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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 12701. |
If f(x-y),f(x)*f(y),f(x+y) are in for all x,y in R " and " f(0) ne 0, then |
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Answer» F'(X) is an even function |
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| 12702. |
The point to which the origin is shifted and the transformed equation are given below. Find the original equation. (-1,2) , x ^(2) + 2y ^(2) + 16 =0 |
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| 12703. |
On which of the following intervals is the function f given by f(x)=x^100+sinx-1 strictly decreasing ? |
| Answer» Answer :D | |
| 12704. |
Find the set of values of x for which the binomial expansions of the following are valid. (2+3x)^(-2//3) |
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| 12705. |
If the sum of five natural numbers is 50. Find the probability that the five numbers are even. |
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| 12706. |
Calculate the area of the triangle ABC (by vector method) where A(1,2,4), B(3,1,-2), C(4,3,1) |
Answer» SOLUTION :  AREA of `TRIANGLE ABC` = `1/2 SQRT(81+144+25) = 1/2 sqrt(250)` |
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| 12707. |
Range of sin^(-1)((x^(2)+1)/(x^(2)+2)) is |
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Answer» `[0,(pi)/(2)]` Now, `2 le x^(2)+2lt oo` for all x ein R `implies(1)/(2)GE (1)/(x^(2)+2)GT0` `implies -(1)/(2) le (-1)/(x^(2)+2) lt 0` `implies(1)/(2) le 1-(1)/(x^(2)+2)lt` `implies (pi)/(6) le sin^(-1)(1-(1)/(x^(2)+2))lt(pi)/(2)` |
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| 12708. |
Assertion (A): If x+y+z=xyz then sum((2x)/(1-x^(2)))=pi((2x)/(1-x^(2))) Reason (R):If tan A +tan B + tan C =tanA tan B tan C then A+B+C=npi, n in N |
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Answer» A is true, R is true and R is correct EXPLANATION of A |
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| 12709. |
Show that the relation R defined in the set A of all polygons as R = {(P _(1), P _(2)): P _(1) and P _(2) have same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3,4 and 5 ? |
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| 12710. |
Prove that the function f(x)= x^(2) is continuous at x=0. |
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| 12711. |
Let f(x) = {{:(1,x le -1),(|x|,-1 lt x lt 1),(0,x ge 1):}, then : |
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Answer» f is continuous at X = -1 |
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| 12712. |
If OT and ON are perpendiculars dropped from the origin to the tanget an d norml to the curve x=a sin^(3)t,y=a cos^(3)t at an arbitary point, then |
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Answer» `4OT^(2)+ON^(2)=a^(2)` |
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| 12713. |
Find intsecx(secx+tanx)dx |
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| 12714. |
If f(x)=[x^2]then f(3/2)=_______ |
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Answer» 0 |
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| 12715. |
How many selections of atleast one red ball can be made from 4 red balls and 3 green balls if balls of same colour are different in size. |
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| 12716. |
Find the area of the triangle formed by the lines represented by ax^2+2hxy+by^2+2gx+2fy+c=0 and axis of x . |
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| 12717. |
From a bag containing 4 white balls and 5 black balls a person draws 3 balls at random. The odds in favour of these 3 balls being black are |
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Answer» `3 : 5` |
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| 12718. |
Which of the following pairs of graphs intersect? (i)y = x^(2) -xandy = 1 (ii)y = x^(2) - 2x + 3 and y= sin x (iii)y = x^(2) - x+1 andy = x-4 |
