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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.
| 501. |
If the length of latus rectum is 5/2 and eccentricity is 1/2, then the equation of the ellipse is |
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Answer» `(x^2)/9 + (y^2)/16 = 1` |
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| 502. |
If A and B are square matrices of the same order and if A =A^(T),B=B^(T) then (ABA)^(T)= |
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Answer» BAB |
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| 504. |
intxcosec^2xdx |
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Answer» SOLUTION :`intxcosec^2xdx` [X=1st `cosec^2x=2nd`] =`x.intcosec^2xdx-int[d/DX(x)xxintcosec^2xdx]dx` =`-xcotx+intcotxdx` =`-xcotx+ Inabs(SINX)+C` |
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| 505. |
Integrate the following rational functions : int(x^(3)-x-2)/(1-x^(2))dx |
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| 506. |
Approximate change in the volume V of a cube of side x metres caused by increasing the side be 3% is |
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Answer» `0.09x^(3)m^(3)` |
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| 507. |
Which of the following set of molecules are having square pyramidaland pyramidal shape respectively. |
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Answer» `ICl_(4)^(-) and SiF_(4)` |
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| 508. |
The order of the differential equation (d^(2)y)/(dx^(2)) + ((dy)/(dx))^(2) = x sin ((d^(2)y)/(dx^(2))) is |
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Answer» 1 |
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| 510. |
Show that the relation R in the set R of real number , defined as R = {(a,b) : a le b^2} is neither reflexive nor symmetric nor transitive. |
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| 511. |
Let overline(a) and overline(b) be non-collinear. If overline(c)=(x-2)overline(a)+overline(b) and overline(d)=(2x+1)overline(a)-overline(b) are collinear, then x= |
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Answer» `(-2)/(3)` |
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| 512. |
The mean deviation of an ungrouped data is 10. If each observation is increased by 4% the revised mean deviations is |
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Answer» `10.0` |
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| 513. |
If the system of equations ax+ay-z=0 bx-y+bz=0 -x+cy+cz=0 (where a,b,c!=-1) has a non trivial solution, then values of 1/(1+a)+1/(1+ b)+1/(1+c) is |
| Answer» ANSWER :A | |
| 514. |
If [.] denotes the greatest integer function, then match the following lists: |
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Answer» `=int_(-1)^(1)3[x]dx=3int_(-1)^(1)[x]dx=3int_(0)^(1)([x]+[-x])dx` `=3` (as `[x]+[-x]=-1`) b. `int_(2)^(5)([x]+[-x])dx=int_(2)^(5)-1dx=-3` c. `sgn(x-[x])={(1,"if",x"is not an integer"),(0,"if",x "is an integer"):}` Hence `int_(-1)^(3) sgn(x-[x])dx=4(1-0)=4` d. LET `I=25int_(0)^(PI//4) (tan^(6)(x-[x])+tan^(4)(x-[x]))dx { :' 0 lt x le (pi)/4implies[x]}` `=25int_(0)^(pi//4)(tan^(6)x+tan^(4)x)dx` `=25int_(0)^(pi//4) tan^(4)x(tan^(2)x+1)dx` `=25int_(0)^(pi//4)tan^(4)xsec^(2)xdx` `=25((tan^(5)x)/5)_(0)^(pi//4)=25xx1/5=5` |
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| 515. |
If f(x)= (3x-2)/(2x-3),AA x in R -{(3)/(2)} , " Find " f^(-1) |
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| 516. |
Find the equation of line passing through the given points using determinants (1,-3),(5,-2) |
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| 517. |
int(20)/(16+9sin^(2)x)dx= |
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Answer» `LOG(16+9sin^(2)x)+c` |
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| 518. |
if P(A)=7/13, P(B)=9/13,P(AnnB)=4/13 then P(A|B) is.....a)9/4 b)16/13 c)4/9 d)11/13 |
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Answer» `9/4` |
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| 519. |
We have 21 identical balls available with us which we need to be distributed amongst 3 boys A,B and C such that A always gets an even number of balls. The number of possible ways of doing this is |
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Answer» 112 |
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| 520. |
