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 3x⁴ -2x³ + 7x² – 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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