InterviewSolution
Saved Bookmarks
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.
| 8601. |
Matchthe following |
|
Answer» `1 - C, 2 - a , 3- d, 4-b` |
|
| 8602. |
The principal solution of costheta=(1-sqrt(3))/(2sqrt(2)) is |
|
Answer» `75^(@)` |
|
| 8603. |
The maximum value of the expression (1)/( sin^(2) theta + 3 sin theta cos theta + 5cos^(2) theta) is |
|
Answer» |
|
| 8604. |
When (0,0) shifted to (2, -2) the transformed equation of (x - 2)^(2) + (y + 2)^(2) = 9 is |
|
Answer» `x^(2) + y^(2) = 9` |
|
| 8605. |
If f(theta) = (1-sin 2 theta + cos 2 theta)/(2 cos 2theta), then value of 8 f(11^(0)).f(34^(0)) is ___________ |
|
Answer» |
|
| 8606. |
Differentiate the following w.r.t. x: (x)/(sin^(n)x) |
|
Answer» |
|
| 8607. |
A die is thrown, find the probability of following events : A prime number will appear. |
|
Answer» |
|
| 8608. |
Find in how many ways can (i) at least one fruit be selected ? (ii) one fruit of each type be selected? (iii) at least one fruit of each type be selected ? Grom 5 organs, 7 mangoes and 8 bananas? |
|
Answer» Solution :(i) No. of ways of selecting at least one fruit `= (5 +1) (7+1) (8+1)-1` `= 6 XX 8 xx 9 - 1` `= 432 - 1 = 431` (ii) No. of ways of selecting one fruit of each type `=.^(5)C_(1) xx .^(7)C_(1) xx.^(8)C_(1) = 5 xx 7 xx 8 = 280`. (iii) No. of ways of selecting at least one orange `= 2^(5) - 1 = 31` No. of ways of selecting at least one mango `= 2^(7) - 1 = 127` No. of ways of selecting at least one banana `= 2^(8) - 1 = 255` `:.` No. of ways of selecting at least one fruit of each type `= 31 xx 127 xx 255 = 1003935` |
|
| 8609. |
If sin^(-1)((2x)/(x^(2)+1))+cos^(-1)((1-x^(2))/(x^(2)+1))=(pi)/3 then x= |
|
Answer» `2-SQRT(3)` |
|
| 8610. |
Write the first five terms of each of the sequences whose n^(th) terms are as following a_(n)= 2n^(2)-n+1 |
|
Answer» |
|
| 8611. |
Match the following |
|
Answer» 1-c,2-a,3-d,4-b |
|
| 8612. |
The two successive terms in the expansion of (1+x)^(24) whose coefficients are in the ratio 1:4 are |
|
Answer» 3RD and 4th |
|
| 8613. |
If 2sqrt3is the inradiusof anequilateraltriangle then the lengthof its side is |
| Answer» ANSWER :B | |
| 8614. |
If a flag staff of 6 mt high placed on the top of a tower throws a shadow of 2sqrt3 mt along the ground then the angle that the Sun makes with the ground is |
|
Answer» ` 45 ^(@) ` |
|
| 8615. |
State whether the given set is finite or infinite. (i)A= Set of all triangles in a plane. (ii) B= set of all points on the circumference (iii) C= set of all lines parallel to the y-axis. (iv) D= set of all leaves on a tree (v)E= set of all positive integers greater than 500 (vi) F={x in R,0 lt x lt 1} (vii)G= {x in Z : x lt 1} (viii) H ={ x in Z : -15 lt x lt 15} (ix)J={x: in N and x " is prime"} (x)K={x:x in N and x "is odd "} (xi)L= set of all circles passing through the origin (0,0). |
|
Answer» 2 (ii) infinite (III) infinite (iv) finite (v) infinite (vi) infinite (vii) infinite (VIII) finite (ix) infinite (XI) infinite |
|
| 8616. |
Between 1 and 31, m numbers have been inserted in such a way that the resulting sequence is an A. P. and the ratio of 7^(th)and (m - 1)^(th)numbers is 5 : 9. Find the value of m. |
|
Answer» |
|
| 8617. |
( a cos A + b cos B + c cos C )/(a +b +c )= |
|
Answer» `(R)/(2R)` |
|
| 8618. |
Two trees A and B are the same side of a river. From point c in the river the distance of the trees A and B is 250mand300m respectively. If the angle C is 45^(@), find the distance between the trees. (Use sqrt(2)=1.44) |
|
Answer» |
|
| 8619. |
If 3theta is not an odd multiple of pi/2 then prove that tanthetatan(60^(@)+theta) tan(60^(@)-theta)=tan3theta and deduce that tan6^(@) tan42^(@) tan66^(@) tan78^(@)=1. |
|
Answer» |
|
| 8620. |
"tan"^(-1)(5/12)+sin^(-1)(24/25)=cos^(-1)(x) implies x= |
