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The projection of the line segment joining the points (1,-1,3) and (2,-4,11) on the line joining the points (-1,2,3) and (3,-2,10) is

Solution: Answer: (8)... View Article

If vectors p, q and r are coplanar

If the vectors then value of λ isSolution: As vectors p, q and r are coplanar, R1 R1 + R2 + R3 C2 C2 - C1 and C3 C3 - C1 3a + 1 = 0a... View Article

In a box, there are 20 cards out of which 10 are labelled as A and remaining 10 are labelled as B

In a box, there are 20 cards out of which 10 are labelled as A and remaining 10 are labelled as B. Cards are drawn at random, one after the other... View Article

The integral is equal to:

a) b) c) d) (where C is a constant of integration) Solution: Answer: (c)... View Article

Let the observations x_i(1 ≤ i ≤ 10) satisfy the equations

Let the observations xi(1 ≤ i ≤ 10) satisfy the equations, Answer (c)... View Article

If the number of five digit numbers with distinct digits and 2 at the 10th place is 336k, then k is equal to:

a) 8b) 7c) 4d) 6Solution: Total numbers that can be formed are = 8×8×7×6= 8×336k = 8Answer (a)... View Article

A pack of cards has one card missing.

A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a... View Article

Let a complex number z, |z| ≠ 1, satisfy log_1/√2 [(|z| + 11) / (|z| – 1)²] ≤ 2.

Let a complex number z, |z| ≠ 1, satisfy log1/√2 [(|z| + 11) / (|z| - 1)2] ≤ 2. Then, the largest value of |z| is equal to ____ a. 5... View Article

Let the functions f: R→R and g: R →R be defined as:

Let the functions f: R→R and g: R →R be defined as: Then, the number of points in R where (fog)(x) is NOT differentiable is equal... View Article

The range of a ∈ R for which the function f (x) = (4a – 3) (x + log_e5) + 2 (a – 7) cot (x / 2) sin² (x / 2),

The range of a ∈ R for which the function f (x) = (4a – 3) (x + loge 5) + 2 (a – 7) cot (x / 2) sin2 (x / 2), x... View Article

If for a>0, the feet of perpendiculars from the points A

If for a>0, the feet of perpendiculars from the points A (a, –2a, 3) and B (0, 4, 5) on the plane lx + my + nz = 0 are points C (0,... View Article

Let a vector [latex]alpha hat{i}+beta hat{j}[/latex] be obtained by rotating

Let a vector by an angle 45° about the origin in counterclockwise direction in the first quadrant. Then the area of triangle having... View Article

Consider three observations a, b and c such that b = a+c. If the standard deviation of a+2, b+2, c+2 is d, then which of the following is true?

a. b2 = a2 + c2 + 3d2 b. b2 = 3 (a2 + c2) - 9d2 c. b2 = 3 (a2 + c2) + 9d2 d. b2 = 3 (a2 + c2 + d2) Answer: (b) For a, b, c mean = = [a + b + c]... View Article

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Archives

The projection of the line segment joining the points (1,-1,3) and (2,-4,11) on the line joining the points (-1,2,3) and (3,-2,10) is

If vectors p, q and r are coplanar

In a box, there are 20 cards out of which 10 are labelled as A and remaining 10 are labelled as B

The integral is equal to:

Let the observations x_i(1 ≤ i ≤ 10) satisfy the equations

If the number of five digit numbers with distinct digits and 2 at the 10th place is 336k, then k is equal to:

A pack of cards has one card missing.

Let a complex number z, |z| ≠ 1, satisfy log_1/√2 [(|z| + 11) / (|z| – 1)²] ≤ 2.

Let the functions f: R→R and g: R →R be defined as:

The range of a ∈ R for which the function f (x) = (4a – 3) (x + log_e5) + 2 (a – 7) cot (x / 2) sin² (x / 2),

If for a>0, the feet of perpendiculars from the points A

Let a vector [latex]alpha hat{i}+beta hat{j}[/latex] be obtained by rotating

Consider three observations a, b and c such that b = a+c. If the standard deviation of a+2, b+2, c+2 is d, then which of the following is true?

Let e denote the base of the natural logarithm.

For a polynomial g( ) with real coefficients

In a triangle PQR, let [latex]vec{a} = vec{QR}, vec{b} = vec{RP}: and : vec{c} = vec{PQ}[/latex].

Let f : [0, 2] ⟶ R be the function defined by

Let ₁, ₂, ₃,… be a sequence of positive integers in arithmetic progression

Let m be the minimum possible value of [latex]log_{3}(3^{y_{1}} + 3^{y_{2}} + 3^{y_{3}})[/latex],

Which of the following inequalities is/are TRUE?

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