WBJEE Mathematics Sample Paper I - JEE MCQ

The equation of straight line is parallel to x-axis which means slope is 0
equation of straight line , y = mx + c
here, m = 0 , y = c
As it is given c = c/2
y = +-c/2

Polar is xy₁ + x₁y = 2c².. (1)
Let  normal chord at (h,k) be
hx - ky = h² - k²...... (2)
From 1 and
And hk = c² eliminate h, k and λ

hx + ky - xy = 0
let asymptotes be hx + ky - xy + c = 0 ; This represents a pair of straight lines if Δ =  0
i.e. c =-hk ∴ asymptotes are xh+yk-xy-hk =0 ⇒ (x - k) (y - h) = 0

The chord of a parabola through the focus and perpendicular to the axis is called the latus rectum.

Given directrix of parabola ⇒ x+y=2
and force is origin vertex is A(0,0)
We know that perpendicular distance from vertex  of the parabola to directrix is equal to 'a'  where 4a is the Latus Rectum of the 
Parabola 

The sine formula is 
a/sinA = b/sinB 
⇒ a sin B = b sin A
(a) b sin A = a 
⇒ a sin B = a 
⇒ B = π/2 
Since, ∠A  < π/2 therefore, the triangle is possible.
(b) b sin A < a 
⇒ a sin B < a 
⇒ sinB < 1 
⇒ ∠B exists 
Now, b > a 
⇒ B > A since A < π/2 
∴ The triangle is possible.

(b+c) cos A + (c + a) cos B + (a + b) cos C
⇒ b cos A + c cos A + c cos B + a cos B + a cos C + b cos C
⇒ (b cos C + c cos B) + (c cos A + a cos C) + (a cos B + b cos A) ...(1)
Using projection formula,
a = (b cos C + c cos B) ...(2)
b = (c cos A + a cos C) ...(3)
c = (a cos B + b cos A) ...(4)

On adding the projection formula, we get the initial expression
i.e. (2) + (3) + (4) = (1)
∴ (b + c) cos A + (c + a) cos B + (a + b) cos C = a + b + c

y = sec x is periodic function. The period of y = sec x is 2π.

xe^x = t
(xe^x + e^x) dx = dt
= e^x(x + 1) dx = dt
= ∫dt/sin^2t
= ∫cosec^2t dt
= -cot(xe^x) + c

Commutative law, in mathematics, either of two laws relating to number operations of addition and multiplication, stated symbolically: a + b = b + a and ab = ba

Therefore, tangent at (2, 3) is y – 3 = ½ (x – 2). i.e. x – 2y +4 = 0 . therefore required area is 

θ in 2nd quad Cosθ < 0

cos^–1x < sin^–1x is

√5<3  No solution

Addition is defined if order of A is equal to order of B
A B
nxm nxm is defined if m = n
⇒ A, B are square matrices of same order

A = A^T

= Real

y = a sin θ
x = a cos θ.