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This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
25 people for programme A, 50 people for programme B, 10 people for both. So, number of employee employed only A isA. 15B. 20C. 35D. 40 |
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Answer» Correct Answer - A 25 people for programme …………. `n(A-B) = n(A)- n(AnnB) = 25-10 = 15` |
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| 2. |
Statement - 1 : If `x gt 1` then `log_(10)x lt log_(3)x lt log_(e )x lt log_(2)x`. Statement - 2 : If `0 lt x lt 1`, then `log_(x)a gt log_(x)b implies a lt b`.A. Statement - 1 is True, Statement - 2 si True , Statement -2 is a correct explanation for Statement - 1B. Statement -1 is True, Statement -2 si True, Statemetn -2 is NOT a correct explanation for Statement -1C. Statement - 1 is True, Statement - 2 is FalseD. Statement - 1 is False, Statement - 2 is True |
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Answer» Correct Answer - B Statement -1 : If `x gt 1` then ………….. Since `10gt 3gt egt2` If `x gt 1, then log, 10 gt log_(x)3 gt log_(x)e gt log_(x)2` `implies (1)/(log_(10)) gt (1)/(log_(3)x)gt (1)/(log_(e )x)gt (1)/(log_(2)x)` `implies log_(10)x lt log_(3)x lt log_(e )x lt log_(2)x` |
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| 3. |
The inequality `x(lambda - x)lt y(lambda - y)AA x, y` with `x lt y lt 1` is always true ifA. `lambda le 2`B. `lambda ge 2`C. `lambda lt -1`D. for no value of `lambda` |
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Answer» Correct Answer - B The inequality `x(lambda-x)lt` ………….. `lambda x-x^(2)lt lambda y - y^(2)` `x^(2)-y^(2)-lambda x + lambda y gt 0` `(x-y)(x+y)-lambda(x-y)lt 0` `(x-y)(x+y-lambda)gt0` `x+y-lambda lt 0` `x+y lt lambda` |
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| 4. |
Let `A = {x,y,z} and B = {a,b,c,d}` . Which one of the following is not a relation from A to BA. `{(x,a), (x,c)}`B. `{(y,c), (y,d)}`C. `{(z,a), (z,d)}`D. `{(z,b), (y,b), (a,d)}` |
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Answer» Correct Answer - D Let `A = {x, y, z}` and …………. In option (D), ordered pair `(a,d) epsilon AxxB` . Thus is not a relation. |
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| 5. |
If `2le||x-2|-1|le3`, then `x` belongs to intervalA. `[-2, -1]uu[5, 6]`B. `[-4, 6]`C. `(-oo, -4]uu[6, oo]`D. `[0, 1]uu[5,6]` |
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Answer» Correct Answer - A If `2 le ||x-2|-1|le3` ……….. `2le||x-2|-1|le3` (i) `|x-2|-1|ge2 or |x-2|-1le -2` `x ge 5 , or , x le -1` (ii) `le 3` `-3 le |x-2|-1le3` `-2le |x-2|le 4` `|x-2|le4` `-2le x le 6` `(i)nn(ii) implies x epsilon [-2, -1]uu[5,6]` |
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| 6. |
Consider the number `N = 8 7 a 2 7 9 3 1 b` , where a , b are single digit whole numbers. Number of values of a + b for which N is divisible by 11 is |
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Answer» Correct Answer - C Number of value ………………. N is divisible by 11, if `(b+3+7+a+8) - (1+9+2+7) = a+b-1` is divisible bt 11 `i.e. a+b = 1 to 12` `:.` number of values of a `a+b` is 2 |
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| 7. |
Consider the number `N = 8 7 a 2 7 9 3 1 b` , where a , b are single digit whole numbers. Number of possible ordred pairs (a, b) for which N is divisible by 72 is |
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Answer» Correct Answer - B Number of possible …………. N is divisible by 72 if it is divisible by 8 and 9 both N is divisible by 8 if b = 2 N is divisible by 9 if `8+7+a+2+7+9+3+1+b` `= a+b = 37 = a+39` is divisible by 9 `:. A = 6` `:.` possible pairs `(a,b) = (6,2)` |
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| 8. |
Consider the number `N = 8 7 a 2 7 9 3 1 b` , where a , b are single digit whole numbers. The least value of a for which N is is divsible by 12 is |
