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41

NIELIT 2019 Feb Scientist C - Section D: 8
If $x=\cos1^{\circ} \cdot \cos2^{\circ} \cdot \cos3^{\circ}\dots\cos89^{\circ}$ and $y=\cos2^{\circ}\cos6^{\circ}\cos10^{\circ}\dots\cos86^{\circ}$ then what the integer is nearest to $\dfrac{2}{7}\log _{2} \left( \dfrac{y}{x}\right )$is: $19$ $17$ $15$ $21$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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42

NIELIT 2019 Feb Scientist C - Section D: 15
The simplified form of $\left[ \left ( \left( \dfrac{a+1}{a-1}\right)^2+3 \right)\div \left( \left( \dfrac{a-1}{a+1}\right)^2+3\right) \right] \div \left [\left( \dfrac{a^{3}+1}{a^{3}-1}\right)-\dfrac{2a}{a-1} \right]$ is: $a-1$ $1-a$ $-1$ $1$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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43

NIELIT 2019 Feb Scientist C - Section D: 13
Two persons start walking on a road that diverge at an angle of $120^{\circ}$. If they walk at the rate of $3$km/h and $2$km/h respectively. Find the distance between them after $4$hrs. $4\sqrt{19}$ km $5$ km $7$ km $8\sqrt{19}$ km

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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44

NIELIT 2019 Feb Scientist C - Section D: 12
A conical tent is to accommodate $10$ persons. Each person must have $6m^{2}$ space to sit and $30m^{3}$ of air to breath. What will be height of cone? $37.5$ m $150$ m $75$ m $15$ m

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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45

NIELIT 2019 Feb Scientist C - Section D: 14
The sum of the squares of the fifth and the eleventh term of an AP is $3$ and the product of the second and fourteenth term is equal to $x$. Find the product of the first and fifteenth term of an AP. $\dfrac{(58x-39)}{45} \\$ $\dfrac{(98x-39)}{72} \\$ $\dfrac{(116x-39)}{90} \\$ $\dfrac{(98x-39)}{90}$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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46

NIELIT 2019 Feb Scientist C - Section D: 16
If $cosec\theta-\sin\theta=1$ and $\sec\theta-\cos\theta=m$, then $l^{2}m^{2}(l^{2}+m^{2}+3)$ equals to: $1$ $2$ $2 \sin\theta$ $\sin\theta \cos\theta$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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47

NIELIT 2019 Feb Scientist C - Section D: 17
If ${m_1}$ and ${m_2}$ are the roots of equation $x^{2}+(\sqrt{3}+2)x+\sqrt{3}-1=0$ then area of the triangle formed by the lines $y={m_1}x, \: \: y={m_2}x, \: \: y=c$ is: $\bigg(\dfrac{\sqrt{33}+\sqrt{11}}{4}\bigg) c^{2} $ ... $\bigg (\dfrac{\sqrt{33}+\sqrt{10}}{4} \bigg ) c^{2}$ $\bigg( \dfrac{\sqrt{33}+\sqrt{21}}{4} \bigg) c^{3}$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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48

NIELIT 2019 Feb Scientist C - Section D: 18
If $8v-3u=5uv \: \: \& \: \: 6v-5u=-2uv$ then $31u+46v$ is: $44$ $42$ $33$ $55$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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49

NIELIT 2019 Feb Scientist C - Section D: 19
If $x=\dfrac{\sqrt{10}+\sqrt{2}}{2}, \: \: y=\dfrac{\sqrt{10}-\sqrt{2}}{2}$ then the value of $\log _{2}(x^{2}+xy+y^{2})$ is: $0$ $1$ $2$ $3$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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50

NIELIT 2019 Feb Scientist C - Section D: 23
Rs.$6500$ were divided among a certain number of persons. If there had been $15$ more persons, each would have got $Rs.30$ less. Find the original number of persons. $50$ $60$ $45$ $55$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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51

NIELIT 2019 Feb Scientist C - Section D: 22
If $S_1,S_2,S_3,\dots\dots,S_m$ are the sum of first $n$ terms of $m$ arithmetic progressions, whose first terms are $1,4,9,16,\dots,m^{2}$ and common differences are $1,2,3,4,\dots m$ respectively, then the value of $S_1+S_2+S_3+\dots \dots +S_m$ ... $\dfrac{mn(2m+1)}{3} \\$ $\dfrac{mn[3(m+1)+1]}{6} \\$ $\dfrac{mn(m+1)(4m+3n-1)}{12}$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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52

NIELIT 2019 Feb Scientist C - Section D: 21
Find the number of numbers between $300$ to $400$ (both included) that are not divisible by $2,3,4$ and $5$ $50$ $33$ $26$ $17$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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53

