Questions by Shubham Sharma 2

The equations $3 x^{2}-5 x+p=0$ and $2 x^{2}-2 x+q=0$ have one common root. The sum of the other roots of these two equations is$\dfrac{8}{3}-p+\dfrac{3}{2} q$$\dfrac{2}{...

If $\log _{64} x^{2}+\log _{8} \sqrt{y}+3 \log _{512}(\sqrt{y} z)=4$, where $x, y$ and $z$ are positive real numbers, then the minimum possible value of $(x+y+z)$ is$48$$...

Rita and Sneha can row a boat at $5 \mathrm{~km} / \mathrm{h}$ and $6 \mathrm{~km} / \mathrm{h}$ in still water, respectively. In a river flowing with a constant velocity...

Suppose $a, b, c$ are three distinct natural numbers, such that $3 a c=8(a+b)$. Then, the smallest possible value of $3 a+2 b+c$ is

Let $f(x)=\dfrac{x}{(2 x-1)}$ and $g(x)=\dfrac{x}{(x-1)}$. Then, the domain of the function $h(x)=f(g(x))+g(f(x))$ is all real numbers except$-1, \dfrac{1}{2}$, and $1$$\...

A loan of Rs $1000$ is fully repaid by two installments of Rs $530$ and Rs $594$, paid at the end of first and second year, respectively. If the interest is compounded an...

Two tangents drawn from a point $\text{P}$ touch a circle with center $\text{O}$ at points $\text{Q}$ and $\text{R}$. Points $\text{A}$ and $\text{B}$ lie on $\text{PQ}$ ...

The number of divisors of $\left(2^{6} \times 3^{5} \times 5^{3} \times 7^{2}\right)$, which are of the form $(3 r+1)$, where $r$ is a non-negative integer, is$36$$56$$24...

Let $\text{ABCDEF}$ be a regular hexagon and $\text{P}$ and $\text{Q}$ be the midpoints of $\text{AB}$ and $\text{CD}$, respectively. Then, the ratio of the areas of trap...

If $a, b, c$ and $d$ are integers such that their sum is $46$, then the minimum possible value of $(a-b)^{2}+(a-c)^{2}+(a-d)^{2}$ is

The ratio of expenditures of Lakshmi and Meenakshi is $2: 3$, and the ratio of income of Lakshmi to expenditure of Meenakshi is $6:7$. If excess of income over expenditur...

Let $a_{n}$ be the $n^{\text {th }}$ term of a decreasing infinite geometric progression. If $a_{1}+a_{2}+a_{3}=52$ and $a_{1} a_{2}+a_{2} a_{3}+a_{3} a_{1}=624$, then th...

A mixture of coffee and cocoa, $16 \%$ of which is coffee, costs Rs $240$ per kg . Another mixture of coffee and cocoa, of which $36 \%$ is coffee, costs Rs $320$ per kg....

In a $\triangle \text{ABC}$, points $\text{D}$ and $\text{E}$ are on the sides $\text{BC}$ and $\text{AC}$, respectively. $\text{BE}$ and $\text{AD}$ intersect at point $...

Ankita is twice as efficient as Bipin, while Bipin is twice as efficient as Chandan. All three of them start together on a job, and Bipin leaves the job after $20$ days. ...

A certain amount of money was divided among Pinu, Meena, Rinu and Seema. Pinu received $20\%$ of the total amount and Meena received $40\%$ of the remaining amount. If Se...

Five jumbled sentences (labelled $1, 2, 3, 4$, and $5$), related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the ...

Comprehension:The passage below is accompanied by a questions. Based on the passage, choose the best answer for the question.Often the well intentioned music lover or the...

Comprehension:The passage below is accompanied by a questions. Based on the passage, choose the best answer for the question.Often the well intentioned music lover or the...

Comprehension:The passage below is accompanied by a questions. Based on the passage, choose the best answer for the question.Often the well intentioned music lover or the...

Comprehension:The passage below is accompanied by a questions. Based on the passage, choose the best answer for the question.Often the well intentioned music lover or the...

The four sentences (labelled $\text{A, B, C}$, and $\text{D}$) given below, when properly sequenced, would yield a coherent paragraph. Decide on the proper sequencing of ...

The given sentence is missing in the paragraph below. Decide where it best fits among the options $1,2,3$, or $4$ indicated in the paragraph.Sentence: "Everything is old-...

The given sentence is missing in the paragraph below. Decide where it best fits among the options $1,2,3$, or $4$ indicated in the paragraph.Sentence: Historically, silve...

Comprehension:The passage below is accompanied by four questions. Based on the passage, choose the best answer for each question.Understanding the key properties of compl...

Comprehension:The passage below is accompanied by a question. Based on the passage, choose the best answer for the question.Understanding the key properties of complex sy...

Comprehension:The passage below is accompanied by a question. Based on the passage, choose the best answer for the question.Understanding the key properties of complex sy...

Comprehension:The passage below is accompanied by a question. Based on the passage, choose the best answer for the question.Understanding the key properties of complex sy...

The four sentences (labelled $\text{A, B, C}$, and $\text{D}$) given below, when properly sequenced, would yield a coherent paragraph. Decide on the proper sequencing of ...

The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.Zombie cells may contribute to age-related chronic ...

Comprehension:The passage below is accompanied by a question. Based on the passage, choose the best answer for the question.How can we know what someone else is thinking ...

Comprehension:The passage below is accompanied by a question. Based on the passage, choose the best answer for the question.How can we know what someone else is thinking...

Comprehension:The passage below is accompanied by a question. Based on the passage, choose the best answer for the question.How can we know what someone else is thinking ...

Comprehension:The passage below is accompanied by a question. Based on the passage, choose the best answer for the question.How can we know what someone else is thinking ...

Five jumbled sentences (labelled $\text{A, B, C, D,}$ and $\text{E}$), related to a topic, are given below. Four of them can be put together to form a coherent paragraph....

Comprehension:The passage below is accompanied by a question. Based on the passage, choose the best answer for the question.Studies showing that income inequality plays a...

Comprehension:The passage below is accompanied by a question. Based on the passage, choose the best answer for the question.Studies showing that income inequality plays a...

Comprehension:The passage below is accompanied by a question. Based on the passage, choose the best answer for the question.Studies showing that income inequality plays a...

Comprehension:The passage below is accompanied by a question. Based on the passage, choose the best answer for the question.Studies showing that income inequality plays a...

The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.In the dynamic realm of creativity, artists often f...