Recent questions tagged isi2018-dcg

The digit in the unit place of the number $7^{78}$ is$1$$3$$7$$9$

If the co-efficient of $p^{th}, (p+1)^{th}$ and $(p+2)^{th}$ terms in the expansion of $(1+x)^n$ are in Arithmetic Progression (A.P.), then which one of the following is ...

Let $A$ be the set of all prime numbers, $B$ be the set of all even prime numbers, and $C$ be the set of all odd prime numbers. Consider the following three statements in...

A die is thrown thrice. If the first throw is a $4$ then the probability of getting $15$ as the sum of three throws is$\frac{1}{108}$$\frac{1}{6}$$\frac{1}{18}$none of th...

You are given three sets $A,B,C$ in such a way that the set $B \cap C$ consists of $8$ elements,the set $A\cap B$ consists of $7$ elements, andthe set $C\cap A$ consists ...

A Pizza Shop offers $6$ different toppings, and they do not take an order without any topping. I can afford to have one pizza with a maximum of $3$ toppings. In how many ...

Let $f(x)=1+x+\dfrac{x^2}{2}+\dfrac{x^3}{3}...+\dfrac{x^{2018}}{2018}.$ Then $f’(1)$ is equal to $0$$2017$$2018$$2019$

Let $f’(x)=4x^3-3x^2+2x+k,$ $f(0)=1$ and $f(1)=4.$ Then $f(x)$ is equal to$4x^4-3x^3+2x^2+x+1$$x^4-x^3+x^2+2x+1$$x^4-x^3+x^2+2(x+1)$none of these

Let $A=\{10,11,12,13, \dots ,99\}$. How many pairs of numbers $x$ and $y$ are possible so that $x+y\geq 100$ and $x$ and $y$ belong to $A$?$2405$$2455$$1200$$1230$

In a certain town, $20\%$ families own a car, $90\%$ own a phone, $5 \%$ own neither a car nor a phone and $30, 000$ families own both a car and a phone. Consider the fol...

In a room there are $8$ men, numbered $1,2, \dots ,8$. These men have to be divided into $4$ teams in such a way thatevery team has exactly $2$ members, andthere are no ...

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is$6$$9$$12$$18$

Let $A=\begin{pmatrix} 1 & 1 & 0\\ 0 & a & b\\1 & 0 & 1 \end{pmatrix}$. Then $A^{-1}$ does not exist if $(a,b)$ is equal to$(1,-1)$$(1,0)$$(-1,-1)$$(0,1)$

The value of $^{13}C_{3} + ^{13}C_{5} + ^{13}C_{7} +\dots + ^{13}C_{13}$ is$4096$$4083$$2^{13}-1$$2^{12}-1$

If $x+y=\pi, $ the expression $\cot \dfrac{x}{2}+\cot\dfrac{y}{2}$ can be written as$2 \: \text{cosec} \: x$$\text{cosec} \: x + \text{cosec} \: y$$2 \: \sin x$$\sin x+\...

The area of the region formed by line segments joining the points of intersection of the circle $x^2+y^2-10x-6y+9=0$ with the two axes in succession in a definite order (...

The value of $\tan \left(\sin^{-1}\left(\frac{3}{5}\right)+\cot^{-1}\left(\frac{3}{2}\right)\right)$ is$\frac{1}{18}$$\frac{11}{6}$$\frac{13}{6}$$\frac{17}{6}$

A box with a square base of length $x$ and height $y$ has an open top and its volume is $32$ cubic centimetres, as shown in the figure below. The values of $x$ and $y$ th...

Let the sides opposite to the angles $A,B,C$ in a triangle $ABC$ be represented by $a,b,c$ respectively. If $(c+a+b)(a+b-c)=ab,$ then the angle $C$ is$\frac{\pi}{6}$$\fra...

Let $A$ be the point of intersection of the lines $3x-y=1$ and $y=1$. Let $B$ be the point of reflection of the point $A$ with respect to the $y$-axis. Then the equation ...

Let $[x]$ denote the largest integer less than or equal to $x.$ The number of points in the open interval $(1,3)$ in which the function $f(x)=a^{[x^2]},a\gt1$ is not diff...

There are three circles of equal diameter ($10$ units each) as shown in the figure below. The straight line $PQ$ passes through the centres of all the three circles. The ...

The area of the region bounded by the curves $y=\sqrt x,$ $2y+3=x$ and $x$-axis in the first quadrant is$9$$\frac{27}{4}$$36$$18$

$\sum_{n=1}^{\infty}\frac{1}{n(n+1)}$ is$2$$1$$\infty$not a convergent series

Let $f(x)=e^{-\big( \frac{1}{x^2-3x+2} \big) };x\in \mathbb{R} \: \: \& x \notin \{1,2\}$. Let $a=\underset{n \to 1^+}{\lim}f(x)$ and $b=\underset{x \to 1^-}{\lim} f(x)$....

Let $0.01^x+0.25^x=0.7$ . Then$x\geq1$$0\lt x\lt1$$x\leq0$no such real number $x$ is possible.