A cube is painted red on the two adjacent faces and black on the surfaces opposite to red surfaces and orange on the remaining faces. Now the cube is divided into 216 smaller cubes of equal size. How many smaller cubes will have no surface painted?
In the given figure (not drawn to scale), AD is parallel to BC. JDK, GHCI, EABF are straight and parallel lines.
(i) ∠GHD – ∠HDC (ii) ∠BCI + ∠HAB.
The factors of 8a3 + b3 - 6ab + 1 are
A (2a + b - 1)(4a2 + b2 + 1 - 3ab - 2a)
B (2ab - b + 1)(4a2 + b2 - 4ab + 1 - 2a + b)
C (2a + b + 1)(4a2 + b2 + 1 - 2ab - b - 2a)
D (2a - 1 + b)(4a2 + 1 - 4a - b - 2ab)
please also give the solution of this question
Following are the steps of construction of a ΔPQR, given that QR = 3 cm, ∠PQR = 45° and QP - PR = 2 cm. Arrange them and select the correct option.
(i) Make an angle XQR = 45° at point Q of base QR.
(ii) Join SR and draw the perpendicular bisector of SR say AB.
(iii) Draw the base QR of length 3 cm.
(iv) Let bisector AB intersect QX at P. Join PR.
(v) Cut the line segment QS = QP - PR = 2 cm from the ray QX.
A (iii) → (ii) → (i) → (v) → (iv)
B (iii) → (i) → (ii) → (v) → (iv)
C (iii) → (i) → (ii) → (iv) → (v)
D (iii) → (i) → (v) → (ii) → (iv)