Let R be a relation on N defined by x+2y=8. The domain of R is |
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Answer» {2,4,8} |
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| 521. |
Solve the following differential equations (i) (dy)/(dx) = (x^(2)+y^(2))/(2x^(2)) (ii) y^(2)dx + (x^(2) - xy)dy = 0 (iii) (dy)/(dx) = ((x+y)^(2))/(2x^(2)) (iv) (dy)/(dx) = (x-y)/(x+y) (v) (x^(2) + y^(2)) dy = 2xydx (vi) (x^(2) - y^(2))dx - xydy = 0 |
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Answer» (iii) `log x = 2Tan^(-1)((y)/(x)) + c` (iv) `x^(2) - 2xy - y^(2) = c` (v) `K(x^(2) - y^(2)) = y` (vi) `x^(2)(x^(2) - 2Y^(2)) = k` |
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| 522. |
Using matrix method, find the quadratic defined by f(x) = ax^(2) + bx + c if f(1) = 0, f(2) = -2 and f(3) = -6. Hence find the value of f(-1). |
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| 523. |
Let f(x)=2+|x-1| and g(x)=mn f(t) where x le t le x^(2)+x+1. Discuss the continuity and differentiability of g(x). |
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| 524. |
Let f: [0,1]rarr[0,oo] be a continuous function such that int_(0)^(1) f(x)dx=10. Which of the following statements is NOT necessarily true ? |
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Answer» `underset(0)overset(1)inte^(-x)f(x)dxle10` `underset(0)overset(1)intf(x)^(2)dxle100` not necessarily ture. because `(f(x))^(2)` can take very high was values then are bounded by `(f(x))^(2),` xaxis & x=0 to 1 MAY cross 100. |
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| 525. |
The middle term of expansion (10/x+x/10)^(10) is |
| Answer» Answer :A | |
| 526. |
What is the solution set to the equation 0=(3a+1)^2(a-4)? |
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Answer» `{1/3,-4}` |
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| 527. |
If f(x) = sqrt(x),g(x) = e^(x) - 1 and h(x) = tan^(-1)x then the antiderivative of f o g (x) is |
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Answer» 2[g o F (X) - g o f o h (x)] + C |
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| 528. |
Find the equation of the normal to the circlex^(2)+y^(2)-4x -6y +11 0at (3,2)Also find the other where the normal meets the circles. |
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Answer» `3x-4y=0` |
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| 529. |
int (2x + 2)/(sqrt(x^(2) - 4x - 5)) dx is equal to |
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Answer» `sqrt(x^(2) - 4X - 5) + LOG |x + sqrt(x^(2) - 4x - 5)| + C` |
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| 530. |
A feasible region of a system of linear inequalities is said to be ………… if it can be enclosed within a circle. |
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| 531. |
Find the shortest distance of the point (0, c) from the parabola y=x^(2), where (1)/(2)le c le 5. |
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| 532. |
Evaluation of definite integrals by subsitiution and properties of its : int_(-2)^(3)|1-x^(2)|dx=........... |
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Answer» `(28)/(3)` |
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| 533. |
Evaluate the following integrals intsqrt(1+secxdx) |
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| 534. |
Iftherootsofax^3+ bx^2+ cx +d=0are in G.Pthen therootsof ak^3 x^3+bk^2 x^2 + ck x+d=0are in |
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Answer» A.P |
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| 535. |
Read the following comprehension carefully, Let Delta ne 0 Delta^c denotes the determinant of cofactors , then Delta^c=Delta^(n-1) where n(gt 0) is the order of Delta. Suppose a,b,c in R ,a+b+c gt 0 , A=bc-a^2,B=ca-b^2 and C=ab-c^2 and |{:(A,B,C),(B,C,A),(C,A,B):}|=49 "then" |{:(a,b,c),(b,c,a),(c,a,b):}| equals |
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Answer» `-7` |
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| 536. |
Read the following comprehension carefully, Let Delta ne 0 Delta^c denotes the determinant of cofactors , then Delta^c=Delta^(n-1) where n(gt 0) is the order of Delta. if a,b,c are the roots of the equation x^3-px^2+r=0 then the value of |{:(bc-a^2,ca-b^2,ab-c^2),(ca-b^2,ab-c^2,bc-a^2),(ab-c^2,bc-c^2,ca-b^2):}| |
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Answer» `p^2` |