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Answer» Correct Answer - A The least value ………….. N is divisible by 12, if N is divisible by 3 as well as by 4 for divisiblity by 4, we have `b = 2,6` For divisibility by 3, we have `8+7+a+2+7+9+3+1+b= a+b+37` is divisible by 3 i.e. `a+b+1` is divisible by 3 (i) when b = 2, N is divisible by 3 if `a = 0, 3, 6, 9` (ii) when b = 6, N is divisible by 3 if `a = 2, 5, 8` `:.` least value of a is 0 |
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| 9. |
If a,b,c are rational numbers `(a gt b gt c gt 0)` and quadratic equation `(a+b-2x) x ^(2) + (b+c-2a) x+ (c+a-2b)=0` has a root in the interval `(-1,0)` then which of the following statement (s) is/are correct ?A. `c+alt2b`B. both roots are rationalC. the equation `ax^(2)+2bx+c=0` have both negative real rootsD. the equation `cx^(2)+2ax+b=0` have both positive roots |
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Answer» Correct Answer - D If `a, b, c` are the ……….. `f(-1)f(0)lt 0` `(2a-b-c)(c+a-2b)lt 0` `((a-b)+(a-c))(c+a-2b)lt 0` Since `f(1) = 0` one root is 1 other : `(c+a-2b)/(a+b-2c)` using `(c+a-2b)` both roots of `{:(ax^(2)+2bx+c=0),(cx^(2)+2ax+b=0):}}` are real and negative `alpham, beta = (-2b+- sqrt(4b^(2)-4ac))/(2a)` `= (-b+- sqrt(b^(2)-4ac))/(2a)` `{:(=(-b+-sqrt(b^(2)-4ac))/(a)),(= -b+- ("less than b")):}}-ve` |
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| 10. |
Consider the number `N = 8 7 a 2 7 9 3 1 b` , where a , b are single digit whole numbers. Number of values of a + b for which N is divisible by 11 isA. `0`B. `1`C. `2`D. `3` |
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Answer» Correct Answer - C Number of values ………… N is divisible by 11 if `(b+3+7+a+8) - (1+9+2+7)=a+b-1` is divisible by 11 i.e. `a+b = 1 or 12` `:.` number of values of `a + b` is 2. |
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| 11. |
Given the relation `R= {(2,3),(3,4)}` on the set `A = {2, 3, 4}`. The number of minimum ordered pasirs to be added to R so that R is reflexive and symmetricA. `4`B. `6`C. `7`D. `5` |
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Answer» Correct Answer - D Given the relation …………. `R = {(2,2),(3,3,),(2,3),(3,2),(3,4),(4,3),(4,4)}` Extra … Pairs = 5 |
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| 12. |
If R is a relation on N as `R= {(1+ x, 1+x^2): x |
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Answer» Correct Answer - C If R is a relation …………. Given `x le 5` So `R = {(2,2), (3,5), (4,10), (5,17), (6,26)}` Domain `= {2, 3, 4, 5, 6}` Range `= {2, 5, 10, 17, 16}` |
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| 13. |
the comon difference of an a.p, whose Nth turm is an(3n+7),is |
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Answer» In the given problem, nth term is given by, an = 3n + 7. To find the common difference of the A.P., we need two consecutive terms of the A.P. So, let us find the first and the second term of the given A.P. First term (n=1) , a1 = 3(1) + 7 = 3 + 7 = 10 Second term ( n = 2 ), a2 = 3 (2) + 7 = 6 + 7 = 13 Now, the common difference of the A.P. (d) = a2 - a1 = 13 - 10 = 3 Therefore, the common difference is d = 3 . |
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| 14. |
Solution set of `(5x-1)lt (x+1)^(2)lt (7x -3)` isA. `(1, 4)`B. `[2, 4]`C. `(2, 4)`D. `(-oo, 1)uu(2, oo)` |
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Answer» Correct Answer - C Solution set of `(5x - 1)` …………. `(5x - 1) lt (x + 1)^(2) lt (7x - 3)` `implies 5x - 1lt(x+1)^(2)lt(7x-3)` `implies 5x-1lt(x+1)^(2) and (x+1)^(2)lt7x-3` `implies (x+1)^(2)-5x+1gt0 and (x+1)^(2)- 7x+3 lt0` `implies x^(2)-3x +2 gt 0 and x^(2) - 5x +4 lt 0` `implies (x-1)(x-2)lt0 and (x-1)(x-4)lt0` `implies x epsilon(-oo, 1)uu(2, oo) and 1 lt x lt 4` `implies 2 lt x lt 4` |
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| 15. |
If `x=1/(2-sqrt(3)),`find the value of `x^3-2x^2-7x+5`A. `1`B. `2`C. `3`D. `4` |