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Answer» Solution :(i) ` y = x^(2) - x ANDY = 1" intersect if "x^(2) - x = 1or x^(2)-x-1 = 0`, which has real roots . Hence, THEGRAPHS intersect. (II) ` y = x^(2) - 2X+3 and y = sin x` intersect if ` x^(2) - 2x+3 = sin x or (x-1)^(2) + 2=sin x`, which is not possible SINCE L.H.S. has least value 2, while R.H.S. has maximum value 1. `(iii) y = x^(2)-x + 1 and y = x - 4" intersect if " x^(2) - x+1 = x-4or x^(2) -2x + 5 = 0`, which has non-real roots. Hence, the graph do not intersect. |
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| 12719. |
60 employees are there in a college. The number of ways can a cooperative committee with 10 directors be formed in which exactly 2 members would be from the commerce department of 5 members is |
| Answer» Answer :A | |
| 12720. |
Prove the following : sinA-sin3A+sin5A= sin3A(2cos2A-1) |
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Answer» SOLUTION :L.H.S. = sinA-SIN3A+sin5A = sinA+sin5A-sin3A =sin5A+sinA-sin3A 2sin5A+A/2cos5A-A/2-sin3A 2sin3Acos2A-sin3A sin3A(2cos2A-1)=R.H.S. |
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| 12721. |
A industry produces two types of modelsM_(1),M_(2) EachM_(1) model needs 4 hours for grinding and 2 hours for polishing , whereas eachM_(2) model needs 2 hours for grinding and 5 hours for polishing . Each grinder can work for 80 hours a week while each polisher can work for 180 hours a week . Each M_(1)model earns a profit of Rs.3 andM_(2) model earns Rs 4 profit . To ensure the maximum profit the profuction capacity allocated to two types of models in a week is |
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Answer» (0,36) |
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| 12722. |
Solve system of linear equations, using matrix method in examples 7 to 14 2x+y+z=1 x-2y-z=3/2 3y-5z=9 |
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| 12723. |
Let a, b, c be three non-coplanar vectors. Let S_(i)(i=1, 2, 3, 4, 5, 6) denonte the six scalar triple products formed by all possible permutations of a, b,c . If i, j, k, l are randomly chosen distinct numbers from 1 to 6 and if x=S_(i)/S_(j)+S_(k)/S_(l), y=S_(i)/S_(j)-S_(k)/S_(l), then x^(2)+y^(2)= |
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Answer» 1 |
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| 12724. |
The polars of two points A(1,3), B(2,-1) w.r.t to circle x^(2)+y^(2)=9 intersect at C then polarof C w.r.t to the circle is |
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Answer» x+3y=9 |
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| 12725. |
For the matrixA=[[1,5],[6,7]], verify that A-A^T is a skew symmetric matrix |
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Answer» SOLUTION :`A-A^T = [(0,-1),(1,0)] implies (A+A^T)^T = [(0,1),(-1,0)] = -(A-A^T)` `therefore `A-A^T` is SKEW SYMMETRIC |
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| 12726. |
For the matrixA=[[1,5],[6,7]], verify that A+A^T is a symmetric matrix |
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Answer» SOLUTION :We have `A^T = [(1,6),(5,7)] THEREFORE A+A^T = [(2,11),(11,14)]` `(A+A^T)^T = [(2,11),(11,14)] = A+A^T IMPLIES A+A^T` is SYMMETRIC |
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| 12727. |
I. underset(theta to 0)"Lt" (sin (theta^(2)))/(theta)=pi/200 II. f(x)=x^(2) sin (1//x) (x ne 0)" is a continuous at x=0" |
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Answer» only I is true |
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| 12728. |
If overline(a), overline(b), overline(c) are non-coplanar vectors and overline(d)=lambdaoverline(a)+muoverline(b)+gammaoverline(c), then lambda= |
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Answer» `([[OVERLINE(d), overline(B), overline(C)]])/([[overline(b), overline(a), overline(c)]])` |
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| 12730. |
Find the points where the following function are not differentiable.e^(|x|) |
| Answer» SOLUTION :`E^(|X|)`is not DIFFERENTIABLE at x=0because |x|is not differentiable at x=0 | |
| 12731. |
The solution of the differential equation (x)/(x^(2)_y^(2))dy+((y)/(x^(2)+y^(2))-1)dx, is |
