b - q) = 1 and (x)/(c) +(y)/(c - p) + (z)/(c - p) = 1 then x equals |
| Answer» Answer :A | |
| 4. |
According to Newton's law of cooling, the body cools from 80^(@)Cand50^(@)C at room temperature of 25^(@)C in 30 minutes. After 1 hours, the temperature of the body is |
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Answer» `11.36^(@)C` |
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| 5. |
Two of the lines represented by x^(3)-6x^(2)y+3xy^(2)+dy^(3)=0 are perpendicular for |
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Answer» all REAL values of d |
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| 6. |
If |veca+vecb|=60,|veca-vecb|=40 and |veca|=22 then find |vecb|. |
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Answer» `vec|b|=46` |
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| 7. |
If the value ofA for which the equation cot^(3)A+cot^(2)A|cotA+x|+|cot^(2) Ax+1|=1 has not less than 6 different solutions which are integers are [cot^(-1)alpha, pi)uu[cot^(-1)beta,cot^(-1)gamma] then |
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Answer» `|a^(3)+a^(2)x|+|a^(2)x+1|=(a^(2)+1)-(a^(2)x+a^(3))` `|ALPHA|+|beta|=alpha=beta` So, `alpha ge 0` and `beta LE0` Now take cases: `a le -1`and `-1 lt le 0` & `0lt ale 1` Finally we get `aepsilon (-oo,-5]uu[1/(sqrt(5)),1/(sqrt(6))]` |
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| 8. |
If I=int((lnx)^(5))/(sqrt(x^(2)+x^(2)(lnx)^(3)))dx=ksqrt((lnx)^(3)+1)((lnx)^(3)-2)+c (where c is the constant of integration), then 9k is equal to |
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Answer» 4 |
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| 9. |
Classify 5 seconds measures as scalar and vector. |
| Answer» SOLUTION :Time-scalar | |
| 10. |
A: f(x)=1/(1+e^(1//x)) (x ne 0) and f(0)=0 is right continuous at x=0 R: underset(x to 0)"Lt" (1)/(1+e^(1//x)=0 |
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Answer» Both A and R are TRUE and R is the correct explanation of A |
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| 11. |
" Prove that " : int(2 sin x +3 cos x)/(3sin x+4 cos x) dx = (18x)/(25) +(1)/(25)log|3s sin x+ 4cosx|c |
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| 12. |
z_(1) , z_(2) are two complex numbers with|z_(1) - z_(2)| ltk. If the complex number z satisfies the condition |z_(1) - z_(2)| + |z - z_(2)| = k , then z lies on |
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Answer» a parabola |
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| 13. |
Evalute the following integrals int ((1)/(sqrt(x + a) sqrt(x + b)) )dx = |
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Answer» `(3)/(2(a - B)) ((X + b)^(3//2) - (x + b)^(3//2) ) + c ` |
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| 14. |
If A , B and C are square matrices of same order, thenAB=AC always implies that B=C. |
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| 15. |
Two circles are inscribed and circumscribed about a square ABCD, ength of each side of the square is 32. P and Q are two points respectively on these circes, then [sum (QA)^(2) -- sum (PA)^(2) ] is equal ot |
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| 16. |
Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(2){x}dx=....... where {x} denotes fractional part of x. |
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Answer» 0 |
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| 17. |
The value of f(k)=int_(0)^(pi//2) log (sin ^(2) theta +k^(2) cos^(2) theta) d thetais equal to |
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Answer» `PI LOG (1+k)- pi log ^(2)` |
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| 18. |
Let A = {4,5,6} . A relation R on A is given as R = {(4,5),(5,4)} . The relation R is |
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Answer» Only REFLEXIVE |
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| 19. |
Show that among the points on the ellipse x^2/a^2+y^2/b^2=1 (agtb),(-agt0) is the fatthest point and (a,0) is the nearest point from the focus(ae,0). |
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| 20. |
The vector equation of the plane perpendicular to the vector 3hati-2hatj+3hatk and passing through a pont having position vector hati+hatj+2hatk is |
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Answer» `BARR.(3hati-2hatj+3hatk)-7=0` |
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| 21. |