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Answer» Correct Answer - C If `x = (1)/(2-sqrt(3))`, then the ………….. We have `x = (1)/(2-sqrt(3)) = (1)/(2-sqrt(3))xx(2+sqrt(3))/(2+sqrt(3)) = (2+sqrt(3))/(2^(2)-(sqrt(3))^(2))` `= (2+sqrt(3))/(4-3) = 2 + sqrt(3)` `implies x - 2 = sqrt(3)` `implies (x-2)^(2) = (sqrt(3))^(2)` `implies x^(2)-4x+4=3` `implies x^(2)-4x+1 = 0` ............... (i) `:. x^(2)-2x^(2)-7x+5` `= x(x^(2)-4x+1)+2(x^(2)-4x+1)+3` `= 3` [using (i)] |
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| 16. |
In fig. A2.27, the charge that flows from P to Q when the switch S is closed is A. `3muC`B. `6muC`C. `9muC`D. `15muC` |
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Answer» Correct Answer - C c. The equivalent capacitance `C_(eq)` is `1/C_(eq) = 1/2 + 1/3 = 5/6` or `C_(eq) = 6/5 muF` The charge that flows from P to Q is `Q = C_(eq)V = 6/5 xx 5 = 6muC`. |
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| 17. |
If `(0.2)^((2x-3)/(x-2))gt 5` then complete solution set of values of x isA. `(5//3, 2)`B. `(3//5, 2)`C. `(-oo, -(5)/(3))uu(2,oo)`D. `((5)/(3),oo)` |
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Answer» Correct Answer - A If `(0.2)^((2x-3)/(x-2))gt` then …………. `(0.2)^((2x-3)/(x-2))gt 5` `implies 5^(-(2x-3)/(x-2))gt 5^(1)` `implies -(2x-3)/(x-2)gt 1` `implies (3x-5)/(x-2)lt0` `implies x in (5//3, 2)` |
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| 18. |
Solution set of `x^((log_(10)x)^(2)-3log_(10)x+1)gt 1000` for `x epsilon R` isA. `(10, oo)`B. `(100, oo)`C. `(1000, oo)`D. `(1, oo)` |
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Answer» Correct Answer - C Solution set of `X^((log_(10)xx)^(2)-3log_(10)x+1)` ………… Taking log on both sides base 10 `-[(log_(10)x)^(2) -3log_(10)x+1]log_(10)xgt log_(10)10^(3)` `implies (log_(10)x)^(3) - 3(log_(10)x)^(2)+log_(10)X -3 gt 0` Let `log_(10)X = t` then `t^(3) - 3t^(2)+ t- 3 gt 0` `implies (t^(2)+1)(t-3)gt0` `implies t - 3 gt 0` `implies log_(10)x gt 3 implies x gt 10^(3)` `implies x epsilon(10^(3), oo)` |
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| 19. |
18. Factorise: \( 4 p 2-9 q 2 \) |
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Answer» 4p2−9q2 ⇒(2p)2−(3q)2[a2−b2=(a+b)(a−b)] ⇒(2p+3q)(2p−3q) |
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| 20. |
Let `R_(1)= {(x,y)in RxxR :x = lambda y implies lambda in Q}` is a relation, R is set of real numbers then `R_(1)` isA. equivalenceB. only symmetricC. not symmetricD. not reflexive |
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Answer» Correct Answer - C Let `R_(1) = {(x,y)in RxxR : x = lambda y}` ………. `x = lambda x implies lambda = 1 epsilon Q` reflexive `(x)/(y)= lambda` is rotional `implies (y)/(x) = (1)/(lambdas)` may or may not be rational for example `lambda = 0` `epsilon Q` But `(1)/(lambda) = (1)/(0)cancelepsilon Q` so not symmetric |
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| 21. |
Initially, switch S is connected to position 1 for a long time . The net amount of heat generated in the circuit after it is shifted to position 2 is . A. `C/2 (epsilon_1 + epsilon_2)epsilon_2`B. `C(epsilon_1+epsilon_2)epsilon_2`C. `C/2 (epsilon_1 + epsilon_2)^2`D. `C(epsilon_1 + epsilon_2)^2` |
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Answer» Correct Answer - C c. `U_i = 1/2 C epsilon_(1)^2` `U_f = 1/2 C epsilon_(2)^(2) , Delta U = 1/2 C (epsilon_(2)^(2) - epsilon_(1)^(2))` `Q_("in") = + Cepsilon_1, Q_f = -Cepsilon_2, DeltaQ = abs(Q_f-Q_i) = C (epsilon_2+epsilon_1)` Work done by battery `W_b = epsilon_2 DeltaQ = C (epsilon_2+epsilon_1)epsilon_2` Heat generated `= W_b - DeltaU` `= C epsilon_(2)^(2) + Cepsilon_1epsilon_2 - 1/2 C (epsilon(2)^(2) - epsilon_(1)^(2))` `= 1/2 C (epsilon_(2)^(2) + epsilon_(1)^(2) + 2epsilon_1epsilon_2) = 1/2 C(epsilon_1 + epsilon_2)^2` . |
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| 22. |
(a)State Kirchhoff's rules. (b)Use these rules to write the expressions for the currents I1, I2 and I3 in the circuit diagram shown. |
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Answer» Refers to the below link http://bit.ly/2XriIX8 |
