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The value of [latex]sec^{-1}(1/4 \sum_{k=0}^{10} sec(7\pi/12 + k\pi/2))sec(7\pi/12 + (k+1)\pi/2))[/latex]

The value of in the interval [-π/4, 3π/4] equals Solution: The answer is 0.... View Article

Let x ϵ R and let P

Let x ϵ R and let And R = PQP-1. Then which of the following options is/are correct? a) For x = 1, there exists a unit vector b) There... View Article

Let P₁ = I = [latex]begin{bmatrix} 1 &0 &0 \ 0 & 1 & 0\ 0& 0 & 1 end{bmatrix}[/latex]

Where PKT denotes the transpose of the matrix PK. Then which of the following options is/are correct? a) X – 30I is an invertible matrix... View Article

For non-negative integers n, let f(n)

For non-negative integers n, let Assuming cos-1x takes value in [0, π], which of the following options is/are correct? a) If α = tan... View Article

Let F: R -> R be a function. We say that f has

Let F: R -> R be a function. We say that f has Then which of the following options is/are correct? a) f(x) = x|x| has PROPERTY 2 b) F(x) =... View Article

Three lines L1: [latex]vec{r}=lambda hat{i}, lambda epsilon R[/latex], L2: [latex]vec{r}= hat{k}+mu hat{j}, mu epsilon R[/latex] and L3: [latex]vec{r}= hat{i}+hat{j}+nu hat{k}, nu epsilon R[/latex] are given

Three lines L1: are given. For which point(s) Q and L2 can we find a point P on L1 and a point R on L3 so that P, Q and R are... View Article

For a ∈ R, |a|> 1, let [latex]\lim_{n \to \infty }\left ( \frac{1+\sqrt[3]{2}+…\sqrt[3]{n}}{n^{\frac{7}{3}}(\frac{1}{(an+1)^{2}}+\frac{1}{(an+2)^{2}}+…\frac{1}{(an+n)^{2}})} \right ) = 54[/latex]

For a ∈ R, |a| > 1, let . Then the possible value(s) of a is/are: a) 8 b) –9 c) –6 d) 7 Solution: Answer: a, b... View Article

Let f: R -> R be given by f(x) = (x – 1) (x – 2) (x – 5).

Let f: R -> R be given by f(x) = (x - 1) (x - 2) (x - 5). Define F(x) = . Then which of the following options is/are correct? a) F has a... View Article

Let the curve y=y(x) be the solution of the differential equation, dy / dx = 2 (x + 1).

Let the curve y=y(x) be the solution of the differential equation, dy / dx = 2 (x + 1). If the numerical value of area bounded by the curve y =... View Article

Let [latex]P=\begin{bmatrix} -30 &20 &56 \\ 90&140 &112 \\ 120&60 &14 \end{bmatrix}[/latex] and [latex]A=\begin{bmatrix} 2 &7 &\omega ^2 \\ -1&-\omega &1 \\ 0&-\omega &-\omega+1 \end{bmatrix}[/latex] where 𝛚 = (- 1 + i √3) / 2, and I₃ be the identity matrix of order 3.

Let where = (- 1 + i √3) / 2, and I3 be the identity matrix of order 3. If the determinant of the matrix (P-1AP- I3)2 is ɑ 2, then the... View Article

Let z and w be two complex numbers such that [latex]w=zbar{z}-2z+2[/latex], |(z + i) / (z – 3i)| = 1 and Re (w) has a minimum value.

Let z and w be two complex numbers such that , |(z + i) / (z - 3i)| = 1 and Re (w) has a minimum value. Then, the minimum value of n ∈ N,... View Article

Let ABCD be a square of the side of unit length.

Let ABCD be a square of the side of unit length. Let a circle C1 centred at A with a unit radius is drawn. Another circle C2 which touches C1 and... View Article

If lim_x→0 [ae^x – b cosx + ce^-x] / [x sinx] = 2,

If limx→0 [aex - b cosx + ce-x] / [x sinx] = 2, then a + b + c is equal to ______ Answer: (4) a – b + c = 0 & a – c = 0... View Article

If the normal to the curve y (x) = ∫₀^x (2t² – 15t + 10) dt at a point (a, b)

If the normal to the curve y (x) = ∫0x (2t2 - 15t + 10) dt at a point (a, b) is parallel to the line x + 3y = – 5, a>1, then the... View Article

Consider an arithmetic series and a geometric series having four initial terms from the set {11, 8, 21, 16, 26, 32, 4}.

Consider an arithmetic series and a geometric series having four initial terms from the set {11, 8, 21, 16, 26, 32, 4}. If the last terms of... View Article

Let f:R→R be a continuous function such that f (x) + f (x + 1) = 2, for all x ∈ R.

Let f:R→R be a continuous function such that f (x) + f (x + 1) = 2, for all x ∈ R. If I1 = ∫08 f (x) dx and I2 = ∫-13 f (x) dx,... View Article

The total number of 3 × 3 matrices A having entries from the set {0, 1, 2, 3} such that the sum of all the diagonal entries of AA^T is 9, is equal to

Solution: (766) Tr (AAT) = x2 + y2 + z2 + a2 + b2 + c2 + d2 + e2 + f2 = 9 all→1 =1 one 3, rest = 0 (9! / 8!) = 9 two 2 , one 1 &... View Article