# Recent questions tagged nielit2019feb-scientistc

41

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 ...

42

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...

43

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...

44

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$75$...

45

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...

46

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$

47

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 $y={m_1}x, \: \: y={m_2}x, \: \: y=c$ i...

48

If $8v-3u=5uv \: \: \& \: \: 6v-5u=-2uv$ then $31u+46v$ is:$44$$42$$33$$55$

49

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$

50

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$$...

51

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...

52

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$

53

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 bel...

54

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...

55

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 ban...

56

$A,B,C$ 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 ...

57

If $x+y+z=2, \:\: xy+yz+zx=-1$ then the value of $x^{3}+y^{3}+z^{3}$ is:$20$$16$$8$$0$

58

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 t...

59

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 giv...

60

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$

61

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

62

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$

63

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$

64

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 a...

65

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) sh...

66

By which one of the following should we multiply $152207$ so that the product is $11111111$?$53$$63$$73$$83$

67

$A$ 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...

68

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 $A$’...

69

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\%$

70

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 $9$ an...

71

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$

72

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...

73

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�...

74

$A$ 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 comple...

75

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.?$...

76

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 existsOnly two such pairs existMany suc...

77

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 respectiv...

78

If $a^{x}=b, b^{y}=c$ and $c^{z}=a$, then $xyz$ equals:$abc$$\dfrac{1}{abc}$$1$None

79

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$

80

$A$ 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. C...