Maths questions series #4

Very important Maths questions for SSC

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Q. If O is the circumcentre of ?ABC and ?OBC = 350, then the ?BAC is equal to-

a. 550
b. 1100
c. 700
d. 350

We know ?BAC = 1/2 * 1100 = 550

Q. If I is the incentre of ? ABC and angle BIC = 1350, then &Delta ABC is-

a. Acute angled
b. Equilateral
c. Right angled
d. Obtuse angled

angle BIC = 1350
=> B/2 + C/2 = 1800 – 1350 = 450
=> angle B + angle C = 900
We know angle A = 1800 – ( angle B + angle C) = 900
i.e., ? ABC is a right angled.

Q. The length of a shadow of a vertical tower is 1//?3 times its height. The angle of elevation of the Sun is-

a. 300
b. 450
c. 600
d. 900

We know that tan ? = h/1?3 h = ?3 = tan 600

Q. The graphs of x +2y =3 and 3x-2y = 1 meet the Y-axis at two points having distance-

a. 8/3 units
b. 4/3 units
c. 1 unit
d. 2 units

Q. If x+1/16x = 1, then the value of 64×3 + 1/64×3 is-

a. 4
b. 52
c. 64
d. 76

Q. If a, b, c, are three non-zero real numbers such that a + b + c = 0, and b2 ? ca, then the value of a2 + b2 + c2/ b2 –ca is-

a. 3
b. 2
c. 0
d. 1

Q. If a4 + a2 b2 + b4 = 8 and a2 + ab + b2 = 4, then the value of ab is-

a. -1
b. 0
c. 2
d. 1

Q. If a = 25, b = 15, c = -10, then the value of a3 + b3 + c3 – 3abc/ (a-b)2 + (b-c)2 + (c-a)2 is-

a. 30
b. -15
c. -30
d. 15

Q. A, B, C are three points on a circle. The tangent at A meets BC produced at T, angle BTA = 400, angle CAT = 440. The angle subtended by BC at the centre of the circle is-

a. 840
b. 920
c. 960
d. 1040

angle ACB = 400 + 440 = 840
We know angle ACO = 900 – 440 = 460 = angle OAC
=> angle OCB = angle ACB – angle ACO
= 840 – 460 = 380 = angle OBC
We know angle BOC = 1800 – ( angle OCB + angle OBC)
= 1800 – (380 + 380) = 1040