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1 votes
1 answer
2041
CAT 2019 Set-2 | Question: 80
Let $a_{1},a_{2}\dots$ be integers such that $a_{1}-a_{2}+a_{3}-a_{4}+\dots+(-1)^{n-1}a_{n}=n$, for all $n\geq 1$ Then $a_{51}+a_{52}+\dots+a_{1023}$ equals $-1$ $10$ $0$ $1$
Let $a_{1},a_{2}\dots$ be integers such that $a_{1}-a_{2}+a_{3}-a_{4}+\dots+(-1)^{n-1}a_{n}=n$, for all $n\geq 1$ Then $a_{51}+a_{52}+\dots+a_{1023}$ equals$-1$$10$$0$$1$...
1 votes
1 answer
2043
CAT 2019 Set-2 | Question: 82
In a triangle $\text{ABC}$, medians $\text{AD}$ and $\text{BE}$ are perpendicular to each other, and have lengths $12$ cm and $9$ cm, respectively. Then, the area of triangle $\text{ABC}$, in sq cm. is $68$ $72$ $78$ $80$
In a triangle $\text{ABC}$, medians $\text{AD}$ and $\text{BE}$ are perpendicular to each other, and have lengths $12$ cm and $9$ cm, respectively. Then, the area of tria...
4 votes
1 answer
2046
CAT 2019 Set-2 | Question: 85
How many factors $2^{4}\times3^{5}\times10^{4}$ are perfect squares which are greater than $1$ _______
How many factors $2^{4}\times3^{5}\times10^{4}$ are perfect squares which are greater than $1$ _______
1 votes
1 answer
2047
CAT 2019 Set-2 | Question: 86
What is the largest positive integer $n$ such that $\frac{n^{2}+7n+12}{n^{2}-n-12}$ is also a positive integer? $8$ $12$ $16$ $6$
What is the largest positive integer $n$ such that $\frac{n^{2}+7n+12}{n^{2}-n-12}$ is also a positive integer?$8$$12$$16$$6$
1 votes
1 answer
2048
CAT 2019 Set-2 | Question: 87
Let $a,b,x,y$ be real numbers such that $a^{2}+b^{2}=25,x^{2}+y^{2}=169$, and $ax+by=65$. If $k=ay-bx$, then $k=0$ $0< k\leq \frac{5}{13}$ $k=\frac{5}{13}$ $k> \frac{5}{13}$
Let $a,b,x,y$ be real numbers such that $a^{2}+b^{2}=25,x^{2}+y^{2}=169$, and $ax+by=65$. If $k=ay-bx$, then$k=0$$0< k\leq \frac{5}{13}$$k=\frac{5}{13}$$k \frac{5}{13}$
1 votes
1 answer
2049
CAT 2019 Set-2 | Question: 88
Let $A$ be a real number. Then the roots of the equation $x^{2}-4x-\log _{2}A=0$ are real and distinct if and only if $A> \frac{1}{16}$ $A> \frac{1}{8}$ $A< \frac{1}{16}$ $A< \frac{1}{8}$
Let $A$ be a real number. Then the roots of the equation $x^{2}-4x-\log _{2}A=0$ are real and distinct if and only if$A \frac{1}{16}$$A \frac{1}{8}$$A< \frac{1}{16}$$A< \...
1 votes
1 answer
2052
CAT 2019 Set-2 | Question: 91
John gets Rs $57$ per hour of regular work and Rs $114$ per hour of overtime work. He works altogether $172$ hours and his income from overtime hours is $15\%$ of his income from regular hours. Then, for how many hours did he work overtime _________
John gets Rs $57$ per hour of regular work and Rs $114$ per hour of overtime work. He works altogether $172$ hours and his income from overtime hours is $15\%$ of his inc...
1 votes
1 answer
2054
CAT 2019 Set-2 | Question: 93
Let $\text{ABC}$ be a right-angled triangle with hypotenuse $\text{BC}$ of length $20$ cm. If $\text{AP}$ is perpendicular on $\text{BC}$, then the maximum possible length of $\text{AP}$, in cm, is $10$ $6\sqrt{2}$ $8\sqrt{2}$ $5$
Let $\text{ABC}$ be a right-angled triangle with hypotenuse $\text{BC}$ of length $20$ cm. If $\text{AP}$ is perpendicular on $\text{BC}$, then the maximum possible lengt...
2 votes
1 answer
2055
CAT 2019 Set-2 | Question: 94
The base of a regular pyramid is a square and each of the other four sides is an equilateral triangle, length of each side being $20$ cm. The vertical height of the pyramid, in cm, is $8\sqrt{3}$ $12$ $5\sqrt{5}$ $10\sqrt{2}$
The base of a regular pyramid is a square and each of the other four sides is an equilateral triangle, length of each side being $20$ cm. The vertical height of the pyram...
1 votes
1 answer
2056
CAT 2019 Set-2 | Question: 95
Let $f$ be a function such that $f (mn) = f (m) f (n)$ for every positive integers $m$ and $n$. If $f (1), f (2)$ and $f (3)$ are positive integers, $f (1) < f (2),$ and $f (24) = 54$, then $f (18)$ equals _______
Let $f$ be a function such that $f (mn) = f (m) f (n)$ for every positive integers $m$and $n$. If $f (1), f (2)$ and $f (3)$ are positive integers, $f (1) < f (2),$ and $...
