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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.
| 11201. |
Two equal sides of isosceles triangle are given by equation 7x-y+3=0 and x+y-3=0. The slope of the thrid side is |
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Answer» `-3,1//3` |
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| 11202. |
If tan^(2) theta + cot^(2) theta = 2 then |
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Answer» `n pi pm (pi)/(6), n in Z` |
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| 11204. |
If the order pairs (x+1, y-2) and (3,10) are equal then respective values ofx and y are …..... . |
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| 11206. |
One side of a rectangle lies along the line 4x+7y+5=0.Two of its vertices are (-3,1)a n d(1,1)dotFind the equations of the other three sides. |
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| 11207. |
If three vectors vec(a), vec(b), vec(c ) are such that vec(a) ne vec(0) and vec(a) xx vec(b)=2 (vec(a) xx vec(c )), |vec(a)| = |vec(c )| =1, |vec(b)|=4 and the angle between vec(b) and vec(c ) is cos^(-1) ((1)/(4)), then vec(b)-2vec(c )= lamda vec(a) where lamda= |
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Answer» 0 |
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| 11208. |
sin ^(-1) ((2^(x +1))/( 1 + 4 ^(x))) ({:(put), ( 2 ^(x) = tan theta ):}) |
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| 11209. |
If the transformed equation of curve is X^(2)+Y^(2)=4 when the axes are translated to the point (-1,2) then find the original equation of the curve. |
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| 11210. |
A family is using Liquefied petroleum gas (LPG) of weight 14.2 kg for conumption.(Full weight 29.5 kg includes the empty cylinders tare weight of 15.3 kg). If it is use with constant rate then it lasts for 24 days. Then the new cylinder is replaced Q (i) Find the equation relating the quantity of gas in the cylinder to the days. |
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| 11211. |
(d ^(20))/(dx ^(20)) [ 2 cos x cos 3x]= |
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Answer» `2^(20)(cos 2x - 2^(20) cos 3X)` |
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| 11212. |
If a variable line in two adjacent positions has direction cosines (l,m,n) and (l + delta l, m + delta m, n + delta n) , then show that the small angle delta theta between the two position is given by (delta theta)^(2) = (delta l)^(2) + (delta m)^(2)+ (delta n)^(2) |
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| 11213. |
If the sides of a triangle are 4 cm, 5 cm, 6 cm then ratio of the cosine of the least and the greatest angles is |
| Answer» Answer :A | |
| 11214. |
If (x - a) cos theta + ysin theta =(x - a ) cos phi + y sin phi = a and tan (theta//2)- tan (phi//2) =2b , then |
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Answer» `y^2=2ax-(1-B^2)x^2` |
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| 11215. |
An experiment has the four possible mutually exculusive and exhaustive outcomes A,B,C and D. Check whether the following assignments of probability are permissible.(i)P(A)=0.15,P(B)=0.30,P(C)=0.43,P(D)=0.12(ii)P(A)=0.22,P(B)=0.38,P(C)=0.16,P(D)=0.34(iii)P(A)=2/5,P(B)=3/5,P(C)=-(1)/(5),P(D)=1/5 |
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Answer» <P> (iii)` P (C) = (-1)/5` |
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| 11216. |
If the centriod of a triangle formed by the points (a,0,0),(0,b,0),(0,0,c) is (2/3,1/3,1) then ascending order of a,b,c is |
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Answer» a,B,c |
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| 11217. |
In a triangle ABC let angle C=pi//2. If r is the inradius and R is the circumradius of the the triangle ABC, then 2(r+R)= |
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Answer» `a+b` |
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| 11218. |
sin h^(-1) (2 alpha) = 2 cos h^(-1) (beta) then |
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Answer» `ALPHA^(2) + beta^(2) = alpha^(4)` |
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| 11219. |
Let A_(0)A_(1)A_(2)A_(3)A_(4)A_(5) be a regular hexagon inscribed in acircle of unit radius. Then the product of the length of the line segments A_(0)A_(1),A_(0)A_(2)andA_(0)A_(4) is |
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Answer» `3//4` |
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| 11220. |
A longer side of a parallelogram is 10 cm and the shorter is 6cm. If the longer diagonal makes an angle 30^(@) with the longer side, then the length of the longer diagonal (in cm) is |
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Answer» `5sqrt(3)+SQRT(11)` |
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| 11221. |
How many different words can be formed of the letters of the word 'MALKENKOV' so that no two values are together |
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| 11223. |