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| 23. |
The potential energy of a `4kg` particle free to move along the x-axis varies with x according to following relationship : `U(x) = ((x^(3))/(3)-(5x^(2))/(2)+6x+3)` Joules, where `x` is in meters. If the total mechanical energy of the particle is `25.5` Joules, then the maximum speed of the particle is `x m//s`, find `x` |
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Answer» Correct Answer - 3 The potential ………….. `U(x) = (x^(3))/(3)-(5x^(2))/(2)+6x+3` `(dU)/(dx) = x^(2) - 5x+6=0` `x = 2, 3` `(d^(2)U)/(dx^(2)) = 2x -5` At `x = 2m, (d^(2)U)/(dx^(2)) = -1`, which is a negative value this `U` is maximum At `x = 3 m, (d^(2)U)/(dx^(2)) = +1`, which is a positive value thus `U` is minimum `U_(min) = U(x=3)=7.5J` `T.M.E = 25.5J` `K_(max)+U_(min)= 25.5J` `K_(max) = 25.5-7.5=18J` `(1)/(2)(4)V^(2)max=18` `implies V_(max)^(2) = 9 implies V_(max) = 3m//s` |
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| 24. |
Initialy spring is in the natural length and blocks `A & B` are at rest. Find maximum value of constant force `F` that can be applied on `B` such that block `A` remains at rest. `(g = 10 m//s^(2))` (given answer in Newton) |
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Answer» Correct Answer - 3 Initially spring …………….. Values of `mu mg` for A and B are `2N & 2N` Worck energy theorm on `B` gives `Fx-2x-(K//2)x^(2)=0` `F=2+kx//2` ……(i) For equilibrium of `A kx = mu mg = 2` so `F = 2+1=3N` |
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| 25. |
A particle of mass M is moving in a circular path of radius 2m. Its speed depends on the distance covered by the particle from the hegining according to the relation c = ks, where k is a positive constant and s is the distance covered. The power of force acting on teh particle when the particle has covered half of the circular path will be :A. `pi^(2)k^(2)M`B. `2pi^(2)k^(3)M`C. `4pi^(2)k^(3)M`D. `8pi^(2)k^(2)M` |
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Answer» Correct Answer - C P = Fv `S = pi R` `v = ks rArr v = k.pi R` `a = v (dv)/(ds) = ks.k = k^(2)s` `s = piR` `a = k^(2).piR rArr F = mk^(2). pi R` `P = mk^(2) pi R . kpi R = mk^(3) pi^(2)R^(2)` `M = 4 pi^(2)k^(3)m` |
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| 26. |
State two ways to prevent the rusting of iron. |
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Answer» (i) Corrosion of metals can be prevented by coating the metal surface with a thin layer of paint, varnish or grease. (ii) By galvanisation. |
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| 27. |
What are the ions present in NaCl? |
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Answer» Na+ (cation) and Cl– (anion) |
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| 28. |
What is amphoteric oxide? Give two examples of amphoteric oxides. |
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Answer» Those oxide which can behave as acid as well as base. Ex. ZnO, Al2O3 etc. |
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| 29. |
A mixture of oxygen and ethyne is burnt for welding. Explain why a mixture of ethyne and air is not used. |
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Answer» Because air contains large proportion of nitrogen which do not support for combustion |
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| 30. |
Write the names of the following compounds. |
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Answer» (i) Pent-1-yne (ii) propanal |
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| 31. |
What is homologous series? Explain with examples |
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Answer» Homologous series may be defined as a series of similarly constituted compounds in which the members possess similar chemical characteristics and the two consecutive members differ in their molecular formula by – CH2. e.g Homologous series of alkanes : General formula : CnH2n+2
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| 32. |
