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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. |
Thestandard deviations of x_(i) (i=1,2,. . . ,10) and y_(i) (i=1, . . . , 10)are respectively 'a' and 'b' .bar(x), bar(y)are the means of these two sets of observation respectively . If z_(i) = (x_(i) - bar(x))(y_(i) - bar(y)) and underset(i = 1)overset(10)sum z_(i) =cthen the standard deviations of the observation= (x_(i) - y_(i)) ,(i = 1, 2, . . . , 10)is |
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Answer» `sqrt(a^(2) +B^(2)+(c)/(5))` |
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| 2. |
Unit vector barc is inclined at an angle theta to unit vector bara times barb which are perpendicular . IF c=lamda(bara +barb)+mu(bara times barb),lamda,mu real then theta belongs to |
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Answer» `(-PI/4,0)` |
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| 3. |
The variance of 20 observations is 5. If each of the observations is multiplied by 2. Find the variance of theresulting observations. |
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| 4. |
Statement-1 : A function f : R rarr R satisfies thef(x) - f(y) = x+y, AA x, y in R, f(0), f(1) gt 0, then f(x) = x+1. and Statement-2 : If function f : R rarr R satisfied the above relationship then f(1) + f(0) + f(3) is equal to 7. |
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Answer» Statement-1 is TRUE, Statement-2 is True, Statement-2 is a correct EXPLANATION for Statement-1. |
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| 5. |
C_0^2 + C_1^2 + C_2^2 - ………-C_15^2 = |
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Answer» 1 |
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| 6. |
f(x)= {((sin (p+1)x + sin x)/(x)",",x lt 0),(q",",x=0),((sqrt(x+x^(2))-sqrtx)/(x^((3)/(2)))",",x gt 0):}. If f(x) is continuous for x in R then find the value of p and q. |
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Answer» <P> |
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| 7. |
A fair dice is rolled 6 times. If "getting a prime number" is a "success" , the probability of no seccess is ………… |
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Answer» `(1)/(64)` |
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| 8. |
Two circles are given as x^2+y^2+14x-6y+40=0 and x^2+y^2-2x+6y+7=0with their centres as C_1 and C_2 . If equation of another circle whose centre C_3 lies on the line 3x+4y-16=0 and touches the circle C_1 externallyand also C_1C_2+C_2C_3+C_3C_1 is minimumis x^2+y^2+ax+by+c=0 then the value of (a+b+c) is |
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Answer» 2 |
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| 9. |
If (cos(theta_(1)-theta_(2)))/(cos(theta_(1)+theta_(2)))+(cos (theta_(3)+theta_(4)))/(cos(theta_(3)-theta_(4)))=0 then tan theta_(1).tan theta_(2).tan theta_(3).tan theta_(4)= |
| Answer» ANSWER :C | |
| 10. |
If a hyperbola passes through a focus of the ellipse and it transverse and conjugate axes coincides with major and minor axis of the ellipse and the product of their eccentricities is 1, then (i) Show that the equation of the hyperbola is x^(2)/9-y^(2)/(16)=1 (ii) Find the focus of the hyperbola. |
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| 11. |
int(dx)/((x+1)^(5)sqrt(x^(2)+2x)). |
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| 12. |
Find the number of integralvalues of x in ((pi)/(2),(5pi)/(2)) such thatmax(x^(2)+cos x-1,1-x^(2)-cos x)=max {cos x +x^(2)-1,x^(2)-1-cosx} is satisfied |
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| 13. |
Write the projection of the point (2,3,1) on y-axis is. |
| Answer» SOLUTION :IMAGE of the POINT (2,1,3) with RESPECT to yz-plane is `(-2,1,3)`. | |
| 14. |
IfF(x)=(A)/(pi)=(1)/(16+x^(2))-inftyltxltinfty is a pdf of a continous random variablex then the value of A is |
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Answer» 16 |
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| 15. |
Find which of the operations given above has identity. a"*"b=a-b |