Consideer the following statements : I . Number of ways of placing 'n' objects in k bins (k le n) such that no bin is empty is ""^(n-1)C_(k-1). II. Number of ways of writing a positive integer 'n' into a sum of k positive integers is ""^(n-1)C_(k-1). III. Number of ways of placing 'n' objects in k bins such that atleast one bin is non- empty is ""^(n-1)C_(k-1). IV. ""^nC_k - ""^(n-1)C_k = ""^(n-1)C_(k-1) then which of the above statements are true ? |
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Answer» All the FOUR STATEMENTS |
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| 22. |
On Z, the set of integers define a relation Ras follows: a, b in Z, aRb if 3|(2a + b) Then |
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Answer» R is reflexive, symmetric but not TRANSITIVE |
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| 23. |
Given, n = 5, Sigma x_(i) = 25, Sigma y_(i) = 20, Sigma x_(i) y_(i) = 90 and Sigma x_(i)^(2) = 135, find the regression coefficient of y on x. |
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| 24. |
If 0 le arg (z) le (pi)/4 then least value of sqrt(2)|z – i| is, (where i =sqrt(-1)) |
Answer»  MINIMUM value of `|z-i|` = DISTANCE of point (0,1) from the LINE `y-x=0` `=1/(sqrt(2))`. |
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| 25. |
If f:A rarr B defined by f(x)=sinx-cosx+3sqrt2 is an invertible function, then the correct statement can be |
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Answer» `A=[(PI)/(4),(5pi)/(4)],B=[3sqrt2, 4sqrt2]` |
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| 26. |
Resolve into partial fractions the expression (8x^(3)-5x^(2)+2x+4)/((2x-1)^(2)(3x^(2)+4)) |
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| 27. |
$1,600 worth of $20 bills stacked up that reach 0.35 inches high OR $1,050 worth of $10 bills are also stacked up (assume all denominations are the same thickness) {:("Quantity A","Quantity B"),("The percent by which the height",33.5%),("of the stack of "$10" bills ",),("is greater than that of the stack",),(" of "$20" bills ",):} |
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| 28. |
The slope of the tangent to the curve y=int _(0) ^(x)(dt)/(1+t^3) at the point where x = 1 is |
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Answer» `1/4` |
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| 29. |
The mean of a data set consisting of 20 observations is 40. If on observations 53 was wrongly recorded as 33, then the correct mean will be |
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Answer» 41 |
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| 30. |
If characteristic of three numbers a, b and c and5, -3 and 2, respectively, then find the maximum number of digits in N = abc. |
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Answer» ` log a = 5+p` ` log B =- 3+ q` ` log c = 2 + r` where p,q and r are mantissas. `:.P,q,r in [0, 1)` Adding the above equations, we get ` log(abc) = 4 + (p+q+r)` ` (p+q+r) in [0, 3)` ` :. log (abc) in [4, 7)` `rArrlog N in [4, 7)` ` :. ` MAXIMUM possible characteristic oflog N = 6 `:. ` Maximum number of DIGITS in `N = 6 +1 = 7` |
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| 31. |
int (1)/(log(x^(x)) (log" x" + 1))dx = |
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Answer» `LOG |log X+1|+C` |
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| 32. |
Evaluation of definite integrals by subsitiution and properties of its : inte^(x^(3)).5^(x^(2)).x[2log5+3x]dx=................+C |
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Answer» `e^(x^(3)).5^(x^(2)).x` |
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| 33. |
The probability distribution of random variable X is as follows. Then possible value of E(2X +3) …………. |
| Answer» Answer :D | |
| 34. |
Find the rate of change of the area of a circle with respect to its radius r when r = 4 cm. |
| Answer» SOLUTION :`(DA)/(DR)]_(r=4)=8picm^2//cm` | |
| 35. |
The orthocentre of triangle formed by lines x+y-1=0, 2x+y-1=0 and y=0 is (h, k), then(1)/(k^(2))= |
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| 36. |
Find the orthogonal trajectories for the given family of curves when ‘a’ is the parameter (i) y=ax^2 (ii) cos y =ae^-x (iii) x^k +y^k =a^k (iv) Find the isogonal trajectories for the family of rectangular hyperbolas x^2 – y^2 = a^2 which makes with it an angle of 45^@. |
