# NTSE Sample Questions 2016-17 : Mathematics (Gujrat State) Stage-1

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## NTSE Sample Questions 2016-17 : Mathematics (Gujrat State) Stage-1

**1**. If A={1,2,3,4}, B = {2,4,5,6} , U={1,2,3,4,5,6,7} then A’∩B’ =______

(A)Ø (B) {1,2,3,4,5,6} (C) {7} (D) {3,4,5,6}

**3**. If x-2 is factor of 3x^{4} -2x^{3} + 7x^{2} – 21x +k then the value of K is

(A) 2 (B) 9 (C) 18 (D) -18

**4**. Line x + y = 2 passes through the ________________quadrants.

(A) 1st and 3rd both (B) 2nd and 3rd both

(C) 3rd and 4th both (D) 1st, 2nd and 4th all

**5.** If the measure of the angle of ΔABC are in proportion 1 : 2: 3, then the measures of the smallest angle is

(A) 300 (B) 600 (C) 900 (D) 1200

**6.** ΔABC is an equilateral triangle, Ab=6, The points P,Q and R are midpoints of AB , BC and CA respectively. The perimeter of PBCR is __________

(A) 18 (B) 15 (C) 9 (D) 12

7. In m ABCD, let AM be the altitude corresponding to the base BC and CN the altitude corresponding to the base AB , If AB = 10cm, AM=6cm and CN=12cm then BC = _______cm.

(A) 20 (B) 10 (C) 12 (D) 5

**8.** A circle passes through the vertices of an equilateral ΔABC. The measure of an angle subtended by the side AB at the centre of the circle has measure ________

(A) 30 (B) 60 (C) 90 (D) 120

**9**. If the lengths of the sides of a triangle are in propotion 3:4:5 then the area of triangle is _________sq.units, where perimeter of the triangle is 144

(A) 64 (B) 364 (C) 564 (D) 864

**10**. The ratio of radii of two cones is 2:3 and the ratio of their slant heights is 9:4. Then the ratio of their curved surface area is

(A) 3 :2 (B) 1:2 (C) 1:3 (D) 2:3

11. The probability of getting both heads, when two balanced coins are tossed once is

**12.** The characteristic of the number log 0 003942 = _____

(A) 3 (B) 2 (C) -3 (D) -2

**13**. A number having digit 2 at unit place then its cube has digit _____ at its units place.

(A) 1 (B) 2 (C) 8 (D) 4

**14**. 3-years ago, the sum of ages of a father and his son was 40 years. After 2-year, the sum of ages of the father and his son will be__________

(A)40 (B) 46 (C) 50 (D) 60

**15**. Correspondence ABC →DEF of ΔABC and ΔDEF is similarity. If AB + BC + 10 and DE + EF + 12 and AC = 6 then DF = ______

(A) 6 (B) 5 (C) 7.2 (D) 16

(A) 90 (B) 30 (C) 60 (D) 45

**17.** If 7θ and 2θ are measures of acute angles such than sin 7θ = cos2θ, then sin 3θ - 3 tanθ = ______

(A) 1 (B) 0 (C) -1 (D) 1- 3

**18**. If the angles of elevation of tower from two points a and b (a>b) meters from its foot and the same side of the tower, have measure 30 and 60, then the height of the tower is __________

**19.** A chord of (0,5) touches (0,3). Therefore the length of the chord = ____

(A) 8 (B) 10 (C) 7 (D) 6

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