NIELIT 2019 Feb Scientist C - Section D: 20
If a clock strikes once at one o’clock, twice at two o’clock and twelve times at $12$ o’clock and again once at one o’clock and so on, How many times will the bell be struck in the course of $2$ days? $156$ $312$ $78$ $288$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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54

NIELIT 2019 Feb Scientist C - Section D: 28
The price of an article was increased by $p\%$, later the new price was decreased by $p\%$. If the last price was Re. $1$ then the original price was: $\dfrac{1-p^{2}}{200}\\$ $\dfrac{\sqrt{1-p^{2}}}{100} \\$ $1-\dfrac{p^{2}}{10,000-p^{2}} \\$ $\dfrac{10,000}{10,000-p^{2}}$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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55

NIELIT 2019 Feb Scientist C - Section D: 27
In a bangle shop. If the shopkeeper displays the bangles in the form of a square then he is left with $38$ bangles. If he wanted to increase the size of square by one bangle each side of the square he found that $25$ bangles fall ... completing the square. The actual number of bangles which he had with him the shop was_________. $1690$ $999$ $538$ $1000$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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56

NIELIT 2019 Feb Scientist C - Section D: 26
$A,B,C$ are three towns forming a triangle. A man has to walk from one town to next town, then ride to the next town then again drive towards his starting point. He can walk,ride,drive a km in $a,b,c$ minutes respectively. If he starts ... $c+b-a$ hrs. The length of the triangle is: (assume the motion in anticlockwise direction) $60a$ $50a$ $40a$ $65a$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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57

NIELIT 2019 Feb Scientist C - Section D: 25
If $x+y+z=2, \:\: xy+yz+zx=-1$ then the value of $x^{3}+y^{3}+z^{3}$ is: $20$ $16$ $8$ $0$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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58

NIELIT 2019 Feb Scientist C - Section D: 24
A cylindrical box of radius $5$ cm contains $10$ solid spherical balls each of radius $5$ cm. If the topmost ball touches the upper cover of the box, then the volume of the empty space in the box is: $\dfrac{2500\pi}{3}$ cubic cm $500\pi$ cubic cm $2500\pi$ cubic cm $\dfrac{5000\pi}{3}$ cubic cm

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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59

NIELIT 2019 Feb Scientist C - Section D: 30
A charitable trust donates $28$ different books of Maths, $16$ different books of science and $12$ different books of social science to poor students. Each student is given maximum number of books of only one subject of their interest and each student got equal number of books. Find the total number of students who got books. $14$ $10$ $12$ $15$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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60

NIELIT 2019 Feb Scientist C - Section D: 29
If $(-4,0),(1,-1)$ are two vertices of a triangle whose area is $4$ Sq units then its third vertex lies on: $y=x$ $5x+y+12=0$ $x+5y-4=0$ $x-5y+4=0$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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61

NIELIT 2019 Feb Scientist C - Section C: 3
The factors of $(x^{2}+4y^{2}+4y-4xy-2x-8)$ are: $(x-2y-4)(x-2y+2)$ $(x-y+2)(x-4y-4)$ $(x+2y-4)(x+2y+2)$ None of these

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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62

NIELIT 2019 Feb Scientist C - Section C: 1
If $\log _{e}x+\log _{e}(1+x)=0,$ then: $x^{2}+x-1=0$ $x^{2}+x+1=0$ $x^{2}+x-e=0$ $x^{2}+x+e=0$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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63

NIELIT 2019 Feb Scientist C - Section C: 2
If the ratio of the areas of two squares is $9:1$, the ratios of their perimeters is: $9:1$ $3:1$ $3:4$ $1:3$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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64

NIELIT 2019 Feb Scientist C - Section C: 6
In a class consisting of $100$ students, $20$ know English and $20$ do not know Hindi and $10$ know neither English nor Hindi. The number of students knowing both Hindi and English is: $5$ $10$ $15$ $20$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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65

NIELIT 2019 Feb Scientist C - Section C: 4
An agent buys a T.V set listed at $\text₹10,000$ and gets $10\%$ and $20\%$ successive discounts. He spends $10\%$ of his C.P. on transport. At what price(in rupees) should he sell the T.V. set to earn a profit of $10\%$? $8,692$ $8,702$ $8,712$ $8,722$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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66

NIELIT 2019 Feb Scientist C - Section C: 5
By which one of the following should we multiply $152207$ so that the product is $11111111$? $53$ $63$ $73$ $83$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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67

