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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.
| 7701. |
Which of the following sentences are statement? Give reason for your answer: sqrt(2) is a real number. |
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| 7702. |
Kavita draws a card from a pack of cards . What is the probability that she drawsa club |
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| 7703. |
Let S(K) =1+3+5+….+(2K-1)=k^(2) +3. Then which of the following is true? |
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Answer» `S(1)` is CORRECT |
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| 7704. |
If f(a-x) = f(a+x) and f(b-x)=f(b+x)AA x in Rwhere a, b (a gt b) are constants then the period of f(x) is |
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Answer» 2a |
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| 7705. |
Construct an index for 1998 taking 1997 as base by Average of Relatives. |
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| 7706. |
If H is the orthocentre of DeltaABC and AH=x, BH=y, CH=z then (abc)/(xyz)= |
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Answer» 1 |
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| 7707. |
Evaluate underset(xto(pi)/(6))lim(2-sqrt(3)cosx-sinx)/((6x-pi)^(2)). |
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| 7708. |
If bar(r)=3bar(p)+4bar(q)" and "2bar(r)=bar(p)-3bar(q) then |
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Answer» `bar(r), bar(Q)` have same direction and `abs(bar(r)) LT 2" "abs(bar(q))` |
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| 7709. |
If A="diag "["1-12"],B=" diag "["23-1"] and 3A+4B = diag ["abc"] then the ascending order of a, b, c is |
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Answer» a, b, C |
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| 7710. |
If alpha, beta, gamma are angles of a triangle then [tanalphabari+barj+bark ,bari+tanbetabarj+bark ,bari+barj+tangammabark] is |
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Answer» 0 |
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| 7711. |
If sinalpha+sinbeta=1//2 and cosalpha+cosbeta=sqrt(3)//2 then 3beta+alpha = |
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Answer» `120^(@)` |
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| 7712. |
Differentiate the following functions w.r.t. x: sin x/(3) |
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| 7713. |
Which of the following are sets? Justify your answer. (i) The collection of all whole numbers less than 10. (ii) The collection of good hockey players in India. (iii) The collection of all questions in this chapter. (iv) The collection of all difficult chapters in this book. (v) A collection of Hindi novels written by Manshi Prem Chand. (vi) A team of 11 best cricket players of India. (vii) The collection of all the months of the year whose names begin with the letter M. (viii) The collection of all interesting books. (ix)The collection of all short boys of your class. (x) The collection of all those students of your class whose ages exceed 15 years. (xi) The collection of all rich persons of Kolkata. (xii) The collection of all persons of Kolkata whose assessed annual incomes exceed (say) ₹ 20 lakh in the financial year 2016-17. (xiii) The collection of all interesting drams written by Shakespeare. |
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Answer» (II) Claearly, there is no SPECIFIC criterion to decide whether a given HOCKEY player of India, is good or not. So, the given collection is not a set. (iii) The collection of all question in this chapter is a set, because if a question is given then we can easily decide whether it is a question of the chapter or not. (iv) Clearly, the term 'difficult' is vague. So, the given collection is not well defined and therefore, it is not a set. (v) SUPPOSE we are given a collection of Hindi novals written by Munshi Prem Chand. Now, if we take any Hindi NOVAL then we can celaraly decide whereter it So, the given collection is a set. (vi) The term 'best' is vague. So, the given collection is not a set. (vii) The given collection has definte memers, namely March and May. So, this collection is a set. (viii) The term 'interesting' is vague so, the given collection is not a set. (ix) The term 'short' is vague. os the given collection is not a set. (x) Clearly, it contains definte members. so, it is a set. (xi) The term 'rich' is vague. So, the given collection is not a set (xii) The given collection is clearly well defined , so, it is a set. (xiii) The term ' interesting' is vague.so, the given collection is not a set. |
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| 7715. |
If [Cot^(-1)x]+[Cos^(-1)x]=0 where x is non-negative real number and [*] denotes the greatest integer function, then complete set of values of x is |
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Answer» (COS1, 1] |
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| 7716. |
Find angle between the lines y - sqrt3x - 50 " and " sqrt3 y - x +6 = 0 . |
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| 7717. |
A= {1, 2, 3, 4, 5}, B= {4, 5, 6, 7, 8}, C= {7, 8, 9, 10, 11}, D= {10, 11, 12, 13, 14}. Find the following sets. A cap C |
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| 7720. |
The value of (cos h 2 theta - 1)/(sin h 2 theta) is equal to |
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Answer» `cos H THETA` |
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| 7721. |
If n arithmetic means are inserted between 20 and 80. Such that the ratio of first mean to the last mean is 1: 3, then find the value of n. |
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| 7722. |
Find the sum to n terms of the series whose n^(th) term is 2n^3+3n^2-1 |
| Answer» SOLUTION :`n/2(n^3+4n^2+4n-1)` | |
| 7723. |
