# Recent questions tagged quantitative-aptitude 41
$\left [\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^{2}}+\frac{4}{1+x^{4}}+\frac{8}{1+x^{8}} \right ]$ equal to : $1$ $0$ $\frac{8}{1-x^{8}}$ $\frac{16}{1-x^{16}}$
42
The image of the point $\left (3, 8 \right)$ in the line $x+3y=7$ is : $\left (1, 4 \right)$ $\left (4, 1 \right)$ $\left (-1, -4 \right)$ $\left (-4, -1 \right)$
43
Find the value of $x$ satisfying : $\log_{10} \left (2^{x}+x-41 \right)=x \left (1-\log_{10}5 \right)$ $40$ $41$ $-41$ $0$
44
If $5$ spiders can catch $5$ files in $5$ minutes. How many files can $100$ spiders catch in $100$ minutes : $100$ $1000$ $500$ $2000$
45
The line $x+y=4$ divides the line joining $\text{(-1,1) & (5,7)}$ in the ratio $\lambda : 1$ then the value of $\lambda$ is: $2$ $3$ $\dfrac{1}{2}$ $1$
46
Determine $a+b$ such that the following system of equations: $2x-(a-4)y=2b+1 \text{ and }4x-(a-1)y=5b-1$ infinite solutions. $11$ $9$ $10$ $8$
47
The minute hand is $10$ cm long. Find the area of the face of the clock described by the minute hand between $9$ a.m and $9:35$ a.m. ${183.3\ cm^{2}}$ ${366.6\ cm^{2}}$ ${244.4\ cm^{2}}$ ${188.39\ cm^{2}}$
1 vote
48
If $\theta$ is an acute angle and $\tan\theta+\cot\theta =2$, Find the value of $\tan ^{7}\theta +\cot ^{7}\theta$. $-2$ $1$ $2$ $0$
1 vote
49
In a triangle $XYZ$, $P$ and $Q$ are points on ${XY,XZ}$ respectively such that $XP=2PY$, $XQ=2QZ$, then the ratio, of area of $\triangle XPQ$ and area of $\triangle XYZ$ is: $4:9$ $2:3$ $3:2$ $9:4$
50
The value of $\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+ \dots \dots \dots+\dfrac{1}{90}$ is: $\dfrac{1}{5}\\$ $\dfrac{2}{5} \\$ $\dfrac{3}{5} \\$ $1$
51
Which of the following statement is false? ... Statement(iii) Statement(ii) Statement(iv) Statement(i)
52
The expressions $\dfrac{\tan A}{1-\cot A}+\dfrac{\cot A}{1-\tan A}$ can be written as: $\sin A \ \cos A+1$ $\sec A \ cosec A+1$ $\tan A+ \cot A+1$ $\sec A +cosec A$
53
Let $(x_{1},4),(-2,y_{1})$ lies on the line joining the points $(2,-1),(5,-3)$ then the point $P(x_{1},y_{1})$ lies on the line: $6(x+y)-25=0$ $2x+6y+1=0$ $2x+3y-6=0$ $6(x+y)+25=0$
54
sum of roots of the equation $\dfrac{3x^{3}-x^{2}+x-1}{3x^{3}-x^{2}-x+1}=\dfrac{4x^{3}-7x^{2}+x+1}{4x^{3}+7x^{2}-x-1}$ is : $0$ $1$ $-1$ $2$
55
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: $19$ $17$ $15$ $21$
56
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
57
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
58
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. $\dfrac{(58x-39)}{45} \\$ $\dfrac{(98x-39)}{72} \\$ $\dfrac{(116x-39)}{90} \\$ $\dfrac{(98x-39)}{90}$
1 vote
59
If $cosec\theta-\sin\theta=1$ and $\sec\theta-\cos\theta=m$, then $l^{2}m^{2}(l^{2}+m^{2}+3)$ equals to: $1$ $2$ $2 \sin\theta$ $\sin\theta \cos\theta$
60
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: $\bigg(\dfrac{\sqrt{33}+\sqrt{11}}{4}\bigg) c^{2}$ $\bigg( \dfrac{\sqrt{32}+\sqrt{11}}{16}\bigg ) c$ $\bigg (\dfrac{\sqrt{33}+\sqrt{10}}{4} \bigg ) c^{2}$ $\bigg( \dfrac{\sqrt{33}+\sqrt{21}}{4} \bigg) c^{3}$
61
If $8v-3u=5uv \: \: \& \: \: 6v-5u=-2uv$ then $31u+46v$ is: $44$ $42$ $33$ $55$
1 vote
62
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: $0$ $1$ $2$ $3$
63