1 votes
1 answer
2057
CAT 2019 Set-2 | Question: 96
If $(2n+1)+(2n+3)+(2n+5)+\dots+(2n+47)=5280,$ then what is the value of $1+2+3+\dots+n$ _______
If $(2n+1)+(2n+3)+(2n+5)+\dots+(2n+47)=5280,$ then what is the value of $1+2+3+\dots+n$ _______
1 votes
1 answer
2058
CAT 2019 Set-2 | Question: 97
If $5^{x}-3^{y}=13438$ and $5^{x-1}+3^{y+1}=9686$, then $x+y$ equals _______
If $5^{x}-3^{y}=13438$ and $5^{x-1}+3^{y+1}=9686$, then $x+y$ equals _______
1 votes
1 answer
2060
CAT 2019 Set-2 | Question: 99
The number of common terms in the two sequences: $15, 19, 23, 27,\dots,415$ and $14, 19, 24, 29,\dots,464$ is $18$ $19$ $21$ $20$
The number of common terms in the two sequences: $15, 19, 23, 27,\dots,415$ and $14, 19, 24, 29,\dots,464$ is$18$$19$$21$$20$
3 votes
1 answer
2063
CAT 2018 Set-2 | Question: 67
The value of the sum $7 \times 11 + 11 \times 15 + 15 \times 19 + \dots$ + $95 \times 99$ is $80707$ $80773$ $80730$ $80751$
The value of the sum $7 \times 11 + 11 \times 15 + 15 \times 19 + \dots$ + $95 \times 99$ is$80707$$80773$$80730$$80751$
3 votes
1 answer
2064
CAT 2018 Set-2 | Question: 68
How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits? $5$ $6$ $8$ $7$
How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits?...
2 votes
1 answer
2065
CAT 2018 Set-2 | Question: 69
The smallest integer $n$ such that $n^{3} - 11n^{2} + 32n - 28 >0$ is
The smallest integer $n$ such that $n^{3} - 11n^{2} + 32n - 28 >0$ is
3 votes
1 answer
2069
CAT 2018 Set-2 | Question: 73
A chord of length $5$ cm subtends an angle of $60^\circ$ at the centre of a circle. The length, in cm, of a chord that subtends an angle of $120^\circ$ at the centre of the same circle is $8$ $6\sqrt2$ $5\sqrt3$ $2\pi$
A chord of length $5$ cm subtends an angle of $60^\circ$ at the centre of a circle. The length, in cm, of a chord that subtends an angle of $120^\circ$ at the centre of t...
2 votes
1 answer
2070
CAT 2018 Set-2 | Question: 74
Let $f\left (x \right ) = \max\left \{5x, 52 – 2x^{2}\right \}$ , where $x$ is any positive real numbers. Then the minimum possible value of $f(x)$ is ________
Let $f\left (x \right ) = \max\left \{5x, 52 – 2x^{2}\right \}$ , where $x$ is any positive real numbers. Then the minimum possible value of $f(x)$ is ________
2 votes
1 answer
2073
CAT 2018 Set-2 | Question: 77
If $a$ and $b$ are integers such that $2x^{2}- ax + 2 > 0$ and $x^{2}-bx+8 \geq 0$ for all real numbers $x$, then the largest possible value of $2a-6b$ is _________
If $a$ and $b$ are integers such that $2x^{2}- ax + 2 0$ and $x^{2}-bx+8 \geq 0$ for all real numbers $x$, then the largest possible value of $2a-6b$ is _________
2 votes
1 answer
2075
CAT 2018 Set-2 | Question: 79
If $\text{N}$ and $x$ are positive integers such that $\text{N}^{\text{N}}=2^{160}$ and $\text{N}^{2} + 2^{\text{N}}$ is an integral multiple of $2^{x}$, then the largest possible $x$ is _______
If $\text{N}$ and $x$ are positive integers such that $\text{N}^{\text{N}}=2^{160}$ and $\text{N}^{2} + 2^{\text{N}}$ is an integral multiple of $2^{x}$, then the largest...
2 votes
1 answer
2076
CAT 2018 Set-2 | Question: 80
Let $t_{1}, t_{2},\dots$ be a real numbers such that $t_{1}+t_{2}+\dots+t_{n}=2n^{2}+9n+13$, for every positive integers $n\geq2$.If $t_{k}=103$ , then $k$ equals
Let $t_{1}, t_{2},\dots$ be a real numbers such that $t_{1}+t_{2}+\dots+t_{n}=2n^{2}+9n+13$, for every positive integers $n\geq2$.If $t_{k}=103$ , then $k$ equals
3 votes
1 answer
2077
CAT 2018 Set-2 | Question: 81
If $p^{3}=q^{4}=r^{5}=s^{6}$, then the value of $\log_{s}\left ( pqr \right )$ is equal to $16/5$ $1$ $24/5$ $47/10$
If $p^{3}=q^{4}=r^{5}=s^{6}$, then the value of $\log_{s}\left ( pqr \right )$ is equal to $16/5$$1$$24/5$$47/10$
4 votes
2 answers
2079
CAT 2018 Set-2 | Question: 83
A jar contains a mixture of $175$ ml water and $700$ ml alcohol. Gopal takes out $10\%$ of the mixture and substitutes it by water of the same amount. The process is repeated once again. The percentage of water in the mixture is now $35.2$ $30.3$ $20.5$ $25.4$
A jar contains a mixture of $175$ ml water and $700$ ml alcohol. Gopal takes out $10\%$ of the mixture and substitutes it by water of the same amount. The process is repe...
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