Explore topic-wise InterviewSolutions in Current Affairs.

Write the negation of the following statements :

(i) Bangalore is the capital of Karnataka.

(ii) It rained on July 4, 2005.

(iii) Ravish is honest.

(iv) The earth is round.

(v) The sun is cold.

The polar form of complex number $-3\sqrt{2}+3\sqrt{2}i$ is

If roots of the equation

$x^4-8x^3+b{x}^2+cx+16=0$

are positive, then

Find the equation of the tangents drawn form the point (5,3) to the hyperbola $\frac{x^2}{25}-\frac{y^2}{9}=1.$

Using the property of determinants and without expanding.

$\left|\begin{array}{ccc}2& 7& 65\\ 3& 8& 75\\ 5& 9& 86\end{array}\right|=0$

If a cubic equation $f\left(x\right)$ vanishes at $x=-2$ and has relative maximum/minimum at $x=-1$ and $x=\frac{1}{3}$ and $\underset{-1}{\overset{1}{\int }}f\left(x\right)dx=\frac{14}{3}.$ Then which of the following is/are correct ?

The ratio of the sum of first three terms is to that of first 6 terms of a G.P. is 125 : 152. Find the common ratio.

$Ifcosy=xcos(a+y),withcosa\ne 1,provethat\frac{dy}{dx}=\frac{co{s}^2(a+y)}{sina}.$

Total number of six-digit numbers in which only and all the five digits $1,3,5,7$ and $9$ appear, is

For $a\in R$ (the set of all real numbers), $a\ne -1,$ $\underset{n\to \infty }{lim}\frac{(1^a+2^a+\cdots +n^a)}{{(n+1)}^{a-1}\left[\right(na+1)+(na+2)+\cdots +(na+n\left)\right]}=\frac{1}{60}.$

Then $a=$

Find the domain and range of the follwoing graph.

What is the probability that a leap year will have 53 Fridays or 53 Saturdays ?

If $A$ and $B$ are two sets such that $(A-B)\cup B=A$, then

The number of terms which are free from radical signs in the expansion of $(y^{\frac{1}{5}}+x^{\frac{1}{10}}{)}^{55}$ is

The three lines 4x-7y+10=0, x+y=5, 7x+4y-15=0 form the sides of a triangle. Then the point (1,2) is

Let $\int 2^{\ln x}dx=\frac{\left(f\right(x){)}^{\lambda }}{\lambda }+C,$ then which of the following is/are true (where $C$ is constant of integration)

What are the applications of various maths functions?

Out of $60$ students in a class, anyone who has chosen to study maths elects to do physics as well. But no one does maths and chemistry, $16$ do physics and chemistry. All the students do at least one of the three subjects and the number of people who do exactly one of the three is more than the number who do more than one of the three. Then the range of cardinal number of students who could have done only chemistry is

There are four boxes $A_1,A_2,A-3\text{and}{A}_4$. Box $A_i$ has $i$ cards and on each card, a number is printed. The numbers are from $1\text{to}i$. A box is selected randomly, the probability of selection of box $A_i\text{is}\frac{i}{10}$ then a card is drawn. Let $E_i$ represent the event that a card with number 'i' is drawn. Now answer the following :

If $P\left(E_1\right)$ is $\frac{a}{b}$, then (H.C.F. of a and b is 1)

If $\cos (A+B)\sin (C-D)=\cos (A-B)\sin (C+D),$ then the value of $\tan A\tan B\tan C+\tan D$ is

If A and B are two matrices of the order 3 $\times m$ and 3 $\times$n respectively and m = n, then order of matrix (5A - 2B) is
(a) $m\times 3$ (b) $3\times 3$ (c) $m\times n$
(d) $3\times n$

The value of $\underset{0}{\overset{\pi /3}{\int }}\frac{\tan \theta }{\sqrt{2k\sec \theta }}d\theta$ such that $k>0$ is

If the function $f\left(x\right)=\sqrt{{0.25}^{4-3x}-4^{2x}}$ is defined, then the possible of $x$ is/are

${lim}_{x\to 0}\frac{2sinx-sin2x}{x^3}$

$(r+1{)}^{th}$ term in the expansion of $(1-x{)}^{-4}$ will be

If $x$ is a rational number satisfying

$(1-x)(1+x+x^2+x^3+x^4)$$=\frac{31}{32}.$

Then $1+x+x^2+x^3+x^4+x^5$ is

In a H.P, $t_n$ = $\frac{1}{n}$ . The Harmonic mean of first 10 terms of H.P is

${lim}_{x\to 0}\frac{sin{x}^{\circ }}{x^{\circ }}$