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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.
| 2351. |
For m, n in N and m != n then the value of int_(0)^(pi) sin m x " " sin n x " " dx= |
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Answer» 0 |
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| 2352. |
If int e^(x).(2sin3x + 5 cos 3x ) dx = (e^(x))/(a) [ b sin 3x + c cos 3x ] + K then (a, b ,c ) = |
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Answer» (10 , 17, 1) |
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| 2353. |
Find the centre and radius of each of the circles whose equations are given below. x^(2) + y^(2) + 6x + 8y - 96 =0 |
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| 2354. |
If the straight line y=mx+c is parallel to the axis of the parabola y^(2) =lx and intersects the parabola at ((c^(2))/(8),c)then the length of the latus rectum is |
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Answer» 2 |
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| 2355. |
If int_(0)^(b-c) f(x+c) dx = k int_(b)^(c) f (x) dx then k= |
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Answer» 0 |
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| 2356. |
Uusing the theorem on passing to the limit in inequalities prove underset (n to oo)lim rootn(a)=1 (a gt 0) |
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| 2357. |
Differentiate sin sqrtx+cos(x^2) w.r.t. x |
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| 2358. |
XOZ plane divides the join of (2,3,1) and (6,7,1) in the ratio |
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Answer» `3:7` |
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| 2359. |
ABCDis a square of side length 2 units. C_(1) is the circle touching all the sides of the square ABCD and C_(2) is the circumcircle of square ABCD. L is a fixed line in the same plane and R is fixed point. If a circle is such that it touches the line L and the circle C_(1) externally, such that both the circles are on the same side of the line, then the locus of centre of the circle is |
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Answer» ellipse |
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| 2360. |
ABCDis a square of side length 2 units. C_(1) is the circle touching all the sides of the square ABCD and C_(2) is the circumcircle of square ABCD. L is a fixed line in the same plane and R is fixed point. A line L' through a is drawn parallel to BD. Point S moves scuh that its distances from the line BD and the vertex A are equal. If loucs S cuts L' at T_(2)andT_(3) and AC at T_(1), then area of DeltaT_(1)T_(2)T_(3) is |
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Answer» `(1)/(2)` sq units |
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| 2362. |
A_(1)=[a_(1)] A_(2)=[{:(,a_(2),a_(3)),(,a_(4),a_(5)):}] A_(3)=[{:(,a_(6),a_(7),a_(8)),(,a_(9),a_(10),a_(11)),(,a_(12),a_(13),a_(14)):}]......A_(n)=[.......] Where, a_(r)=[log_(2)r]([.]) denotes greatest integer). Then trace of A_(10) |
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| 2363. |
Al Capone loved balances. He took Tintin to his famous room of Balance, where there was present a huge complex balance as shown in the fig_1. The marks on the stick are at 1 metre distance each and the white small circles represent the point around which the stick is hinged.There are 12 identical looking weights which weigh 1kg, 2kg, 3kg,….. upto 12kg. He asked Tintin to identify the weight of each of the weights given that the system is balanced. Tintin identified 9 of them correctly except the encircled ones, can you help him find the rest by telling the sum of the weights of the encircled ones?For balancing the total system all the sticks that hold the weights need to be balanced in themselves. For each of the sticks being balanced the following condition need to be satisfied – BALANCING of TORQUE : The sum of the products of weight with distance from the hinge on the left side of the hinge should be equal to that on the right side for every rod. Eg. In the system shown beside Torque on the left side=(4kg)x(1m)+(2kg)x(2m)=8 kg-m Torque on the right side=(8kg)x(1m)=8 kg-mAlso if a stick A is connected below another stick B directly at a given distance d then we can consider the stick A as a weight connected to stick B at the same distance d whose weight is equal to the sum of weights connected to stick A. (as shown below) |
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Answer» 17 10 9 11 7 2 12 4 58 163 |
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| 2365. |
If tangents are drawn to the parabola y=x^(2)+bx+c or b and c fixed real number at the points (i,y_(i)) for i=1,2,…,10. Lt l_(1), l_(2), l_(3)…….l_(9) be the point intersection of tangents at (i,y) and (i+1,y_(i+1)) then the least polynomial satisfying whose graph passes through all nine points |
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Answer» `y=X^(2)+bx+c` `y=(2i+B)x-i^(2)+c` Also at `(i+1,y_(i+1)),y=(2i+1)+b)x-(i+1)^(2)+c` Point of INTERSECTION is `x=(2i+1)/2impliesi=(2x-1)/2` Put this `i` in any tangent we get `y=x^(2)+bx+c-1/4` |
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| 2366. |
Find a value of x for which x(hati+hatj+hatk) is a unit vector. |
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| 2368. |
Let A={1,2,3}. Then the number of relations containing (1,2) and (1,3) which are reflexive and symmetric but not transitive is |
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Answer» 1 |
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| 2369. |
Find the equation of the circle passing through (-2,14) and concentric with the circle x^(2)+y^(2)-6x-4y-12=0 |
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| 2370. |
For the matrix A=[{:(1,2,2),(2,1,2),(2,2,1):}]. Show that A^2-4A-5I=0 Hence find A^(-1) |
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| 2371. |
If 4 fair dice are rolled, find the probability that they show different numbers in increasing order. |
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| 2372. |