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| 17. |
If one of the lines in the pair of straight lines given by 4x^(2) + 6xy + ky^(2)=0 bisects the angle between the coordinate axes , then k in |
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Answer» `{-2 , -10}` |
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| 18. |
Evaluate.^(n)C_(0).^(n)C_(2)+2.^(n)C_(1).^(n)C_(3)+3.^(n)C_(2).^(n)C_(4)+"...."+(n-1).^(n)C_(n-2).^(n)C_(n). |
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Answer» ` = .^(n)C_(0).^(n)C_(n-2)+2.^(n)C_(1).^(n)C_(n-3)+3.^(n)C_(2).^(n)C_(n-4)+"....."(n-1).^(n)C_(n-2).^(n)C_(0)` `= underset(r=1)overset(n)sumr.^(n)C_(r-1).^(n)C_(n-r-1)` `= underset(r=1)overset(n)sum((r-1)+1).^(n)C_(r-1).^(n)C_(n-r-1)` `=underset(r=1)overset(n)sum[(r-1).^(n)C_(r-1).^(n)C_(n-r-1)+.^(n)C_(r-1).^(n)C_(n-r-1)]` `= underset(r=1)overset(n)sum[n^(n-1)C_(r-2).^(n)C_(n-r-1)+.^(n)C_(r1).^(n)C_(n-r-1)]` `= n^(2n-1)C_(n-3)+.^(2n)C_(n-2)` |
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| 19. |
If 2cos theta=x+1/x and 2cosvarphi=y+1/y , then |
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Answer» `X^n+1/x^n=2cos (ntheta)` |
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| 20. |
Show that the ar5ea enclosed between the parabolas y^(2)=4a(x+a) and y^(2)=4b(b-x) where a gt 0,b gt 0 is (8)/(3)(a+b)sqrt(ab) sq units. |
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| 21. |
(1+x^2/(2!) +x^4 /(4!) + .....oo)^(2) - (x+x^3/(3!) +x^(5)/(5!) + ....oo)^(2) = |
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Answer» `-1` |
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| 22. |
The statement P(n) 1 x 1! + 2 x 2! + 3 x 3! + …+ n x n! = (n+1)! -1 isTrue for all n gt 1 |
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Answer» TRUE for all n `GT` 1 |
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| 23. |
A :tan theta + 2 tan 2 theta + 4 tan 4 theta + 8 tan 8 theta - 16 cot 6 theta = cot theta R :cot alpha - tan alpha = 2 cot 2 alpha |
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Answer» A is true , R is true and R is CORRECT explanation of A |
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| 24. |
If F(x) =int_(3)^(x) (2 + (d)/( dt) cos t) dt then F'(pi/6) is equal to |
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Answer» `1//2` |
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| 25. |
Obtain the following integrals : int((x^(2)+2))/(x+1)dx |
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| 26. |
If the lines 2x+3y+1=0, 6x+4y+1=0 intersect the co-ordinate axes in 4 points, then the circle passing through the points is |
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Answer» `12X^(2)+12Y^(2)+8x+7y+1=0` |
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| 27. |
Find the equation of Hyperbola with one focus at the origin and directrix x+3=0 and eccentricity sqrt3 |
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| 28. |
On using elementary row operation R_(1)toR_(1)-3R_(2) in the following matrix equation : [{:(4,2),(3,3):}]=[{:(1,2),(0,3):}]*[{:(2,0),(1,1):}] |
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Answer» `[{:(-5,-7),(3,3):}]=[{:(1,-7),(0,3):}]*[{:(2,0),(1,1):}]` |
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| 29. |
show that the given differential equation is homogeneous and solve it. x dy - y dx = sqrt(x^(2) + y^(2)) dx |
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| 30. |
If u-=ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pair of straight lines , prove that the equation of the third pairof straight lines passing through the points where these meet the axes is cu+4(fg+ch)xy=0 . |
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| 31. |
Find the number of onto functions from a set {1, 2, 3, 4, 5} to another set {a_1,a_2,a_3,a_4} such that f^(-1)(a_1) is not a singleton |
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| 32. |
If the coefficients of r^(th),(r + 1)^(th) and (r + 2)^(th) terms in the binomial expansion of (1 + y)^(m) are in A.P., then m and r satisfy the equation |
