Recent questions tagged isi2017-dcg

The value of $\dfrac{1}{\log_2 n}+ \dfrac{1}{\log_3 n}+\dfrac{1}{\log_4 n}+ \dots + \dfrac{1}{\log_{2017} n}\:\:($ where $n=2017!)$ is$1$$2$$2017$none of these

The area of the shaded region in the following figure (all the arcs are circular) is$\pi$$2 \pi$$3 \pi$$\frac{9}{8} \pi$

If $2f(x)-3f(\frac{1}{x})=x^2 \: (x \neq0)$, then $f(2)$ is$\frac{2}{3}$$ – \frac{3}{2}$$ – \frac{7}{4}$$\frac{5}{4}$

If $A$ is a $3 \times 3$ matrix satisfying $A^3 – A^2 +A-I= O$ (where $O$ is the zero matrix and $I$ is the identity matrix) then the value of $A^4$ is$A$$O$$I$none of th...

The sum of the squares of the roots of $x^2-(a-2)x-a-1=0$ becomes minimum when $a$ is$0$$1$$2$$5$

Let $f(x) = \dfrac{x-1}{x+1}, \: f^{k+1}(x)=f\left(f^k(x)\right)$ for all $k=1, 2, 3, \dots , 99$. Then $f^{100}(10)$ is$1$$10$$100$$101$

If $\begin{vmatrix} 10! & 11! & 12! \\ 11! & 12! & 13! \\ 12! & 13! & 14! \end{vmatrix} = k(10!)(11!)(12!)$, then the value of $k$ is$1$$2$$3$$4$

If $x,y,z$ are in $A.P.$ and $a>1$, then $a^x, a^y, a^z$ are in$A.P.$$G.P$$H.P$none of these

The solution of $\log_5(\sqrt{x+5}+\sqrt{x})=1$ is$2$$4$$5$none of these

The value of the Boolean expression (with usual definitions) $(A’BC’)’ +(AB’C)’$ is$0$$1$$A$$BC$

The coefficient of $x^6y^3$ in the expression $(x+2y)^9$ is$84$$672$$8$none of these

Two sets have $m$ and $n$ elements. The number of subsets of the first set is $96$ more than that of the second set. Then the values of $m$ and $n$ are$8$ and $6$$7$ and ...

The value of $\dfrac{x}{1-x^2} + \dfrac{x^2}{1-x^4} + \dfrac{x^4}{1-x^8} + \dfrac{x^8}{1-x^{16}}$ is$\frac{1}{1-x^{16}}$$\frac{1}{1-x^{12}}$$\frac{1}{1-x} – \frac{1}{1-x^...

If $a,b,c$ are the sides of a triangle such that $a:b:c=1: \sqrt{3}:2$, then $A:B:C$ (where $A,B,C$ are the angles opposite to the sides of $a,b,c$ respectively) is$3:2:1...

The number of solutions of $\tan^{-1}(x-1) + \tan^{-1}(x) + \tan^{-1}(x+1) = \tan^{-1}(3x)$ is$1$$2$$3$$4$

If $\cos x = \dfrac{1}{2}$, the value of the expression $\dfrac{\cos 6x+6 \cos 4x+15 \cos 2x +10}{\cos 5x+5 \cos 3x +10 \cos x}$ is$\frac{1}{2}$$1$$\frac{1}{4}$$0$

If $\cos ^{2}x+ \cos ^{4} x=1$, then $\tan ^{2} x+ \tan ^{4} x$ is equal to$1$$0$$2$none of these

If $a,b,c$ are the sides of $\Delta ABC$, then $\tan \frac{B-C}{2} \tan \frac{A}{2}$ is equal to$\frac{b+c}{b-c}$$\frac{b-c}{b+c}$$\frac{c-b}{c+b}$none of these

The angle between the tangents drawn from the point $(-1, 7)$ to the circle $x^2+y^2=25$ is$\tan^{-1} (\frac{1}{2})$$\tan^{-1} (\frac{2}{3})$$\frac{\pi}{2}$$\frac{\pi}{3...

If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes are $(3,2)$, then the equation of the straight line is$2x+3y=12$$3...

If $a,b,c$ are in $A.P.$ , then the straight line $ax+by+c=0$ will always pass through the point whose coordinates are$(1,-2)$$(1,2)$$(-1,2)$$(-1,-2)$

A determinant is chosen at random from the set of all determinants of order $2$ with elements $0$ or $1$ only. The probability of choosing a non-zero determinant is$\frac...

If $f(x) = \begin{vmatrix} 2 \cos ^2 x & \sin 2x & – \sin x \\ \sin 2x & 2 \sin ^2 x & \cos x \\ \sin x & – \cos x & 0 \end{vmatrix},$ then $\int_0^{\frac{\pi}{2}} [ f(x...

The value of $\underset{n \to \infty}{\lim} \bigg( \dfrac{1}{1-n^2} + \dfrac{2}{1-n^2} + \dots + \dfrac{n}{1-n^2} \bigg)$ is$0$$ – \frac{1}{2}$$\frac{1}{2}$none of these

A basket contains some white and blue marbles. Two marbles are drawn randomly from the basket without replacement. The probability of selecting first a white and then a b...

The area (in square unit) of the portion enclosed by the curve $\sqrt{2x}+ \sqrt{2y} = 2 \sqrt{3}$ and the axes of reference is$2$$4$$6$$8$

If $f(x)=e^{5x}$ and $h(x)=f’’(x)+2f’(x)+f(x)+2$ then $h(0)$ equals$38$$8$$4$$0$