Saved Bookmarks
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.
| 6551. |
If f={(-2, 4), (0, 6), (2, 8)} and g={(-2, -1), (0, 3), (2, 5)}, then ((2f)/(3g)+(3g)/(2f))(0)= |
|
Answer» `1//12` |
|
| 6552. |
In triangle ABc, if A-B=120^(@) and R=8r where Rr have their usual meaning then cosC equals |
|
Answer» `3//4` |
|
| 6553. |
Find the maximum area of the rectangle that can be formed with fixed perimeter 20. |
|
Answer» |
|
| 6554. |
Prove that= (sin 5x - 2 sin 3 x + sin x)/( cos 5x - cos x) = tan x |
|
Answer» |
|
| 6555. |
Check the continuity of the functionn 'f' defined by fx={{:((x^(2)-9)/(x^(2)-2x-3),if, 0 lt x lt 5 and x ne3),(1.5,if,x=3):} |
|
Answer» |
|
| 6556. |
Nuber of distinct solutions of sec theta+ tan theta= sqrt(3), 0 le theta le 3pi,is |
|
Answer» 2 |
|
| 6557. |
If sinx + siny + sinz + sinzw =- 4. then the value of sin^(400)x + sin^(300) y + sin^(200) z + sin^(100)w is |
|
Answer» `sin^(400) x.sin^(300) y.sin^(200) z+sin^(100)W` |
|
| 6558. |
sin "" (2pi)/(7) + sin "" (4pi)/(7) + sin "" (8pi)/(7) = |
|
Answer» `SQRT(7)//2` |
|
| 6559. |
Expansion of log(sqrt((1+x)/(1-x))) is : |
|
Answer» `X + x^(3)/3 + x^(5)/5 + ... ` |
|
| 6560. |
ABCDEF is a regular hexagon. bar(AB)+bar(AC)+bar(AD)+bar(EA)+bar(FA)= |
|
Answer» `3bar(AB)` |
|
| 6561. |
If f(x)satisfies the relation f(x+ y) = f ( x) + f( y )for all x, y in R and f(1)= 5 then |
|
Answer» `F(X)` is an odd function |
|
| 6562. |
Planes are drawn parallel to the coordinate planes through the points P(x_(1),y_(1),z_(1)) and Q (x_(2),y_(2),z_(2)) find the length of the edges of the parallopiped. |
|
Answer» |
|
| 6563. |
If a and b are chosen randomly from the set {1,2,3,4} with replacement, then the probability of the real roots of the equation x^(2)+ax+b=0 is: |
|
Answer» `(3)/(16)` |
|
| 6564. |
Express each of the following complex number in the form a+ib: i^(37)xx(1)/(i^(67)) |
|
Answer» |
|
| 6565. |
If tan^(2)theta=2tan^(2)phi+1 then the value of cos(2theta)+sin^(2)phi is ……….. |
|
Answer» `-1` |
|
| 6566. |
Let f:(- pi/2, pi/2) rarr R be given by f(x)=(log (sec x + tanx))^(3). Then |
|
Answer» `F(x)` is an odd function |
|
| 6567. |
Find the sum to indicated number of terms in each of the geometric progressions insqrt7, sqrt(21)3sqrt7 , ........n terms |
|
Answer» |
|
| 6569. |
Statement - I : If |{:(x+1,-3,4),(-5,x+2,2),(4,1,x-6):}|=0 then x=0 Statement - II : If |{:(15-x,11,10),(11-3x,17,16),(7-x,15,13):}|=0 then x=6 Which of the above statement(s) is true ? |
|
Answer» only I is TRUE |
|
| 6570. |
The shadow of a tower standing on a level plane is found to be 50 mt longer when the suns altitude is 30^(@)then that when it45^(@) then the height of the tower is |
|
Answer» ` 25( SQRT3+ 1) ` |
|
| 6571. |
If (1)/("log"_(3) pi) + (1)/("log"_(4) pi) gt x, then the greatest integral value of is |
| Answer» Answer :A | |
| 6572. |
The probability that a student will receive A, B, C or D grade are 0.40, 0.50, 0.15 and 0.10respectively. Find the probability that a student will receive (i) B or C grade (ii) At least C grade. |
|
Answer» |
|
| 6573. |
The points A(1,2),B(3,-4) are two vertices of the rectangle ABCD. The point P(3,8) lies on the CD produced then C= |
|
Answer» `(33//5, 14//5)` |
|
| 6575. |
Ifthetalies in the first quadrant and5 tan theta = 4 , " then " (5 sin theta - 3 cos theta )/( sin theta + 2 cos theta )= |
|
Answer» `5//14` |
|
| 6576. |
The value fo a, b and c such that lim_(x to 0)(ax^(x)-b log (1+x)cx.e^(-x))/(x^(2)sinx)=2 are given by |
