Solution: \(\begin{array}{l}\vec{AB} = \hat{i}-3\hat{j}+8\hat{k}\end{array} \) \(\begin{array}{l}\vec{CD} = 4\hat{i}-4\hat{j}+7\hat{k}\end{array} \) Projection of vector AB on vector CD = \(\begin{array}{l}\frac{\vec{AB}.\vec{CD}}{\left | \vec{CD}... View Article
If the vectors \(\begin{array}{l}\vec{p} = (a+1)\hat{i}+a\hat{j}+a\hat{k}\end{array} \) , \(\begin{array}{l}\vec{q} = a\hat{i}+(a+1)\hat{j}+a\hat{k}\end{array} \) and \(\begin{array}{l}\vec{r} = a\hat{i}+a\hat{j}+(a+1)\hat{k}\end{array} \) (a∈R) are coplanar... View Article
In a box, there are 20 cards out of which 10 are labelled as A and remaining 10 are labelled... View Article
a) \(\begin{array}{l}-\left ( \frac{x-3}{x+4} \right )^{-\frac{1}{7}}+ C\end{array} \) b) \(\begin{array}{l}\frac{1}{2}\left ( \frac{x-3}{x+4} \right )^{\frac{3}{7}}+ C\end{array} \) c) \(\begin{array}{l}\left ( \frac{x-3}{x+4}... View Article
Let the observations xi(1 ≤ i ≤ 10) satisfy the equations, \(\begin{array}{l}\sum_{i=1}^{10}(x_{i}-5)=10\end{array} \) and \(\begin{array}{l}\sum_{i=1}^{10}(x_{i}-5)^{2}=40\end{array} \). If μ and λ... View Article
a) 8 b) 7 c) 4 d) 6 Solution: Total numbers that can be formed are = 8×8×7×6 = 8×336... View Article
A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The... View Article
Let a complex number z, |z| ≠ 1, satisfy log1/√2 [(|z| + 11) / (|z| – 1)2] ≤ 2. Then,... View Article
Let the functions f: R→R and g: R →R be defined as: \(\begin{array}{l}f(x)=\left\{\begin{matrix} x+2, &x\leq 0 \\ x^2& x\geq 0... View Article
The range of a ∈ R for which the function f (x) = (4a – 3) (x + loge 5)... View Article
If for a>0, the feet of perpendiculars from the points A (a, –2a, 3) and B (0, 4, 5) on... View Article
Let a vector \(\begin{array}{l}\alpha \hat{i}+\beta \hat{j}\end{array} \) be obtained by rotating the vector \(\begin{array}{l}\sqrt{3} \hat{i}+\hat{j}\end{array} \) by an angle 45°... View Article
a. b2 = a2 + c2 + 3d2 b. b2 = 3 (a2 + c2) – 9d2 c. b2 =... View Article
Let e denote the base of the natural logarithm. The value of the real number a for which the right-hand... View Article
For a polynomial g(x) with real coefficients, let mg denote the number of distinct real roots of g(x). Suppose S... View Article
In a triangle PQR, let \(\begin{array}{l}\vec{a} = \vec{QR}, \vec{b} = \vec{RP}\: and \: \vec{c} = \vec{PQ}\end{array} \). If \(\begin{array}{l}|\vec{a}| = 3\end{array}... View Article
Let f : [0, 2] ⟶ R be the function defined by \(\begin{array}{l}f(x) = (3-sin(2\pi x))sin\left (\pi x-\frac{\pi }{4} \right) –... View Article
Let 1, 2, 3,… be a sequence of positive integers in arithmetic progression with common difference 2. Also, let 1,... View Article
Let m be the minimum possible value of \(\begin{array}{l}log_{3}(3^{y_{1}} + 3^{y_{2}} + 3^{y_{3}})\end{array} \), where 1, 2, 3 are real... View Article
Which of the following inequalities is/are TRUE? a)\(\begin{array}{l}\int_{0}^{1}xcosx\: dx\geq \frac{3}{8}\end{array} \) b) \(\begin{array}{l}\int_{0}^{1}xsinx\: dx\geq \frac{3}{10}\end{array} \) c) \(\begin{array}{l}\int_{0}^{1}x^{2}cosx\: dx\geq \frac{1}{2}\end{array}... View Article