Name two hydrocarbons which give addition reactions. |
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Answer» Ethene and Ethyne (Unsaturated hydrocarbon) |
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| 33. |
Why are the heating elements of electric toasters and electric irons made of an alloy rather than a pure metal ? |
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Answer» The heating elements of electric toasters and electric irons made of an alloy rather than a pure metal because they have high melting point and don’t oxidize at high temperatures. |
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| 34. |
Bio gas has 55-70%_______, 30-40% _______ and traces of hydrogen sulphide. (a) oxygen, nitrogen (b) carbon, methane (c) methane, oxygen (d) methane, nitrogen |
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Answer» Correct answer is (d) methane, nitrogen |
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| 35. |
Which device is used to store electric energy temporarily? (a) Capacitor (b) Transistor (c) Resistor (d) Thermistor |
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Answer» Correct answer is (a) Capacitor |
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| 36. |
“Who ___ this picture?” the teacher asks. A) is drawn B) drawn C) have drawn D) draws E) has drawn |
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Answer» Correct option is E) has drawn |
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| 37. |
Explain the evolution of Paper money and the advantages of Banking money. |
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Answer» The metallic coins were unsafe to carry from one place to another. Therefore, traders began to carry the written documents issued by well known financiers as evidence of the quantity of money at their command. The written documents were not actual money, but were accepted and exchanged for money. When such documents were issued by governments, they were called as ‘promissory notes’ or currency. Later on the central banks established by the governments started printing notes that had the guarantee of the government. This paper money became legal tender that is the legally acceptable money. No individual can refuse the legal tender in that respective country. The legal tender is called as Rupee in India; Dollar in the USA; Pound in England; Euro in Europe; Yen in Japan; Yuan in China, etc. Advantages of Banking money: As trade and commerce flourished bankers started issuing instruments for still easy transaction. Cheques, drafts, deposit (Credit) receipts etc., thus, came to be used as money. These help inn transactions as well as transfer of money between persons and places. |
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| 38. |
_________ are used to trap the solar energy received and convert it into a usable form of energy like electricity. (a) Solar Panels (b) Magnetic strips (c) Metals panels (d) Carbon Fiber strips |
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Answer» Correct answer is (a) Solar Panels |
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| 39. |
What is ‘Public expenditure’ and ‘Public revenue’? |
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Answer» The expenditure incurred by public authorities like central, state and local governments to satisfy the collective social wants of the people is known as public expenditure. It is incurred on various activities for the welfare of people and also for the economic development, especially in developing countries. ‘Public Revenue: ‘Public Revenue’ is the income mobilized by the Government for purposes of financing Government activities. |
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| 40. |
A particle with a charge of -1.24 x 10 8C is moving with an instantaneous velocity of v (4.19 x 10ʻm/s)i + (-3.85 x 104 m/ s)j. What is the force exerted on this particle by a magnetic field B= (1.40T)i. |
| Answer» 6.66624×10^12 Newton | |