|
Answer» `a=3, b=12, C=9` |
|
| 6578. |
If r le s le n, then prove that .^(n)P_(s) is divisible by .^(n)P_(r). |
|
Answer» Solution :`.^(N)P_(r) = (n!)/((n-r)!)` `=n (n-1) (n-2)... (n-r+1)` `.^(n)P_(s) = (n!)/((n-s)!)` `= n(n-1)(n-2) ...(n-r+1)` `(n-r) ...(n-s+1) ( :' r le s)` Now `(.^(n)P_(s))/(.^(n)P_(r)) = (n-r) (n-r-1).......(n-s+1)` = a positive INTEGER. `:. .^(n)P_(s)` is DIVIDED by `.^(n)P_(r)` Hence PROVED. |
|
| 6579. |
Simiplify :(sqrt((5+12i)) + sqrt((5-12i)))/(sqrt((5+12i))-sqrt((5-12i))) |
|
Answer» |
|
| 6580. |
Statement-I : The coordinates of a point equidistant from the four point (a,0,0),(0,b,0),(0,0,c),(0,0,0) are (a/4,b/4,c/4) Statement-II : The distance between the origin and the centroid for the tetrahedron where vetrtice are (0,0,0),(a,0,0),(0,b,0),(0,0,c) is (sqrt(a^(2)+b^(2)+c^(2)))/4 Which of the above statementsis correct : |
|
Answer» Only I |
|
| 6581. |
If A=(1, 1, 1), B=(1, 2, 3), C=(2, -1, 1) be the vertices of a DeltaABC, then the length of the internal bisector of the angle 'A' is |
|
Answer» `1/2` |
|
| 6582. |
Find the point of intersection of the medians of the triangle with vertices (-1, -3, 4), (4, -2,-7), (2, 3, -8). |
|
Answer» |
|
| 6583. |
Find the values of theta lying between 0^(@) and 360^(@) when sin theta=cos317^(@) |
|
Answer» |
|
| 6584. |
Find equaiton of hyperbola satisfying given conditons Length of the conjugate axis is 7 and passes from (3,-2) |
|
Answer» |
|
| 6586. |
The points whose position vectors are 2bar(i)+3bar(j)+4bar(k), 3bar(i)+4bar(j)+2bar(k) and 4bar(i)+2bar(j)+3bar(k) are the vertices of |
|
Answer» an ISOSCELES triangle |
|
| 6587. |
Let ABC be a triangle with integer sides a,b,c and angle C = 90^(@) The number of triangles with r = 2009is |
|
Answer» 10 |
|
| 6588. |
If the line, (x-3)/(2) = (y+2)/(-1) = (z +4)/(3) lies in the plane, lx + my - z =9, then l ^(2) + m ^(2)is equal to |
|
Answer» 18 |
|
| 6589. |
Show on a diagram the position of the straight line x"cos"30^(@)+y"sin"30^(@)=2 in relation to the co-ordinate axes, indicating clearly which angle is 30^(@) and which length is 2 units. Find (i) the equation of the straight line parallel to that given line and passing through the point (4, 3) and (ii) the length of the perpendicular from the origin on to this line |
|
Answer» |
|
| 6590. |
Show on a diagram the position of the straight line x"cos"30^(@)+y"sin"30^(@)=2 in relation to the co-ordinate axes, indicating clearly which angle is 30^(@) and which length is 2 units. Find (i) the equation of the straight line parallel to that given line and passing through the point (4, 3) and (ii) the distance between the two parallel straight lines. |
|
Answer» |
|
| 6591. |
What is the number of terms in the expansion of the following? (4x^(2) + 12 xy+ 9y^(2) )^(9) |
|
Answer» |
|
| 6592. |
Ab, AC and AD are three adjacent edges of a parallelpiped. The diagonal of the praallelepiped passing through A and direqcted away from it is vector veca. The vector of the faces containing vertices A, B , C and A, B, D are vecb and vecc, respectively , i.e. vec(AB) xx vec(AC) and vec(AD) xx vec(AB) = vecc the projection of each edge AB and AC on diagonal vector veca is |veca|/3 vector vec(AC) is |
|