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Answer» 1. `m^(2) - m(4r - 1) + 4r^(2) + 2 = 0` |
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| 33. |
If the ratio of the 7th term from the beginning to the 7th term from the end in the expansion of (sqrt2+(1)/(sqrt3))^x is 1/6, then x is |
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Answer» 3 |
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| 34. |
Find the total number of exchange in d^8 configuration ? |
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Answer» 10 |
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| 35. |
Let f(x) = sin(2x) + x-|x| AA x in R (where [x] = greatest integer le 5). Then period of f is |
| Answer» ANSWER :D | |
| 36. |
Integrate the functions in exercise. (5x+3)/(sqrt(x^(2)+4x+10)) |
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| 37. |
Let f(y)="sin" (y-a)/2 "tan" (piy)/(2a), y ne a. The value of f(a) so that f is a continuous function is |
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Answer» `pi//a` |
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| 38. |
Consider the system of equations cos^(-1)x + (sin^(-1) y)^(2) = (p pi^(2))/(4) and (cos^(-1) x) (sin^(-1) y)^(2) = (pi^(4))/(16), p in Z The value of p for which system has a solution is |
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Answer» 1 and `sin^(-1) y = b rArr b in [-pi//2, pi//2]` We have `a + b^(2) = (p pi^(2))/(4)`...(i) and `ab^(2) = (pi^(4))/(16)`..(ii) SINCE `b^(2) in [0, pi^(2)//4]`, we GET `a + b^(2) in [0, pi + pi^(2)//4]` So, from Eq. (i) we get `0 le (p pi^(2))/(4) le pi + (pi^(2))/(4)` i.e., `0 le p le (4)/(pi) + 1` Since `p in Z, " so " p = 0, 1 " or " 2` Substituting the value of `b^(2)` from Eq. (i) Eq. (ii), we get `a((p pi^(2))/(4) -a) = (pi^(4))/(16)` `rArr 16a^(2) - 4p pi^(2) a + pi^(4) = 0`...(III) Since `a in R, " we have " D ge 0` i.e., `16^(2) ge 4- 64 pi^(4) ge 0` or `p^(2) ge 4 " or " p ge 2 " or " p =2` Substituting `p =2` in Eq. (iii), we get `16a^(2) -8pi^(2) a + pi^(4) = 0` or `(4a - pi^(2))^(2) = 0` or `a = (pi^(2))/(4) = cos^(-1) x " or " x = cos.(pi^(2))/(4)` From Eq. (ii), we get `(pi^(2))/(4) b^(2) = (pi^(4))/(16)` or `b = +- (pi)/(2) = sin^(-1) y " or " y = +- 1` |
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| 39. |
Find the value of tan75^@ |
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| 40. |
Find the values of the following integrals (where [.] is gif and {.} is fractional part) Evaluate the following int_(0)^(50)(x-[x])dx |
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| 41. |
Let det A=|{:(l,m,n),(p,q,r),(1,1,1):}| and if (l-m)^2 + (p-q)^2 =9, (m-n)^2 + (q-r)^2=16, (n-l)^2 +(r-p)^2=25, then the value ("det." A)^2 equals : |
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Answer» 36 |
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| 44. |
Evaluate the following integrals. int(1)/(5+4sinx)dx |
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| 46. |
Integrate the following function : int(dx)/(sqrt(7-3x-2x^(2)))dx |
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| 47. |
Two blocks each of mass 5 kg are at rest on the ground. The masses are connected by a massless string pasing over a smooth and light pulley. A 200 N force is applied on the pulley. Find the difference in acceleration of blocks in m//s^(2) |
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| 48. |
Show that the vectors vec(a)=hat(i)-2hat(j)+3hat(k) vec(b)=-2i+3hat(j)-4hat(k)vec( c) =hat(i) -3 hat(j) +5hat(k) are coplanar. |
| Answer» Solution :`[VEC(a),vec(B),vec( c)]=|(1,-2,3),(-2,3,-4),(1,-3,5)|=0 THEREFORE vec(a), vec(b) , vec (c )` are coplanar. | |
| 49. |
Solve(y+sqrt(x^(2)+y^(2)))dx-xdy=0 |
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| 50. |
Find the total number of ways in which the letters of the word PRESENTATION can be arranged. |
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Answer» SOLUTION :The NUMBER of letters in the word "PRESENTATION" is 12, out of which there are "2N,\'s,2E's,2T's".So the total number of ARRANGEMENTS `=(12!)/(2!2!2!)=1/8(12)!` |
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