$₹6500/-$ were divided among a certain number of persons. If there had been $15$ more persons, each would have got $₹30/-$ less. Find the original number of persons. $50$ $60$ $45$ $55$
64
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 $S_1+S_2+S_3+\dots \dots +S_m$ is : $\dfrac{mn(m+1)}{2} \\$ $\dfrac{mn(2m+1)}{3} \\$ $\dfrac{mn[3(m+1)+1]}{6} \\$ $\dfrac{mn(m+1)(4m+3n-1)}{12}$
65
Find the number of numbers between $300$ to $400$ (both included) that are not divisible by $2,3,4$ and $5$ $50$ $33$ $26$ $17$
66
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? $156$ $312$ $78$ $288$
67
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: $\dfrac{1-p^{2}}{200}\\$ $\dfrac{\sqrt{1-p^{2}}}{100} \\$ $1-\dfrac{p^{2}}{10,000-p^{2}} \\$ $\dfrac{10,000}{10,000-p^{2}}$
68
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 short of in completing the square. The actual number of bangles which he had with him the shop was_________. $1690$ $999$ $538$ $1000$
69
$A,B,C$ 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 from $B$, he takes $a-b+c$ ... from $A$ he takes $c+b-a$ hrs. The length of the triangle is: (assume the motion in anticlockwise direction) $60a$ $50a$ $40a$ $65a$
70
If $x+y+z=2, \:\: xy+yz+zx=-1$ then the value of $x^{3}+y^{3}+z^{3}$ is: $20$ $16$ $8$ $0$
71
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
72
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. $14$ $10$ $12$ $15$
73
If $(-4,0),(1,-1)$ are two vertices of a triangle whose area is $4$ Sq units then its third vertex lies on: $y=x$ $5x+y+12=0$ $x+5y-4=0$ $x-5y+4=0$
74
An alloy contains copper and zinc in the ratio $5:3$ and another contains copper and tin in the ratio $8:5.$ If equal weights of the two are melted together to form a $3^{rd}$ alloy, find the weight of tin per kg in the new alloy. $40/129$ $5/13$ $5/26$ $28/5$
1 vote
75
Aamir and Birju can cut $5000\;\text{g}$ of wood in $20$ min. Birju and Charles can cut $5000\;\text{g}$ of wood in $40$ min. Charles and Aamir cut $5\;\text{kg}$ of wood in $30$ min. How much time Charles will take to cut $5\;\text{kg}$ wood alone? $120$ min $48$ min $240$ min $120/7$ min
1 vote
76
The difference between the compound interest and the simple interest earned at the end of $3^{rd}$ year on a sum of money at a rate of $10\%$ per annum is Rs. $77.5.$ What is the sum? Rs. $3,500$ Rs. $2,500$ Rs. $3,000$ Rs. $2,000$
77
Line $AB$ is $24$ metres in length and is tangent to the inner one of the two concentric circles at point $C.$ Points $A$ and $B$ lie on the circumference of the outer circle. It is known that the radii of the two circles are integers. The radius of the outer circle is $13$ m $5$ m $7$ m $4$ m
$x$ is a whole number. If the only common factors of $x$ and $x2$ are $1$ and $x,$ then $x$ is ________. $1$ a perfect square an odd number a prime number
A tank can be filled by one tap in $10$ minutes and by another in $30$ minutes. Both the taps are kept open for $5$ minutes and then the first one is shut off. In how many minutes more is the tank completely filled? $5$ $7.5$ $10$ $12$
Assume that a sum of money is divided equally among $n$ girls. Each girl will receive $\$60.$If another girl is added to the group and the sum is divided equally among all the girls, each child girl gets a$\$50$ share. What is the sum of money? $\$3000\$300$ $\$110\$10$