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| 37. |
If the foot of perpendicular from the origin to the plane is (a,b,0) thne the eqution of the plane is ....... |
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Answer» AX + by = a + B |
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| 38. |
Solve: 2x + 3y + 3z=5 x -2y + z=-4 3x -y-2z=3using matrix method |
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| 39. |
1/((x-3)(x^(2)+1)^(2))= |
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Answer» `1/(100(X-3))-(x+3)/(100(x^(2)+1))-(x+3)/(10(x^(2)+1)^(2))` |
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| 40. |
A satellite travels in a circular orbit of radius R. If its x- coordinate decreases at which the abscissa increases? |
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| 41. |
Two non negative integers are chosen at random. Find the probability that sum of their squares is divisible by 5. |
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| 42. |
If the angle between the straight lines joining foci and ends of the minor axis of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(12))= 1 is 90^(@) find the eccentricity |
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| 43. |
If the polars of (x_1,y_1)" and "(x_2,y_2) with respect to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 are at the right angels, where (x_1x_2)b^4+a^2(y_1y_2)=lambda, then lambda the value of is |
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Answer» 0 |
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| 44. |
The straight line 4x+3y=p is tangent to the circle x^(2)+y^(2)+4sqrt(3)-4x-6y=0, then p equals |
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Answer» `10+12sqrt3` |
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| 45. |
If p,q and r are in A.P then which of the following is / are true ? |
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Answer» <P>pth,qth and RTH terms of A.P are in A.P |
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| 46. |
Verify the Rolle's theorem for each of the function in following questions: f(x)= x(x+3).e^(-(x)/(2)), "in" x in [-3, 0] |
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| 47. |
A toy company manufactures two types of dolls A and B. Market research and available resources have indicated that the combined production level should not exceed 1200 dolls per week and thedemand for dolls of type B is at most half of that for dolls of type A. Further the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units. If the company makes profit of Rs. 12 and Rs. 16 per doll respectively on dolls A and B how many of each should be produced weekly in order to maximise the profit? |
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Answer» Solution :Let the company MAKES `x` DOLLS of type Aand `y` dolls to type B. `:.` Maximise `Z=12x+16y` `XGE0,yge0`……………. 1 `x+yle1200`…………….2 `ylex//2impliesx-2yge0`……………3 `xle3y+600impliesx-3yle600`……………….4 First, draw the graph of the line `x+y=1200`  Put `(0,0)` in the inequation `x+yle1200`, `0+le1000implies0le1200` (True) Thus, the half plane contains the origin. Now, draw the graph of the line `x-2y=0`.  Put `(200,0)` in the ineuation `x-2ygt0`, `2002x0ge0implies200ge0` (True) Therefore, half plane is on the side of `x`-axis. Now, draw the graph of the line `x-3y=600`.  Put `(0,0)` in the inequation `x-3yle600` `0+3xx0le600implies0le600` (True) Thus, the half plane contains the origin. Since `x,yge0`. So, the feasible region is in first quadrant. The point of intersection of the lines `x-3y=600` and `x+y=1200` is `B(1050,150)` and for the lines `x=2y` and `x+y=1200` is `C(800,400)`. `:.` Feasible region is OABCO. The vertices of the feasible region are `A(600,0),B(1050,150)` and `C(800,400)`. We find the value of `Z` at these vertices.  Maximum value of `Z` is 16000 at `C(800,400)`. Therefore, to obtain maximum PROFIT of RS. 16000, 800 dolls of type A and 400 dolls of type B should be produced. |
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| 48. |
Statement 1:Equation of tangents to the hyperbola 2x^(2) -3y^(2) =6 which is parallel to theliney= 3x +4is y= 3x-5 and y=3x +5 Statement 2:For given slope two parallel tangents can be drawn to the hyperbola |
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Answer» Both the statement are TRUE and II is the correct explanation of I |
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