Answer» `1/3 veca+ (vecaxx(vecb-vecc))/|veca|^(2)` `vec(AB)xxvec(AC)=vecb` `vec(AD)xxvec(AB)=vecc` `vec(AB).veca/(|veca|)=|veca|/3 Rightarrowvec(AB).veca= (|veca|^(2))/3` `vec(AB).veca/(|veca|)=|veca|/3 Rightarrowvec(AC).veca= (|veca|^(2))/3` ` (vec(AB) xx vec(AC))xxveca = vecb xxveca` `vec(AC)-vec(AB)=3(vecbxxveca)/(|veca|^(2))` `|veca|^(2)=vec(AB).veca+vec(AC).veca+vec(AD).veca` `(|veca|^(2))/3=vec(AD).veca` `(vec(AD)xxvec(AB))xxveca=veccxxveca` `vec(AB)- vec(AD) = 3 (vecc xx veca)/(|veca|^(2))` Now from (ii) and (III), we get `vec(AC) and vec(AD)`as `vec(AC)=1/3veca+ (vecaxx(vecb xx vecc))/(|veca|^(2))+(3(vecbxxveca))/(|veca|^(2))` ` vec(AD)= 1/3veca+ (vecaxx(vecb-vecc))/(|veca|^(2))- (3(vec cxxveca))/(|veca|^(2))` 
|
|
| 6593. |
Ab, AC and AD are three adjacent edges of a parallelpiped. The diagonal of the praallelepiped passing through A and direqcted away from it is vector veca. The vector of the faces containing vertices A, B , C and A, B, D are vecb and vecc, respectively , i.e. vec(AB) xx vec(AC)=vecb and vec(AD) xx vec(AB) = vecc the projection of each edge AB and AC on diagonal vector veca is |veca|/3 vector vec(AB) is |
|
Answer» `1/3 VECA+ (vecaxx(vecb-VECC))/|veca|^(2)` `vec(AB)xxvec(AC)=vecb` `vec(AD)xxvec(AB)=vecc` `vec(AB).veca/(|veca|)=|veca|/3 Rightarrowvec(AB).veca= (|veca|^(2))/3` `vec(AB).veca/(|veca|)=|veca|/3 Rightarrowvec(AC).veca= (|veca|^(2))/3` ` (vec(AB) xx vec(AC))xxveca = vecb xxveca` `vec(AC)-vec(AB)=3(vecbxxveca)/(|veca|^(2))` `|veca|^(2)=vec(AB).veca+vec(AC).veca+vec(AD).veca` `(|veca|^(2))/3=vec(AD).veca` `(vec(AD)xxvec(AB))xxveca=veccxxveca` `vec(AB)- vec(AD) = 3 (vecc xx veca)/(|veca|^(2))` Now from (ii) and (III), we get `vec(AC) and vec(AD)`as `vec(AC)=1/3veca+ (vecaxx(vecb xx vecc))/(|veca|^(2))+(3(vecbxxveca))/(|veca|^(2))` ` vec(AD)= 1/3veca+ (vecaxx(vecb-vecc))/(|veca|^(2))- (3(vec cxxveca))/(|veca|^(2))` 
|
|
| 6594. |
Ab, AC and AD are three adjacent edges of a parallelpiped. The diagonal of the praallelepiped passing through A and direqcted away from it is vector veca. The vector of the faces containing vertices A, B , C and A, B, D are vecb and vecc, respectively , i.e. vec(AB) xx vec(AC) and vec(AD) xx vec(AB) = vecc the projection of each edge AB and AC on diagonal vector veca is |veca|/3 vector vec(AD) is |
|
Answer» `1/3 veca+ (vecaxx(VECB-VECC))/|veca|^(2)` `vec(AB)xxvec(AC)=vecb` `vec(AD)xxvec(AB)=vecc` `vec(AB).veca/(|veca|)=|veca|/3 Rightarrowvec(AB).veca= (|veca|^(2))/3` `vec(AB).veca/(|veca|)=|veca|/3 Rightarrowvec(AC).veca= (|veca|^(2))/3` ` (vec(AB) XX vec(AC))xxveca = vecb xxveca` `vec(AC)-vec(AB)=3(vecbxxveca)/(|veca|^(2))` `|veca|^(2)=vec(AB).veca+vec(AC).veca+vec(AD).veca` `(|veca|^(2))/3=vec(AD).veca` `(vec(AD)xxvec(AB))xxveca=veccxxveca` `vec(AB)- vec(AD) = 3 (vecc xx veca)/(|veca|^(2))` Now from (ii) and (iii), we get `vec(AC) and vec(AD)`as `vec(AC)=1/3veca+ (vecaxx(vecb xx vecc))/(|veca|^(2))+(3(vecbxxveca))/(|veca|^(2))` ` vec(AD)= 1/3veca+ (vecaxx(vecb-vecc))/(|veca|^(2))- (3(vec cxxveca))/(|veca|^(2))` 
|
|
| 6595. |
Assume that an object is launched upward at 980m/seclis position would be given by s=-4.9t^2+980. Find the maximum height attained by the object |
|
Answer» |
|
| 6597. |
1+ (1+3) + (1+3+ 5) + ….n brackets = |
|
Answer» `(n (n+1) (n+2) )/( 6) ` |
|
| 6598. |
Find an approximation of (0.99)^5 using the first three terms of its expansion. |
|
Answer» |
|
| 6599. |
If tan(picostheta)=cot(pisintheta),then prove that cos(theta-(pi)/(4))=pm(1)/(2sqrt(2)) |
|
Answer» `1//2` |
|
| 6600. |
The value of 'a' for which the function f(x) =a sin x+1/3 sin 3x has an extremum at x=pi//3 is |
|
Answer» 1 |
|