A small industrial concern used three raw materials A, B and C in its manufacturing process, the prices of the materials was as shown below: Using 1995 as the base year, calculate a simple aggregate price index for 2005. |
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| 7724. |
If A and B are any two sets, then (A uuB)- (A nnB)= |
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Answer» `A-B` |
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| 7725. |
Find the equation of the circle which passes through the point (2,-2), and (3,4) and whose centre lies on the line x+y=2. |
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| 7726. |
P(0, 5, 6), Q(1, 4, 7), R(2, 3, 7) and S(3, 4, 6) are four points in the space. The point nearest to be origin O(0, 0, 0) is |
| Answer» ANSWER :d | |
| 7727. |
Sin10^(@) - Sin110^(@) + Sin130^(@) = |
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Answer» 0 |
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| 7729. |
Find the distance between the points P(1, -3, 4) and Q(-4, 1, 2). |
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| 7730. |
If sqrt(2)costheta=sqrt((2+sqrt(2+sqrt(2)))/(2)) then the value of theta is |
| Answer» Answer :A | |
| 7731. |
Which of the following quantities is /are positive? |
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Answer» `cos (TAN^(-1)(TAN4))` |
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| 7732. |
Which of the following is a rational number ? |
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Answer» `sin(tan^(-1)3+"tan"^(-1)1/3)` |
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| 7733. |
Find the middle term in expansion of : (x^(2)+a^(2))^(5) |
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| 7734. |
Match the max l min value of function in Column I with corresponding values in Column -II |
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| 7735. |
Determin the mean and standard deviation for the following distribution |
Answer»  `therefore" Mean " barx=(Sigmaf_(i)x_(i))/(Sigmaf_(i))=(239)/(40)=5.975 ~~6` and`sigma=sqrt((Sigmaf_(i)d_(i)^(2))/(Sigmaf_(i))-((Sigmaf_(i)d_(i))/(Sigmaf_(i)))^(2))=sqrt((325)/(40)-((-1)/(40))^(2))` `=sqrt(8.125-0.000625)=sqrt(8.124375)=2.85` |
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| 7736. |
If the complex numbers z_(1) and z_(2) arg (z_(1))- arg(z_(2))=0 then showt aht |z_(1)-z_(2)|=|z_(1)|-|z_(2)|. |
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| 7737. |
Iftan (A+B)=p , tan (A-B)=q , " then " cot 2B= |
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Answer» `(1+pq)/(p-q)` |
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| 7738. |
Find the equation of the line which is at a perpendicular distance from the origin is 5 units and the angle made by the perpendicular with the positive x-axis is 30^(@). |
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| 7739. |
Write the first three terms in each of the following sequences defined by the following a_(n)= (n-3)/(4) |
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| 7741. |
Area of the triangle formed by the lines 2x-y-5=0, x-5y+11=0, x+y-1=0 is |
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| 7742. |
If (sin^(4)theta)/(a)+(cos^(4)theta)/(b)=(1)/(a_+b) then(sin^(8)theta)/(a^(3))+(cos^(8)theta)/(b^(3))= |
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Answer» `(1)/((a+b)^(3))` |
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| 7744. |
Let f(x)=sqrt(|x|-{x}) ( where {.} denote the fractional part of x and x, y are its domain and range, respectively). Then |
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Answer» `X in (-oo, 1/2]` and `y in [1/2, oo)` |
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| 7745. |
If f(x) is a polynomial satisfying f(x)f(1//x)=f(x)+f(1//x) and f(3)=28, then f(4) is equal to |
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Answer» 63 |
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| 7746. |
In the permutations of n things r, taken together, the number of permutations in which m particular things occur together is ""^(n-m)P_(r-m)xx""^(r)P_(m). |
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Answer» Solution :False Arrangement of n things, taken r at a time in which m things occur together, we considered these m things as 1 group. NUMBER of OBJECT excluding those m objects = (r - m) Now, first we have to arrange (r-m+1) objects. Number of ARRANGEMENTS `=(r-m+1)"!"` and m objects which we consider as 1 group, can be ARRANGED in `m"!"` ways. `therefore` Required number of arrangements `=(r-m+1)"!" xx m"!"` |
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| 7747. |
Two circles of radii a and b cut each other at an angle theta then length of common chord is |
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Answer» `(2 AB SIN theta)/sqrt(a^(2) + B^(2) + 2AB COS theta )` |
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| 7748. |
Find the angle between the lines l_(1) : y= (2 - sqrt(3) ) ( x +5) and l_(2) : y=(2+ sqrt(3) ) ( x-7). Thinking Process : If the angle between the lines having the slope m_1 and m_2 is theta then tan theta = | ( m_1 - m_2)/( 1+ m_1 m_2) |. Use this formula to solve the above problem. |
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| 7749. |
A die is thrown. Describe the following events: (i) A: anumber less than? (ii) B: a number greater than 7 (iii) C: a multiple of 3 (iv) D: a number less than 4 (v) E: an even number greater than 4 (vi) F: a number not less than 3 Also find A uu B, A nn B, B uu C, E nn E, D nn E, A - C, D - E, E nn F',F' |
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| 7750. |
Find the number of integer values of m for which the x-coordinate of the point of intersection of the lines 3x+4y=9 and y=mx+1 is also an integer. |
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