| 41. |
Balance the following chemical equations:(a) HNO3 + Ca(OH)2 -------> Ca(NO3)2 + H2O(b) NaOH + H2SO4 --------> Na2SO4 + H2O(c) NaCl + AgNO3 -------> AgCl + NaNO3(d) BaCl2 + H2SO4 ------> BaSO4 + HCI |
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Answer» (a) 2HNO3 + Ca(OH)2 ------> Ca(NO3)2 + 2H2O |
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| 42. |
Give suitable reason for the following statements:(i) We feel burning sensation in the stomach when we overeat.(ii) The crystals of washing soda change to white powder on exposure to air.(iii) An aqueous solution of sodium chloride is neutral but an aqueous solution of sodium carbonate is basic. |
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Answer» (i) When we overeat excess of acid is produced in the stomach which causes burning sensation. |
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| 43. |
If a capacitor is rated for 200V dc, what is its effective ac working voltage? A. 50 V B. 100 V C. 200 V D. 400 V |
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Answer» If a capacitor is rated for 200V dc, what is its effective ac working voltage 200 V. |
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| 44. |
A projectile on its path gets divide into two pieces at its highest point what is true?a-Momentum increasesb-Momentum decreasesc-Kinetic energy increasesd-Kinetic energy decreases |
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Answer» Option (c) is correct. Explanation: The two pieces fly in opposite directions in accordance with the law of conservation of momentum. The energy of explosion will add to the kinetic energy. Hence, the Kinetic energy will increase. At highest point,if the particle gets converted into 2 parts then it's potential energy is converted into Kinetic energy of particles.So,Kinetic energy increases. |
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| 45. |
The type of energy possessed by a simple pendulum when it is at the mean position? |
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Answer» Gravitational potential energy(mean position) |
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| 46. |
A ball is dropped from certain height and another ball is projected horizontally from the same point.Correct statement?a-Both hit the ground at the same velocityb-Both hit the ground at the same speedc-The change of velocity during the path for both the balls is the samed-The change of speed during the path for both the balls is the same |
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Answer» Option [c] is correct For 1st particle final velocity have only vertical component of velocity. For 2nd particle, it will have horizontal as well as vertical component of velocity but the change in velocity is same for both particles. The change in velocity is \(\sqrt{2gh}\) in both the cases. Hence option (c) is correct i.e The change of velocity during the path for both the balls is the same |
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| 47. |
The open-circuit voltage at the terminal of load RL is 60V. Under the condition of maximum power transfer, the load voltage will be: A. 60 V B. 15 V C. 30V D. 20 V |
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Answer» The open-circuit voltage at the terminal of load RL is 60V. Under the condition of maximum power transfer, the load voltage will be 30V. |
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| 48. |
“The number of saving bank account holders is increasing Give reasons. |
Answer»
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| 49. |
What are the vital characteristics required to be an entrepreneur. |
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Answer» The characteristics of an Entrepreneur are :
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| 50. |
The service of B.R. Ambedkar in drafting the Indian Constitution is indispensable justify? |
Answer»
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