Show that the condition that tha concurrent lines with direction cosines (l_(1).m_(1),n_(1)),(l_(2),m_(2),n_(2))and(l_(3),m_(3),n_(3)) are coplanar is l_(1)(m_(2)n_(3)-m_(3)n_(2))+m_(1)(n_(2)l_(3)-n_(3)l_(2))+n_(1)(l_(2)m_(3)-l_(3)n_(2))=0 |
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| 11225. |
If cos alpha + cos beta = 1//2 and sin alpha + sin beta = 1//3, then |
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| 11226. |
If a,b,c,d are the vertices of a rhombus, then |
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Answer» `(bard-barb).(barc-bara)=0` |
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| 11227. |
How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4? |
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| 11228. |
If the median of DeltaABC through A is perpendicular to AB then tan A+2tanB= |
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Answer» 0 |
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| 11229. |
If t(t+x^2)=x and x^2 +t^2 =y then at x = 2 , (dy)/(dx)= |
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Answer» `24/5` |
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| 11230. |
State which of the following sets are finite or infinite. (i) {x : x in N and (x-1) (x-2) =0} (ii) {x : x in N and x^(2)=4} (iii) {x : x in N and 2x-2=0} (iv) {x : x in N" is prime"} (v) {x: x in N and" x is odd"} |
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| 11231. |
A card is selected from a pack of 52 cards. How many points are there in the sample space ? |
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| 11232. |
(1)/(sqrt(x+3)-sqrt(x-4)) |
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| 11233. |
The ratio of the sums of m and n terms of an A.P. is m^2 : n^2.Show that the ratio of m^(th) and n^(th) term is (2m-1) : (2n -1) . |
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| 11234. |
Insert two numbers between 3 and 81 so that the resulting sequence is G.P. |
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| 11237. |
Is the function defined by f(x)={{:(x+5," if "x le1),(x-5," if "x gt 1):} a continuous function? |
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| 11238. |
The price quotations of four different commodities for 2001 and 2009 are as given below, Calculate the index number for 2009 with 2001 as the base year by using weighted average of price relative method. |
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| 11239. |
State in each case whehterA sub B or A cancel(sub)B. (i) A={0,1,2,3} ,B={1,2,3,4,5} (ii) A=phi, B ={0} (iii) A= {1,2,3} , B= {1,2,4} (iv) A ={x:x in Z, x^2=1}, B={x:x in N X^2=1} (v)A= {x:x " is a even natural number "},B={x:x " is a integer " } (vii) A={x:x " is a real number "}, B= {x:x " is a complex number"} (viii) A={x :x " is an isosceles triangle in a planel, B={x:x" is an equilateral triangle in the same plane "} (ix) A={x:x " is a square in a plane "} B={x:x " is a rectangle in the same plane "} (x) A={x:x" is a triangle in a plane "}, B=(x:x " is a rectangle in the same plane"}, (xi) A={x:x " is an even natural number less than " 8} B={x:x " is a natural number which divides" 32}. |
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Answer» (v) `A={2, 4,6,8.....} and B ={ ...., -1, 0,1,2,3,4,5,6,7,8......]`So, ` AsubB`. (vi) Every integer is a RATIONAL number. (VII) We MAY write a real number x as `x ^+0i`. So, every real number is a complex number. (ix) Every square is a RECTANGLE. (xi) `A={2,4,6} and B={1,2,4,8, 16,32}` So, `A cancel(sub) B`. |
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| 11240. |
The sum of the series , sin theta sec 3 theta sec 3^(2) theta + sin3^2theta3^(3) theta + .......... upto n terms , is |
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Answer» `1/2[TAN3^(n) theta-tan3^(n-1)theta]` |
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| 11241. |
Write the negation of the following statements and check whether the resulting statements are true: The sum of 3 and 4 is 9. |
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| 11243. |
Find the modulus and principal argument of the following complex numbers . -1-isqrt(3) |
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| 11244. |
Write the negation of the following statements and check whether the resulting statements are true: There does not exist is quadrilaterial whcilh has all its sides equal. |
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| 11245. |
The value of k if the lines (x+1)/(-3) = (y+2)/(2k ) = (z-3)/(2) and (x-1)/(3k) = (y+5)/(1) = (z+6)/(7) my be perpendicular |
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Answer» 3 |
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| 11247. |
Refer to question 6 above, state true or false : (give reason for your answer) A and C are mutually exclusive |
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| 11249. |
If y = sum_(i=1)^(n)(x-x_(i))^(2), x_(i) are constants, then for what value of x, y is minimum ? |
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