If $\vec{a}=4\hat{j}$ and $\vec{b}=3\hat{j}+4\hat{k}$ , then the vector form of the component of $\vec{a}$ alond $\vec{b}$ is

If $\vec{a}$ and $\vec{b}$ in space, given by $\vec{a}=\frac{\hat{i}-2\hat{j}}{\sqrt{5}}$ and $\vec{b}=\frac{2\hat{i}+\hat{j}+3\hat{k}}{\sqrt{14}}$ , then the value of $(2\vec{a}+\vec{b}).[(\vec{a} \times \vec{b}) \times (\vec{a}-2\vec{b})]$ is

Which letter would be 3rd to the right of the 7th letter from the left

Which letter would be exactly in the middle of eighteenth letter from the beginning and fifteenth from the end?

How many 3-digit numbers divisible by 5, can be formed using the digits 2 3 5 6 7 and 9, without repetition of digits?

Using only 2,5,10,25 and 50 paise coins, what is the smallest number of coins required to pay exactly 78 paise, 69 paise and Rs. 1.01 to three different persons?

Which of the following two patterns will fit in the blanks of the series ZA₅ ,Y₄B, XC₆, W₃D, _________ , _________?

Which of the following numbers comes next in the two-digit decimal number sequence 61, 52, 63, 94, ______?

What is C to A?

How many male members are there in the family?

Who among the following is one of the couples?

Which of the following is true?

How much amount does G have with her?

Which of the following girls have chocolates with them?

Which of the following combination is definitely correct?

Which girl has Rs. 40 with her?

How many times do the hour and the minute hands of a clock overlap in 24 hours?

In a certain code, TOGETHER is coded as RQEGRJCT. In the same code, PAROLE will be written as:

A drawer contains 10 black and 10 brown socks which are all mixed up. What is the smallest number of socks to be taken from the drawer to decide without seeing them, to be sure that there is atleast one pair of socks of the same colour?

Find the missing number in the series: 4, 7, 25, 10, __________, 20, 16, 19

Which of the following is the finish point for farmer F2?

Which stage was ploughed by F5?

What are the starting and ending points of the field ploughed by F4?

What is the starting point for stage?

If ÷ means addition, – means division, × means subtraction and + means multiplication, then the value of $\frac{(36 \times 4)-(8 \times 4)}{4+8 \times 2 +16\div 1}$

Which letter in the word CYBERNETICS occupies the same position as it does in the English alphabet?

The remainder when 2³¹ is divided by 5 is

Let $\vec{a}$ and $\vec{b}$ be two vectors, which of the following vectors are not perpendicular to each other?

If $A=\begin{bmatrix} a &b &c \\ b & c & a\\ c& a &b \end{bmatrix}$ , where $a, b, c$ are real positive numbers such that $abc = 1$ and $A^{T}A=I$ then the equation that not holds true among the following is

The equation of the tangent at any point of the curve $x=acos2t$, $y=2\sqrt{2}a sint$ with $m$ as its slope is

The locus of the mid points of all chords of the parabola $y^{2}=4x$ which are drawn through its vertex, is

The value of $\lim_{x\to a} \frac{\sqrt{a+2x}-\sqrt{3x}}{\sqrt{3a+x}-2\sqrt{x}}$

The value of $\int_{-\pi/3}^{\pi/3} \frac{x sinx}{cos^{2}x}dx$

The foci of the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{b^{2}}=1$ and the hyperbola $\frac{x^{2}}{144}-\frac{y^{2}}{{81}}=\frac{1}{25}$ coincide, then the value of $b^{2}$ is

If $a+b+c=\pi$ , then the value of $\begin{vmatrix} sin(A+B+C) &sinB &cosC \\ -sinB & 0 &tanA \\ cos(A+B)&-tanA &0 \end{vmatrix}$ is

If the mean deviation of the numbers 1, 1 + d, 1 + 2d, ....., 1 + 100d from their mean is 255, then the value of d is

If $P=sin^{20} \theta + cos^{48} \theta $ then the inequality that holds for all values of is

If a, b, c are in geometric progression, then $log_{ax}^{a}, log_{bx}^{a}$ and $log_{cx}^{a}$ are in

The value of the sum $\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+...+\frac{1}{25\sqrt{24}+24\sqrt{25}}$ is

If $\vec{a}=\hat{i}-\hat{k},\, \vec{b}=x\hat{i}+\hat{j}+(1-x)\hat{k}$ and $\vec{c}=y\hat{i}+x\hat{j}+(1+x-y)\hat{k}$ , then $[\vec{a} , \vec{b}, \vec{c}]$ depends on

If $42 (^nP_2)=(^nP_4)$ then the value of n is

The foot of the perpendicular from the point (2, 4) upon $x + y = 1$ is

The value of k for which the equation $(k-2)x^{2}+8x+k+4=0$ has both real, distinct and negative roots is

If (2, 1), (–1, –2), (3, 3) are the midpoints of the sides BC, CA, AB of a triangle ABC, then equation of the line BC is