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Answer» `y=x COT(C-x)` |
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| 12732. |
A conical paper cup 20 cm across the top and 15 cm deep is full of water. The cup springs a leak at the bottom and losses water at 5 cu. cm per minute. The value of (d^(2)h)/(dt^(2))"(""in cm"//min^(2)")" when the water is exactly 7.5 "cm deep and"(d^(2)V)/(dt^(2))=-4/9cm^(3)//min^(2)is |
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Answer» `-2/5` |
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| 12733. |
A conical paper cup 20 cm across the top and 15 cm deep is full of water. The cup springs a leak at the bottom and losses water at 5 cu. cm per minute.The amount of water (in cm^(3)) when the hight of water is 3 cm is |
| Answer» ANSWER :A | |
| 12734. |
A conical paper cup 20 cm across the top and 15 cm deep is full of water. The cup springs a leak at the bottom and losses water at 5 cu. cm per minute. How fast is the water level dropping at the instant when the water is exactly 7.5 cm deep ? |
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Answer» `(1)/(pi)cm//min` |
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| 12735. |
Using determinants find equation of line passess from point (3,1) and (9,3) |
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| 12736. |
IfA ={(x,y} ,x^2 +y^2 le 1 and y^2 le 1 -x}thenthe areaof A is …..Sq. units . |
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Answer» `pi/2-2/3` |
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| 12737. |
State which of the following is true? |
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Answer» `tanx + COTX = secx " cosec "x` is solvable. |
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| 12738. |
Find the value of sum_(i=1)^n sum_(i=1)^n sum_(k=1)^n k |
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| 12739. |
The solution of (x^(2)y^(3) +x^(2))dx + (y^(2)x^(3)+y^(2))dy = 0 is |
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Answer» `(X^(3)+1)(y^(3)+1) = C` |
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| 12740. |
Differentiate the following w.r.t.x (tan^-1x)/x |
| Answer» SOLUTION :`d/dx((tan^-1x)/X)=("x"XX1/(1+x^2)-tan^-1"x"xx1)/x^2=(x-(1+x^2)tan^-1x)/(x^2(1+x^2)` | |
| 12742. |
If 3 cosx ne 2 sin x , then the general solution ofsin^2x-cos2x=2-sin2x is |
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Answer» `npi+(-1)^n pi/2, n in Z` |
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| 12743. |
If veca = 3 hati - 5 hatj and vecb = 6 hati + 3 hatjare two vectors and vecc a vector such that vecc = veca xx vecb, then |veca|:|vecb|:|vecc|= |
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Answer» `sqrt34:sqrt45:sqrt39` |
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| 12744. |
If A=((2,2),(9,4)) and I=((1,0),(0,1)), then 10A^(-1) is equal to : |
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Answer» 6I-A |
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| 12745. |
Find the values of x, y and z from the following equations : (i) [{:(4,3),(x,5):}]=[{:(y,z),(1,5):}] (ii) [{:(x+y,2),(5+z,xy):}]=[{:(6,2),(5,8):}](iii)[{:(x+y+z),(x+z),(y+z):}]=[{:(9),(5),(7):}] |
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| 12746. |
Evaluate int (1)/(x^((1)/(2)) + x^((1)/(3)))dx |
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| 12747. |
Find the asymptotes of the function f(x)=(1)/(x) |
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| 12748. |
If int(dx)/(4-3cos^(2)x+5sin^(2)x)=(1)/(3)f(3tanx)+C then f(x) is equal to |
| Answer» Answer :D | |
| 12749. |
The solution of (x^(2) + y^(2)) dx = 2xy dy is |
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Answer» `C(X^(2)-y^(2)) = x` |
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| 12750. |
A point P lies on a line through Q(1, -2, 3) and is parallel to the line (x)/(1)=(y)/(4)=(z)/(5). If P lies on the plane 2x + 3y – 4z + 22 = 0, then segment PQ equals to |
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Answer» `sqrt42` UNITS |
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