Area of Triangle with Sides Given
Trending Questions
Q. If |a1|>|a2|+|a3|, |b2|>|b1|+|b3| and |c3|>|c1|+|c2|, then show ∣∣
∣∣a1a2a3b1b2b3c1c2c3∣∣
∣∣=0
Q. Let ∣∣
∣
∣∣33x3x2+2a23x3x2+2a23x3+6a2x3x2+2a23x3+6a2x3x4+12a2x2+2a4∣∣
∣
∣∣
then:
then:
- Δ′(x)=0
- ∫10Δ(x)dx=4a6
- Δ(x) is independent of x
- y=Δ(x) is a straight line
Q. If matrix A=⎡⎢⎣01−14−343−34⎤⎥⎦, can be written as B+C where B is symmetric matrix and C is skew-symmetric matrix, then B−C is equal to
- ⎡⎢⎣034−30−7−470⎤⎥⎦
- ⎡⎢⎣01−14−343−34⎤⎥⎦
- ⎡⎢⎣0−3−43074−70⎤⎥⎦
- ⎡⎢⎣0431−3−3−144⎤⎥⎦
Q.
Find the area of the triangle formed by the sides. x = 0, x + 2y = 5, 3x – y = 1
74
14
37
57
Q. If ∣∣
∣∣x2+3xx+1x−2x−11−2xx+4x+3x−43x∣∣
∣∣=Ax4+Bx3+Cx2+Dx+ϱ
Then value of ϱ equals to,
Then value of ϱ equals to,
- -10
- 10
- None of these
- 0
Q. Find the lengths of the normals drawn from the point on the axis of the parabola y2=8x whose distance from the focus is 8.
- 10
- 9
- 8
- None of these
Q. f(x)=∣∣
∣∣x+c1x+ax+ax+bx+c2x+ax+bx+bx+c3∣∣
∣∣ and g(x)=(c1−x)(c2−x)(c3−x)
Which of the following is not a constant term in f(x)?
- bg(a)−ag(b)b−a
- bg(a)−af(−b)b−a
- bf(−a)−ag(b)b−a
- none of these
Q. the area of the triangle formed by the sides. x = 0, x + 2y = 5, 3x – y = 1 is
- 7/4
- 6/4
- 5/4
- 1
Q.
(i)∣∣
∣∣x+42x2x2xx+42x2x2xx+4∣∣
∣∣=(5x+4)(4−x)2
Using the properties of determinants, show that:
(ii)∣∣
∣∣y+kyyyy+kyyyy+k∣∣
∣∣=k2(3y+k)
Q. If the coordinates of the points A, B, C, D be (1, 2, 3), (4, 5, 7), (−4, 3, −6) and (2, 9, 2) respectively, then find the angle between the lines AB and CD
Q. Let f(x)=[x]+[−x], where [x] denotes the greatest integer less than or equal to x.
Then, for any integer m
- limx→mf(x)=f(m)
- limx→mf(x)≠f(m)
- limx→mf(x) does not exist
- None of the above
Q. If α, β are the roots of 2x2−x+1=0, the value of α2+β2 is :
- 1
- 0
- 5/4
- −3/4
Q. Find the value of x and y if [x+10y2+2y0−4]=[3x+430y2−5y]
Q. . Det⎧⎪⎨⎪⎩1+a2−b22ab−2b2ab1−a2+b22a2b−2a1−a2−b2⎫⎪⎬⎪⎭
- (a2+b2)3
- (1+a2+b2)3
- (2−a2−b2)
- (2−a2−b2)2
Q. Find the equation of the plane through the intersection of planes 3x−y+2z−4=0 and x+y−z−2=0 and the point (2, 2, 1)
Q. Three lines are drawn from the origin O with direction cosines proportional to (1, −1, 1), (2−3, 0) and (1, 0, 3). The three lines are
- Not coplanar
- Coplanar
- Perpendicular to each other
- Coincident
Q. Let P(x) be the polynomial x3+ax2+bx+c, where a, b, c ∈ R. If P(−3)=P(+2)=0 and P′(−3)<0, which of the following is a possible value of ′c′?
- −18
- −3
- −27
- −6
Q. Solve the equation ∣∣
∣∣x+axxxx+axxxx+a∣∣
∣∣=0, a≠0
Q. if a≠6, b, c satisfy ∣∣
∣∣a2b2c3bc4ab∣∣
∣∣=0, then abc=
- a+b+c
- 0
- b3
- ab+b−c
Q. Find the general solution of each of the following differential equations:
(1+x2)dydx=xy.
(1+x2)dydx=xy.
Q. Solve: x2−5x+6≥0
- [−∞, 2)∪[3, ∞)
- [−∞, 4)∪[3, ∞)
- [−∞, 2)∪[7, ∞)
- None of these
Q.
∀y∈R, f(y) =∣∣
∣
∣∣1yy+12yy(y−1)y(y+1)3y(y−1)y(y−1)(y−2)y(y2−1)∣∣
∣
∣∣ , then
∫π/2−π/2f(y2+2)dy equals
- π
- 0
- −π
- 2−π
Q.
Find the area of the triangle formed by the sides. x = 0, x + 2y = 5, 3x – y = 1
74
14
37
57
Q. If every pair of equations x2+ax+bc=0, x2+bx+ca=0, x2+cx+ab=0 has a common root, then product of these common roots αβγ=abc.( Enter 1 if true or 0
otherwise)
Q. The determinant ∣∣
∣∣xp+yxypy+zyz0xp+yyp+z∣∣
∣∣=0 if
- x, y, z are in A.P.
- x, y, z are in G.P.
- x, y, z are in H.P.
- xy, yz, zx are in A.P.
Q. ∣∣
∣∣14201−2512x5x2∣∣
∣∣=0 find x
- -1, 2
- 0, 1
- 1, 3
- 2, 0
Q. If matrix A=⎡⎢⎣123−10462−1⎤⎥⎦, then the determinant of matrix A500−2A499 is m, then number of zeros at the end of m is
- 1
- 2
- 0
- 3
Q.
Find the value of the following determinant:
∣∣∣1.20.030.57−0.23∣∣∣- −0.2661
- −0.2471
- −0.2931
- −0.2381
Q. Using definite integral compute the area of the region bounded by the side of the triangle whose vertices are
(i) (2, 0), (4, 5) and (6, 3)
(ii) (-1, 1), (0, 5) and (3, 2)
(i) (2, 0), (4, 5) and (6, 3)
(ii) (-1, 1), (0, 5) and (3, 2)
Q. If a2+b2+c2=−2, and
f(x)=∣∣ ∣ ∣∣1+a2x(1+b2)x(1+c2)x(1+a2)x1+b2x(1+c2)x(1+a2)x(1+b2)x1+c2x∣∣ ∣ ∣∣
then f(x) is a polynomial of degree
f(x)=∣∣ ∣ ∣∣1+a2x(1+b2)x(1+c2)x(1+a2)x1+b2x(1+c2)x(1+a2)x(1+b2)x1+c2x∣∣ ∣ ∣∣
then f(x) is a polynomial of degree
- 0
- 1
- 2
- 3