NIELIT 2019 Feb Scientist C - Section C: 7
$A$ and $B$ start a business with initial investments in the ratio $12:11$ and their annual profits were in the ratio $4:1$. If $A$ invested the money for $11$ months, $B$ invested for: $3$ months $4$ months $\dfrac{11}{3}$ months $6$ months

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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68

NIELIT 2019 Feb Scientist C - Section C: 9
Four milkmen rented a pasture. $A$ grazed $18$ cows for $4$ months, $B$ $25$ cows for $2$ months, $C$ $28$ cows for $5$ months and $D$ $21$ cows for $3$ months. If $A$’s share of rent in $\text₹360$, the total rent of the field (in rupees) is: $1,500$ $1,600$ $1,625$ $1,650$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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69

NIELIT 2019 Feb Scientist C - Section C: 11
For a sphere of radius $10$ cm, the numerical value of the surface area is how many percent of the numerical value of its volume? $26.5\%$ $24\%$ $30\%$ $45\%$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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70

NIELIT 2019 Feb Scientist C - Section C: 8
A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of $2$ kmph and $4$ kmph and passes them completely in $9$ and $10$ seconds respectively. The length of the train(in metres) is: $45$ $54$ $50$ $72$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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71

NIELIT 2019 Feb Scientist C - Section C: 10
A sum of money amounts to $₹6,690$ after $3$ years and to $₹10,035$ after $6$ years on compound interest. The sum is: $₹4,400$ $₹4,460$ $₹4,520$ $₹4,445$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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72

NIELIT 2019 Feb Scientist C - Section C: 16
A can contains a mixture of two liquids $\text{A}$ and $\text{B}$ in proportion $7:5$. When $9$ litres of mixture are drawn off and the can is filled with $\text{B}$, the proportion of $\text{A}$ and $\text{B}$ becomes $7:9$. How many litres of liquid $\text{A}$ was contained by the can initially? $25$ $10$ $20$ $21$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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73

NIELIT 2019 Feb Scientist C - Section C: 14
Kamla got married $6$ years ago. Today her age is $1\dfrac{1}{4}$ times of her age at the time of marriage. Her son’s age is $\dfrac{1}{10}$ times of her age. Her son’s age is : $2$ years $3$ years $4$ years $5$ years

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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74

NIELIT 2019 Feb Scientist C - Section C: 13
$A$ and $B$ can complete a task in $30$ days when working together. After $A$ and $B$ have been working together for $11$ days, $B$ is called away and $A$, himself completes the task in the next $28$ days. Had $A$ been working alone, the number of days ... would have been: $\dfrac{379}{9} \\$ $\dfrac{840}{19} \\$ $\dfrac{520}{11} \\$ $\dfrac{590}{11}$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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75

NIELIT 2019 Feb Scientist C - Section C: 15
Tarun bought a T.V with $20\%$ discount on the labelled price. If he had bought it with $25\%$ discount, he would have saved $₹500$. At what price did he buy the T.V.? $₹8,000$ $₹10,000$ $₹12,000$ $₹16,000$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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76

NIELIT 2019 Feb Scientist C - Section C: 12
About the number of pairs which have $16$ as their H.C.F. and $136$ as their L.C.M., we can definitely say that: Only one such pair exists Only two such pairs exist Many such pairs exist No such pair exists

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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77

NIELIT 2019 Feb Scientist C - Section C: 17
A man invests an amount of $\text₹15,860$ in the names of his three sons $A,B$ and $C$ in such a way that they get the same interest after $2,3$ and $4$ years respectively. If the rate of simple interest is $5\%$ ... $\dfrac{1}{10} : \dfrac{1}{15}:\dfrac{1}{20}$ $\dfrac{1}{110}:\frac{1}{115}:\frac{1}{120}$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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78

NIELIT 2019 Feb Scientist C - Section C: 19
If $a^{x}=b, b^{y}=c$ and $c^{z}=a$, then $xyz$ equals: $abc$ $\dfrac{1}{abc}$ $1$ None

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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79

NIELIT 2019 Feb Scientist C - Section C: 18
On dividing $50$ into two parts such that the sum of their reciprocals is $\dfrac{1}{12}$, we get the parts as: $20,30$ $24,26$ $28,22$ $36,14$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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80

NIELIT 2019 Feb Scientist C - Section C: 20
$A$ has to pay $\text ₹220$ to $B$ after $1$ year. $B$ asks $A$ to pay $\text ₹110$ in cash and defer the payment of $\text ₹110$ for $2$ years. $A$ agrees to it. Counting, the rate of interest at $10\%$ per annum in this new mode of payment: There is no gain or loss to anyone $A$ gains $\text ₹7.34$ $A$ loses $\text ₹7.34$ $A$ gains $\text ₹11$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

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