|
Answer» `(-31)/325` |
|
| 8621. |
If cos(alpha+beta)=(4)/(5)andsin(alpha+beta)=(5)/(13), where alpha lie between 0and(pi)/(4), then find that value of tan(2alpha). |
|
Answer» |
|
| 8622. |
Find the condition for the chord lx + my=1 of the circle x^(2)+y^(2)=a^(2) to subtend a right angle at the origin. |
|
Answer» |
|
| 8623. |
The 4^(th) term of a G.P is 4. Find the product of its first five terms. |
| Answer» Answer :C | |
| 8624. |
The range of sin^(-1)[x^(2)+1/2] + cos^(-1)[x^(2)- 1/2], where [.] denotes the greatest integer function, is |
|
Answer» `{PI/2, pi}` |
|
| 8625. |
Prove that the equation 3x^(2)+7xy+2y^(2)+5x+5y+2=0 represents a pair of straight lines. Find the point of intersection. Also find the angle between them. |
|
Answer» |
|
| 8626. |
(1+cosec theta - cot theta)/(1+cosec theta + cot theta)= |
|
Answer» `(1-SIN THETA)/(COS theta)` |
|
| 8628. |
If k=sin((pi)/(18))sin((5pi)/(18))sin((7pi)/(18)), then the numerical value of k is ……….. |
|
Answer» |
|
| 8629. |
Find the distance between the parallel line (15x+8y-34)=0 and (15x+8y+31) =0? |
|
Answer» |
|
| 8630. |
If bar(i)+2bar(j)+3bar(k), 3bar(i)+2bar(j)+bar(k) are sides of a parallelogram then a unit vector parallel to one of the diagonals of the parallelogram is |
|
Answer» `(BAR(i)+bar(j)+bar(K))/sqrt(3)` |
|
| 8631. |
Let Q be the set of all rational number in [0, 1] and f:[0, 1]rarr[0, 1] be defined by f(x)={{:(x," for ", x in Q),(1-x," for ", x cancel(in)Q):} Then the set S={x in [0, 1] (fof)(x)=x} is equal to |
| Answer» ANSWER :D | |
| 8632. |
Draw the graphs of the following : y = sqrt( 1- x^(2)) |
|
Answer» |
|
| 8634. |
sin 10^(@) + sin 20^(@) + sin30^(@) + .......sin 360^(@)= |
|
Answer» 0 |
|
| 8635. |
Find the probability of getting the sum as a prime number when two dice are thrown together. |
|
Answer» |
|
| 8636. |
A straight line through the point (h,k) where hgt0andkgt0 , makes positive intercepts on the coordinate axes . Then the minimum length of line intercepted between the coordinate axes is |
|
Answer» `(H^((2)/(3))+K^((2)/(3)))^((3)/(2))` |
|
| 8637. |
Find the square root of the following complex numbers i |
|
Answer» |
|
| 8638. |
Choose the correct or the most suitable answer from the given four alternatives. lim_(xrarr0)(8^x -4^x -2^x +1^x )/(x^2)= |
| Answer» Answer :B | |
| 8639. |
Two straight line u=0 and v = 0 passes through the origin and the angle between them is tan^(-1)(7/9). If the ratio of slopes of u=0 and v=0 is 9/2 then their equations care |
|
Answer» `y+3x=0 and 3y+2x=0` |
|
| 8641. |
Number of solutions to the equation |2e^(sin x) - 3 - e^(2 sin x)|= | e^(sin x) - e^(2 sinx) - 1| i n [0, 2 pi]is |
|
Answer» zero |
|
| 8642. |
Find the locus of the point P such that PA^2+PB^2=2c^2:where"A(a,0),B(-a,0) and 0 lt |a| lt |c|. |
|
Answer» |
|
| 8643. |
The period of f(x)=[x]+[2x]+[3x]+[4x]+.....+[nx] - (n(n+1))/(2)x, where n in N , is ( where [.] erpresents greatest integer function) |
|
Answer» n |
|
| 8644. |
Ifthe line joining the points (1,4,2) and (-2,1,2) is inclined at an angle of (pi)/(3) to the line joining the points (1,2,3), (2,lambda,1) then lambda = |
|
Answer» `PM sqrt(7)` |
|
| 8646. |
Write the new coordinates of the following point (0,5) when the axes are rotated through to an angle 30^(@) |
|
Answer» |
|
| 8647. |
Obtain the equation of the parabola with given conditions:Focus (1,-1) and one vertex (2,1) |
|
Answer» |
|
| 8648. |
Find the mean deviation about the median for the data in {:("x"_(i),15,21,27,30,35),("f"_(i),3,5,6,7,8):} |
|
Answer» |
|
| 8649. |
The longest side of a triangle is at least 61 cm, find the minimum length of the shortest side. |
|
Answer» |
|
| 8650. |
If (vec(a), vec(b))= pi, then |4vec(a) xx 5vec(b) + vec(b) xx vec(a)|= |
|
Answer» 0 |
|