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| 537. |
Read the following comprehension carefully, Let Delta ne 0 Delta^c denotes the determinant of cofactors , then Delta^c=Delta^(n-1) where n(gt 0) is the order of Delta. If a,b,c are the roots of the equation x^3-3x^2+3x+7=0 then the value of |{:(2bc-a^2,c^2,b^2),(c^2,2ac-b^2,a^2),(b^2,a^2,2ab-c^2):}| |
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Answer» 9 |
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| 538. |
If A=[{:( alpha, beta ),( 0,alpha ) :}] is then n^(th )root of I_2 then choose the correct statement |
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Answer» If N is ODD `alpha -1 ,beta = 0` |
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| 539. |
If alpha and betaare the roots of x^(2)-ax+b^(2)=0 , thenalpha^(2) +beta^(2) is equal to_______ |
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Answer» `a^(2) + B^(2)` |
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| 540. |
Consider f(x)=Lim_(nto oo) ((a^(n)+b^(n))^((1)/(n))sinx+{e^(x)}^(n))([(1)/(ncot^(-1)n)]+1),AAx inR where agtbgt0. [Note : sgn alpha denote signum function of alpha.] Number of points where G(x)=|f(x)|+f(|x|) is non-differentiable in (-3pi,3pi), is |
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Answer» 6 `:.""f(x)=(asinx+0)(1+1)` `:.""f(x)=2asinx` (i) `H(x)=sgn (2asinx-3)` has EXACTLY one point of discontinuty in `[0,2pi]`, then `2a sinx-3=0` must have one real ROOT in `[0,2pi],SIN(3)/(2a)` `:." "a=(3)/(2)` only `:.""` Number integral value of a is zero. `G(x)=|2asinx|+2asin|x|` (ii)  Number of non-differential point of G(x) is `x=-2pi,-pi,0,pi,2pi` separately we can PROVE that G(x) is non-differentiable at x=0. |
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| 541. |
If x^2 + 3x + 5 = 0 and ax^2 + bx + c = 0 have a common root and a, b, c in N, then the minimum value of (a + b + c) is: |
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| 542. |
Using cofactors of elements of second row evaluate |{:(1,-3,2),(4,-1,2),(3,5,2):}|" |
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| 543. |
If range of function f(x) = (2log_(2)^(1//4) x - 3log_(27)(x^(2)+1)^(2)-2x)/(7^(4)log_(49)x-x-1) is [a, infty], then 4a is equal to |
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Answer» `therefore f_("min ") = -B/(4A) = 3/4` `therefore " range "=[3/4, INFTY] therefore a=3` |
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| 544. |
Amelia wants to buy a bare bones car and has narrowed her choice to two models . Model A sells for $12,500 , gets 25 miles to the gallon, and costs $350 per year for insurance. Model B sells for $16,100 , gets 48 miles to the gallon and costs $425 per year for insurance . 1) Suppose Amelia drives 36,000 miles per year and gas costs $ 3.50 gallon. within how many year, to the nearest hundredth of a year, to the nearest hundredth of ayear. does it become cheaper for amelia to own model B? |
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| 546. |
Match the Column I with Column II and mark the correct option from the given codes. |
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Answer» `{:(i,ii,iii,iv),(p,Q,R,s):}` |
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| 547. |
Maximise z = x + y subject ot x+4y le 8, 2x+3y le 12, 3x+y le 9, x ge 0, y ge 0. |
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| 548. |
Let A ={(x,y): x gt 0, y gt 0, x^(2) + y^(2) =1} and let B={(x,y) : x gt 0, y gt 0, x^(6) + y^(6) =1}. The A cap B |
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Answer» A |
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| 549. |
Ages of the First 12 United States Presidents at the Beginning of Their Terms in Office The table above lists the ages of the first 12 United States presidents when they began their terms in office. According to the table, what was the mean age, in years, of these presidents at the beginning of their terms? (Round your answer to the nearest tenth.) |
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| 550. |
Two teams A and B have the same mean and their coefficients of variance are 4, 2 respectively. If sigma_(A), sigma_(B) are the standard deviations of teams A, B respectively then the relation between item is |
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Answer» `sigma_(A) = sigma_(B)` |
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