The sum of all values of integers n for which (n^2-9)/(n-1) is also an integer is |
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| 2373. |
Find the number of proper divisors of 2520. (i) How many of them are odd. Find their sum. |
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| 2374. |
A square is inscribed in the circle x^(2)+y^(2)-2x+4y-93=0 with its sides are parallelto coordinate axes then vertices of square are |
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Answer» (-6,-9)(-6,5)(8,5)(8,-9) |
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| 2375. |
Which of the following is a sequence ? |
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Answer» `f(x)=[x],x INR` |
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| 2376. |
If x=a+bt+ct^2 , where x is length and t is time then a,b and c respectively can be :- |
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Answer» LENGTH , VELOCITY , ACCELERATION |
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| 2377. |
If hati+hatj+hatk,2hati+5hatj,3hati+2hatj-3hatk and hati-6hatj-hatk are the position vectors of points A, B, C and D respectively, then find the angle between vec(AB) and vec(CD). Deduce that vec(AB) and vec(CD) are collinear. |
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| 2379. |
If A,B,C are three independent events of an experiment. Such that P(AcapB^(C)capC^(C))=(1)/(4) P(A^(C)capBcapC^(C))=(1)/(8),P(A^(C)capB^(C)capC^(C))=(1)/(4) then find P(A),P(B)and P( C). |
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| 2380. |
Let p,q and r be any three logical statements. Which one of the following is true? |
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Answer» `~[p^^(~Q)]-=(~p)^^q` |
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| 2381. |
show that [((x+y)^2 , zx , zy),( zx, (z+y)^2 ,xy),(zy,xy,(z+x)^2)]=2xyz (x +y+z)^3 |
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| 2382. |
Let A be an upper triangular 3xx3 real matrices such that det (A) =0 det (A+2.1I_(3)) =0 and det (A-3.2 I_(3)) =0 then tr (A) is equal to ___________ . |
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| 2383. |
The value of 'c' in Lagrange's mean value theorem for f(x) = ( x - a)m (x - b)^(m)[a, b]^(n) is [a,b] is |
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Answer» `(mb+na)/(m+n)` |
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| 2385. |
Find the equation of line passing through (2, -1, 3) and equally inclined to the axes . |
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| 2386. |
(i) int (2x)/((x^2+1)(x^2+3)) dx (ii) int (2x)/((1+x^3)(2+x^3)) dx |
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Answer» (II) `1/3` |
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| 2387. |
If PSP' is a focal chord of the ellipse (x^(2))/(7)+(y^(2))/(9)=1 then (SP.SP')/(SP+SP')= |
| Answer» Answer :B | |
| 2388. |
Find the number of 4 - digit numbers which can be formed using the digits 0,2,5,7,8 that are divisible by (i) 2 (ii) 4 when repetition is allowed. |
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| 2389. |
If a point P moves such that its distances from the point A(1,1) and the line x+y+2=0 are equal, then the locus of P is |
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Answer» a STRAIGHT LINE |
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| 2390. |
Match the following {:("List-I","List-II"),((I)""^(n)C_(r+1)+2""^(n)C_(r)+""^(n)C_(r-1),(a)""^((n+2))C_(r+1)),((II)""^((n+1))C_(3)-""^(n-1)C_(3),(b)(n-1)^(2)),((III)""^(2n)C_(2)-2""^(n)C_(2),(c)n^(2)),(,(d)""^(n+1)C_(r+1)):} The correct match is |
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Answer» a,b,C |
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| 2391. |
Find the rank of the matrix [{:(2,-2,4,-3),(-3,4,-2,-1),(6,2,-1,7):}] by reducing it to an echelon form. |
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Answer» <P> |
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| 2392. |
As show in the figure , the five circles are tangent to one another consecutively and to the lines L_(1) and L _(2). If the radius of the largest circle is 18 and that of the smaller one is 8, if radius of the middle circle is r, then find the value of r/2. |
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| 2393. |
If |x| lt 1 , then the coefficient of x^n in expansion of (1+x+x^2 + x^3 +…….)^2 is |
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Answer» n |
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| 2394. |
Let p be the statement 'Ravi races' and let q be the statement 'Ravi wins'. Then the verbal translation of ~(pvv~q) is |
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Answer» RAVI does not RACE and Ravi does not win |
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| 2395. |
Ifalpha , beta , gammaare the rootsofx^3+ px^2+qx-r=0thenalpha^2+ beta^2 + gamma^2 = |
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Answer» `p^2 -2Q` |
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| 2396. |
If vec(p)xxvec(q)=2hat(i)+3hat(j),vec(r)xxvec(s)=3hat(j)+2hat(k)," then "vec(p).(vec(q)xx(vec(r)xxvec(s))) is |
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Answer» 9 |
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| 2397. |
A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2m and volume is 8m^(3). If building of tank costs Rs. 70 per sq. metres for the base and Rs. 45 per square metre for sides. What is the cost of least expensive tank ? |
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| 2398. |
vec(a)=3hati+2hatj+9hatk and vec(b)=hati+p hatj+3hatk. If the vector vec(a) and vec(b) are parallel then find the value of P. |
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| 2399. |
Using Cofactors of elements of third column , evaluate , Delta ={:|( 1,x,yz),(1,y,zx),( 1,z,xy) |:} |
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| 2400. |
Which of the following is formed by condensation polymerisation. |
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Answer» Nylon-66 |
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