If a fair dice is rolled successively, then the probability that 1 appears in an even numbered throw is

Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=\hat{i}-\hat{j}+\hat{k}$ and $\vec{c}=\hat{i}-\hat{j}-\hat{k}$ be three vectors. A vector $\vec{v}$ in the plane of $\vec{a}$ and $\vec{b}$ whose projection on $\frac{\vec{c}}{|\vec{c}|}$ is $\frac{1}{\sqrt{3}}$, is

The number of bit strings of length 10 that contain either five consecutive 0’s or five consecutive 1’s is

If $0 < x < \pi $ and $cos x + sin x = \frac{1}{2}$ , then the value of tan x is

If $\vec{a}, \vec{b}$ and $\vec{c}$ are the position vectors of the vertices A, B, C of a triangle ABC, then the area of the triangle ABC is

If $\int e^{x}(f(x)-f'(x))dx=\phi(x)$ , then the value of $\int e^x f(x) dx$ is

If $3x + 4y + k = 0$ is a tangent to the hyperbola ,$9x^{2}-16y^{2}=144$ then the value of $K$ is

$a, b, c$ are positive integers such that $a^{2}+2b^{2}-2bc=100$ and $2ab-c^{2}=100$. Then the value of $\frac{a+b}{c}$ is

If $(– 4, 5)$ is one vertex and $7x – y + 8 = 0$ is one diagonal of a square, then the equation of the other diagonal is

Out of $2n + 1$ tickets, which are consecutively numbered, three are drawn at random. Then the probability that the numbers on them are in arithmetic progression is

A circle touches the X-axis and also touches another circle with centre at (0, 3) and radius 2. Then the locus of the centre of the first circle is

Let $\bar{P}$ and $\bar{Q}$ denote the complements of two sets P and Q. Then the set $(P-Q)\cup (Q-P) \cup (P \cap Q)$ is

With the usual notation $\frac{d^{2}x}{dy^{2}}$

The radius of the circle passing through the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}$and having it centre at (0, 3) is

A function $f : (0,\pi) \to R$ defined by $f(x) = 2 sin x + cos 2x$ has

A matrix $M_r$ is defined as $M_r=\begin{bmatrix} r &r-1 \\ r-1&r \end{bmatrix} , r \in N$ then the value of $det(M_1) + det(M_2) +...+ det(M_{2015})$ is

If $\vec{AC}=2\hat{i}+\hat{j}+\hat{k}$ and $\vec{BD}=-\hat{i}+3\hat{j}+2\hat{k}$ then the area of the quadrilateral ABCD is

The value of $sin^{-1}\frac{1}{\sqrt{2}}+sin^{-1}\frac{\sqrt{2}-\sqrt{1}}{\sqrt{6}}+sin^{-1}\frac{\sqrt{3}-\sqrt{2}}{\sqrt{12}}+...$ to infinity , is equal to

If two circles $x^{2}+y^{2}+2gx+2fy=0$ and $x^{2}+y^{2}+2g'x+2f'y=0$ touch each other then whichof the following is true?

$\int_0^\pi [cotx]dx$ where [.] denotes the greatest integer function, is equal to

In a right angled triangle, the hypotenuse is four times the perpendicular drawn to it from the opposite vertex. The value of one of the acute angles is

A is targeting B, B and C are targeting A. Probability of hitting the target by A, B and C are $\frac{2}{3}, \frac{1}{2}$ and $\frac{1}{3}$ respectively. If A is hit then the probability that B hits the target and C does not, is

If the angles of a triangle are in the ratio 2 : 3 : 7, then the ratio of the sides opposite to these angles is

Suppose that A and B are two events with probabilities $P(A) =\frac{1}{2} \, P(B)=\frac{1}{3}$ Then which of the following is true?

The number of one-to-one functions from {1, 2, 3} to {1, 2, 3, 4, 5} is

If $x, y, z$ are three consecutive positive integers, then $log (1 + xz)$ is

A professor has 24 text books on computer science and is concerned about their coverage of the topics (P) compilers, (Q) data structures and (R) Operating systems. The following data gives the number of books that contain material on these topics: $n(P) = 8, n(Q) = 13, n(R) = 13, n(P \cap R) = 3, n(P \cap R) = 3, n(Q \cap R) = 3, n(Q \cap R) = 6, n(P \cap Q \cap R) = 2 $ where $n(x)$ is the cardinality of the set $x$. Then the number of text books that have no material on compilers is

The value of $tan(\frac{7\pi}{8})$ is

If $\vec{a}$ and $\vec{b}$ are vectors such that $|\vec{a}|=13$, $|\vec{b}|=5$ and $\vec{a} . \vec{b} =60$then the value of $|\vec{a} \times \vec{b}|$ is

Two towers face each other separated by a distance of 25 meters. As seen from the top of the first tower, the angle of depression of the second tower’s base is 60° and that of the top is 30°. The height (in meters) of the second tower is