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The intersection of three lines x – y = 0 and x + 2y = 3 and 2x + y = 6 is a:

a. Equilateral triangleb. Right angled trianglec. Isosceles triangled. None of the aboveAnswer: (c)AB = AC = √5, BC = √2Hence,... View Article

Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of A² is 1, then the possible number of such matrices is : a.6 b. 1 c. 4 d. 12

Answer: (c)Let A = \(\begin{array}{l}\begin{bmatrix} a &b \\ b&c \end{bmatrix}\\\end{array} \)\(\begin{array}{l}A^{2}=\begin{bmatrix} a &b \\ b&c \end{bmatrix}\begin{bmatrix} a &b \\ b&c... View Article

If (sin^-1x) / a = (cos^-1 x) / b) = (tan^-1 y) / c; 0 < x < 1, then the value of cos (πc / [a + b]) is:

a. [1 – y2] / 2y b. [1 – y2] / [1 + y2] c. 1 – y2 d. [1... View Article

The value of [latex]\begin{bmatrix} (a+1)(a+2) & a+2 & 1\\ (a+2)(a+3) & a+3 & 1\\ (a+3)(a+4) & a+4 & 1 \end{bmatrix}[/latex] is

a. –2 b. (a + 1) (a + 2) (a + 3) c. 0 d. (a + 2) (a +... View Article

The sum of the infinite series 1 + (2 / 3) + (7 / 3²) + (12 / 3³) + (17 / 3⁴) + (22 / 3⁵) + …… is equal to : a. 9 / 4 b. 15 / 4 c. 13 / 4 d. 11 / 4

s = 1 + (2 / 3) + (7 / 32) + (12 / 33) + (17 / 34) +... View Article

Which one of the following is true for given three planes.

Consider the three planes P1 : 3x + 15y + 21z = 9, P2 : x – 3y – z... View Article

In an increasing geometric series, the sum of the second and the sixth term is 25 / 2 and the product of the third and fifth term is 25. Then, the sum of 4^th, 6^th and 8^th terms is equal to

a. 35 b. 30 c. 26 d. 32 Answer: (a) Let a be the first term and r be the... View Article

If [latex]\vec{a}[/latex] and [latex]\vec{b}[/latex] are perpendicular, then [latex]\vec{a}\times(\vec{a}\times(\vec{a}\times(\vec{a}\times\vec{b})))[/latex] is equal to :

a. (1 / 2) |\(\begin{array}{l}\vec{a}\end{array} \)|4 \(\begin{array}{l}\vec{b}\\\end{array} \) b. \(\begin{array}{l}\vec{a}\times\vec{b}\\\end{array} \) c. |\(\begin{array}{l}\vec{a}\end{array} \)|4 \(\begin{array}{l}\vec{b}\\\end{array} \) d. \(\begin{array}{l}\vec{0}\\\end{array} \) Answer:... View Article

The rate of growth of bacteria in a culture is proportional to the number of

The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria... View Article

The value of ∑_n=1¹⁰⁰ ∫_n-1ⁿ e^x-[x] dx, where [x] is the greatest integer ≤ x, is

a. 100 (e – 1) b. 100e c. 100 (1 – e) d. 100 (1 + e) Answer: (a) ∑n=1100... View Article

The maximum value of the term independent of ‘t’ in the expansion of

The maximum value of the term independent of ‘t’ in the expansion of [(tx1/5 + {(1 – x)1/10 / t}]10... View Article

The number of seven-digit integers with the sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only is:

a. 77 b. 42 c. 35 d. 82 Answer: (a) Case – I: 1, 1 , 1, 1, 1, 2,... View Article

If the curve y = y(x) represented by the solution of the differential equation (2xy² – y)dx + xdy = 0, passes through the intersection of the lines, 2x – 3y = 1 and 3x + 2y = 8, then |y(1)| is equal to

Answer:1 Given, (2xy2 – y)dx + xdy = 0 ⇒ dy/dx + 2y2 – y/x = 0 ⇒ (–1/y2) .... View Article

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Latest Posts

The intersection of three lines x – y = 0 and x + 2y = 3 and 2x + y = 6 is a:

Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of A² is 1, then the possible number of such matrices is : a.6 b. 1 c. 4 d. 12

If (sin^-1x) / a = (cos^-1 x) / b) = (tan^-1 y) / c; 0 < x < 1, then the value of cos (πc / [a + b]) is:

The value of [latex]\begin{bmatrix} (a+1)(a+2) & a+2 & 1\\ (a+2)(a+3) & a+3 & 1\\ (a+3)(a+4) & a+4 & 1 \end{bmatrix}[/latex] is

The sum of the infinite series 1 + (2 / 3) + (7 / 3²) + (12 / 3³) + (17 / 3⁴) + (22 / 3⁵) + …… is equal to : a. 9 / 4 b. 15 / 4 c. 13 / 4 d. 11 / 4

Which one of the following is true for given three planes.

In an increasing geometric series, the sum of the second and the sixth term is 25 / 2 and the product of the third and fifth term is 25. Then, the sum of 4^th, 6^th and 8^th terms is equal to

If [latex]\vec{a}[/latex] and [latex]\vec{b}[/latex] are perpendicular, then [latex]\vec{a}\times(\vec{a}\times(\vec{a}\times(\vec{a}\times\vec{b})))[/latex] is equal to :

The rate of growth of bacteria in a culture is proportional to the number of

The value of ∑_n=1¹⁰⁰ ∫_n-1ⁿ e^x-[x] dx, where [x] is the greatest integer ≤ x, is

The maximum value of the term independent of ‘t’ in the expansion of

The number of seven-digit integers with the sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only is:

If the curve y = y(x) represented by the solution of the differential equation (2xy² – y)dx + xdy = 0, passes through the intersection of the lines, 2x – 3y = 1 and 3x + 2y = 8, then |y(1)| is equal to

Find the value of ab if vectors a and b are given

The total number of two digit numbers ‘n’, such that 3ⁿ+7ⁿ is a multiple of 10, is

If the curves x = y⁴ and xy = k cut at right angles, then (4k)⁶ is equal to

A function f is defined on [–3,3] as

A line L passing through origin is perpendicular to the lines

If the remainder when x is divided by 4 is 3, then the remainder when (2020+x)²⁰²² is divided by 8 is

The value of [latex]\int_{-2}^2|3x^2-3x-6|dx[/latex] is