Answer: \[Option\text{ }\left( A \right)\text{ }0\]
The number of distinct real roots of = 0 in the interval -ฯ/4 โค x โค ฯ/4 is (A) 0 (B) 2 (C) 1 (D) 3
Answer: \[Option\text{ }\left( C \right)\text{ }1\]
The determinant equals (A) abc (bโc) (c โ a) (a โ b) (B) (bโc) (c โ a) (a โ b) (C) (a + b + c) (b โ c) (c โ a) (a โ b) (D) None of these
Answer: Option (D) \[None\text{ }of\text{ }these\]
The area of a triangle with vertices (โ3, 0), (3, 0) and (0, k) is 9 sq. units. The value of k will be (A) 9 (B) 3 (C) โ 9 (D) 6
Option \[\left( B \right)\text{ }3\] According to the question, the area of a triangle with vertices \[({{x}_{1}},\text{ }{{y}_{1}}),\text{ }({{x}_{2}},\text{ }{{y}_{2}})\text{ }and\text{...
The value of determinant (A) a3 + b3 + c3 (B) 3 bc (C) a3 + b3 + c3 โ 3abc (D) none of these
ANSWER: Option \[\left( C \right)~{{a}^{3}}~+~{{b}^{3}}~+~{{c}^{3}}~\text{ }3abc\] Given,
If then, value of x is (A) 3 (B) ยฑ 3 (C) ยฑ 6 (D) 6
ANSWER: Option \[~\left( C \right)\text{ }\pm \text{ }6\] On equating the determinants, we get \[2{{x}^{2}}-\text{ }40\text{ }=\text{ }18\text{ }+\text{ }14\] \[2{{x}^{2}}~=\text{ }72\]...
If x + y + z = 0, prove that
Answer: According to the question, the determinant can be solved as
Prove that is divisible by a + b + c and find the quotient.
Answer: According to the question, the determinant can be solved as
If a + b + c ยน 0 and then prove that a = b = c.
Answer: According to the question, the determinant can be solved as
Given find BA and use this to solve the system of equations y + 2z = 7, x โ y = 3, 2x + 3y + 4z = 17.
Answer: According to the question, the determinant can be solved as
Using matrix method, solve the system of equations 3x + 2y โ 2z = 3, x + 2y + 3z = 6, 2x โ y + z = 2.
Answer: Given equations are: \[3x~+\text{ }2y-\text{ }2z~=\text{ }3\] \[x~+\text{ }2y~+\text{ }3z~=\text{ }6\]and \[2x~-y~+~z~=\text{ }2\] Or, \[AX\text{ }=\text{ }B\]
If A = , find A-1. Using Aโ1, solve the system of linear equations x โ 2y = 10 , 2x โ y โ z = 8 , โ2y + z = 7.
Answer: According to the question, the determinant can be solved as
Find Aโ1 if and show that A-1 = (A2 โ 3I)/ 2.
Answer: According to the question, the determinant can be solved as
Show that the DABC is an isosceles triangle if the determinant
Answer: According to the question, the determinant can be solved as
Show that the points (a + 5, a โ 4), (a โ 2, a + 3) and (a, a) do not lie on a straight line for any value of a.
Given focuses are \[\left( a\text{ }+\text{ }5,\text{ }a\text{ }\text{ }4 \right),\text{ }\left( a\text{ }\text{ }2,\text{ }a\text{ }+\text{ }3 \right)\]and \[\left( a,\text{ }a \right).\]...
If a1, a2, a3, โฆ, ar are in G.P., then prove that the determinant is independent of r.
Answer: According to the question, the determinant can be solved as So, it is independent of r.
If , then find values of x.
Answer: According to the question, the determinant can be solved as
Find the value of q satisfying
Answer: According to the question, the determinant can be solved as
If the co-ordinates of the vertices of an equilateral triangle with sides of length โaโ are (x1, y1),(x2, y2), (x3, y3), then
Answer: According to the question, the determinant can be solved as
If A + B + C = 0, then prove that
Answer: According to the question, the determinant can be solved as
Prove that:
Answer: According to the question, the determinant can be solved as
Prove that:
Answer: According to the question, the determinant can be solved as
Prove that:
Answer: According to the question, the determinant can be solved as
Evaluate the following determinant:
Answer: According to the question, the determinant can be solved as Now, expanding along\[R1\], we have \[=\text{ }\left( a\text{ }+\text{ }b\text{ }+\text{ }c \right)\text{ }[1\text{ }x\text{...
Evaluate the following determinant:
Answer: According to the question, the determinant can be solved as
Evaluate the following determinant:
Answer: [Expanding along first column] \[=\text{ }\left( x\text{ }+\text{ }y\text{ }+\text{ }z \right)\text{ }.\text{ }1\left[ 3y\left( 3z\text{ }+\text{ }x \right)\text{ }+\text{ }\left(3z...
Evaluate the following determinant:
Answer: According to the question, the determinant can be solved as
Evaluate the following determinant:
Answer: According to the question, the determinant can be solved as
Evaluate the following determinant:
Answer: \[=\text{ }({{x}^{2}}-\text{ }2x\text{ }+\text{ }2)\text{ }.\text{ }\left( x\text{ }+\text{ }1 \right)\text{ }-\text{ }\left( (x)\text{ }-\text{ }1 \right)\text{ }.\text{ }0\] \[=\text{...